TSTP Solution File: NUM862+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM862+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n027.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 10:41:07 EDT 2023

% Result   : Theorem 10.97s 11.30s
% Output   : CNFRefutation 10.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   74
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  304 (  30 unt;  16 typ;   0 def)
%            Number of atoms       :  758 (  34 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  781 ( 311   ~; 437   |;  20   &)
%                                         (   9 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  12   >;  19   *;   0   +;   0  <<)
%            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   :  540 (   9 sgn;  88   !;   1   ?;   0   :)

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

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

tff(decl_24,type,
    summation: $i > $i ).

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

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

tff(decl_27,type,
    model_max: ( $i * $i * $i ) > $o ).

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

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

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

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

tff(decl_32,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_33,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_34,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_35,type,
    esk4_0: $i ).

tff(decl_36,type,
    esk5_0: $i ).

tff(decl_37,type,
    esk6_0: $i ).

fof(max_is_ub_1,conjecture,
    ! [X1,X2,X3] :
      ( minsol_model_ub(X1,X2,X3)
    <=> minsol_model_max(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',model_max_5) ).

fof(max_1,axiom,
    ! [X1,X2] :
      ( max(X1,X2) = X1
      | ~ lesseq(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.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/sandbox/benchmark/theBenchmark.p',minsol_model_max) ).

fof(lesseq_total,axiom,
    ! [X1,X2] :
      ( lesseq(X1,X2)
      | lesseq(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_total) ).

fof(ub,axiom,
    ! [X1,X2,X3] :
      ( ub(X1,X2,X3)
    <=> ( lesseq(X1,X3)
        & lesseq(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ub) ).

fof(max_2,axiom,
    ! [X1,X2] :
      ( max(X1,X2) = X2
      | ~ lesseq(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_2) ).

fof(lesseq_ref,axiom,
    ! [X1] : lesseq(X1,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_ref) ).

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

fof(lesseq_antisymmetric,axiom,
    ! [X1,X2] :
      ( ( lesseq(X1,X2)
        & lesseq(X2,X1) )
     => X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_antisymmetric) ).

fof(sum_monotone_1,axiom,
    ! [X1,X2,X3] :
      ( lesseq(X1,X2)
    <=> lesseq(sum(X3,X1),sum(X3,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_monotone_1) ).

fof(summation_monotone,axiom,
    ! [X1,X2] :
      ( lesseq(X1,X2)
    <=> lesseq(summation(X1),summation(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.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,
    ! [X28,X29,X30,X32,X33,X34,X35] :
      ( ( ub(X28,X29,esk1_3(X28,X29,X30))
        | ~ model_ub(X28,X29,X30) )
      & ( lesseq(sum(c,summation(esk1_3(X28,X29,X30))),X30)
        | ~ model_ub(X28,X29,X30) )
      & ( ~ ub(X32,X33,X35)
        | ~ lesseq(sum(c,summation(X35)),X34)
        | model_ub(X32,X33,X34) ) ),
    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,
    ! [X25,X26,X27] :
      ( ( ~ model_max(X25,X26,X27)
        | lesseq(sum(c,summation(max(X25,X26))),X27) )
      & ( ~ lesseq(sum(c,summation(max(X25,X26))),X27)
        | model_max(X25,X26,X27) ) ),
    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,
    ! [X44,X45,X46,X47,X48,X49,X50] :
      ( ( model_ub(X44,X45,X46)
        | ~ minsol_model_ub(X44,X45,X46) )
      & ( ~ model_ub(X44,X45,X47)
        | lesseq(X46,X47)
        | ~ minsol_model_ub(X44,X45,X46) )
      & ( model_ub(X48,X49,esk3_3(X48,X49,X50))
        | ~ model_ub(X48,X49,X50)
        | minsol_model_ub(X48,X49,X50) )
      & ( ~ lesseq(X50,esk3_3(X48,X49,X50))
        | ~ model_ub(X48,X49,X50)
        | minsol_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)],[minsol_model_ub])])])])])]) ).

fof(c_0_19,negated_conjecture,
    ( ( ~ minsol_model_ub(esk4_0,esk5_0,esk6_0)
      | ~ minsol_model_max(esk4_0,esk5_0,esk6_0) )
    & ( minsol_model_ub(esk4_0,esk5_0,esk6_0)
      | minsol_model_max(esk4_0,esk5_0,esk6_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,
    ! [X18,X19] :
      ( max(X18,X19) = X18
      | ~ lesseq(X19,X18) ),
    inference(variable_rename,[status(thm)],[c_0_17]) ).

fof(c_0_23,plain,
    ! [X36,X37,X38,X39,X40,X41,X42] :
      ( ( model_max(X36,X37,X38)
        | ~ minsol_model_max(X36,X37,X38) )
      & ( ~ model_max(X36,X37,X39)
        | lesseq(X38,X39)
        | ~ minsol_model_max(X36,X37,X38) )
      & ( model_max(X40,X41,esk2_3(X40,X41,X42))
        | ~ model_max(X40,X41,X42)
        | minsol_model_max(X40,X41,X42) )
      & ( ~ lesseq(X42,esk2_3(X40,X41,X42))
        | ~ model_max(X40,X41,X42)
        | minsol_model_max(X40,X41,X42) ) ),
    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(esk4_0,esk5_0,esk6_0)
    | minsol_model_max(esk4_0,esk5_0,esk6_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(esk4_0,esk5_0,esk6_0)
    | model_ub(esk4_0,esk5_0,esk6_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(esk4_0,esk5_0,esk6_0)
    | model_max(esk4_0,esk5_0,esk6_0) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

fof(c_0_32,plain,
    ! [X11,X12] :
      ( lesseq(X11,X12)
      | lesseq(X12,X11) ),
    inference(variable_rename,[status(thm)],[lesseq_total]) ).

cnf(c_0_33,negated_conjecture,
    ( model_ub(esk4_0,esk5_0,esk6_0)
    | model_ub(X1,X2,esk6_0)
    | ~ ub(X1,X2,esk4_0)
    | ~ lesseq(esk5_0,esk4_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,
    ! [X22,X23,X24] :
      ( ( lesseq(X22,X24)
        | ~ ub(X22,X23,X24) )
      & ( lesseq(X23,X24)
        | ~ ub(X22,X23,X24) )
      & ( ~ lesseq(X22,X24)
        | ~ lesseq(X23,X24)
        | ub(X22,X23,X24) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ub])])]) ).

cnf(c_0_36,negated_conjecture,
    ( model_ub(esk4_0,esk5_0,esk6_0)
    | model_ub(X1,X2,esk6_0)
    | lesseq(esk4_0,esk5_0)
    | ~ ub(X1,X2,esk4_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(esk4_0,esk5_0,esk6_0)
    | model_ub(X1,X2,esk6_0)
    | lesseq(esk4_0,esk5_0)
    | ~ lesseq(X2,esk4_0)
    | ~ lesseq(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

fof(c_0_40,plain,
    ! [X5] : lesseq(X5,X5),
    inference(variable_rename,[status(thm)],[lesseq_ref]) ).

fof(c_0_41,plain,
    ! [X20,X21] :
      ( max(X20,X21) = X21
      | ~ lesseq(X20,X21) ),
    inference(variable_rename,[status(thm)],[c_0_38]) ).

cnf(c_0_42,negated_conjecture,
    ( model_ub(esk4_0,esk5_0,esk6_0)
    | model_ub(X1,X2,esk6_0)
    | lesseq(esk4_0,esk5_0)
    | lesseq(esk4_0,X2)
    | ~ lesseq(X1,esk4_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(esk4_0,esk5_0,esk6_0)
    | model_ub(esk4_0,X1,esk6_0)
    | lesseq(esk4_0,esk5_0)
    | lesseq(esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

fof(c_0_46,plain,
    ! [X6,X7,X8] :
      ( ~ lesseq(X6,X7)
      | ~ lesseq(X7,X8)
      | lesseq(X6,X8) ),
    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(esk4_0,esk5_0,esk6_0)
    | lesseq(esk4_0,esk5_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(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,X1)
    | ~ model_max(esk4_0,esk5_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(esk4_0,esk5_0,esk6_0)
    | lesseq(sum(c,summation(esk5_0)),esk6_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(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,sum(c,summation(max(esk4_0,esk5_0)))) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_58,negated_conjecture,
    ( model_ub(esk4_0,esk5_0,esk6_0)
    | model_max(esk5_0,X1,esk6_0)
    | ~ lesseq(X1,esk5_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(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,sum(c,summation(esk5_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,esk2_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(esk4_0,esk5_0,esk6_0)
    | model_max(esk5_0,esk5_0,esk6_0) ),
    inference(spm,[status(thm)],[c_0_58,c_0_43]) ).

cnf(c_0_63,negated_conjecture,
    ( model_ub(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,X1)
    | ~ model_max(X2,esk5_0,X1)
    | ~ lesseq(X2,esk5_0) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_64,negated_conjecture,
    ( minsol_model_max(esk5_0,esk5_0,esk6_0)
    | model_ub(esk4_0,esk5_0,esk6_0)
    | model_max(esk5_0,esk5_0,esk2_3(esk5_0,esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

fof(c_0_65,plain,
    ! [X9,X10] :
      ( ~ lesseq(X9,X10)
      | ~ lesseq(X10,X9)
      | X9 = X10 ),
    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,esk2_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(esk5_0,esk5_0,esk6_0)
    | model_ub(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,esk2_3(esk5_0,esk5_0,esk6_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,
    ! [X13,X14,X15] :
      ( ( ~ lesseq(X13,X14)
        | lesseq(sum(X15,X13),sum(X15,X14)) )
      & ( ~ lesseq(sum(X15,X13),sum(X15,X14))
        | lesseq(X13,X14) ) ),
    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(esk5_0,esk5_0,esk6_0)
    | model_ub(esk4_0,esk5_0,esk6_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(esk5_0)) = esk6_0
    | model_ub(esk4_0,esk5_0,esk6_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(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,X1)
    | ~ model_max(esk5_0,esk5_0,X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_70]) ).

fof(c_0_74,plain,
    ! [X16,X17] :
      ( ( ~ lesseq(X16,X17)
        | lesseq(summation(X16),summation(X17)) )
      & ( ~ lesseq(summation(X16),summation(X17))
        | lesseq(X16,X17) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[summation_monotone])]) ).

cnf(c_0_75,negated_conjecture,
    ( model_ub(esk4_0,esk5_0,esk6_0)
    | lesseq(summation(esk5_0),X1)
    | ~ lesseq(esk6_0,sum(c,X1)) ),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_76,negated_conjecture,
    ( model_ub(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,sum(c,summation(max(esk5_0,esk5_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(esk4_0,esk5_0,esk6_0)
    | lesseq(summation(esk5_0),summation(max(esk5_0,esk5_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(esk4_0,esk5_0,esk6_0)
    | lesseq(esk5_0,max(esk5_0,esk5_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(esk5_0,esk5_0) = esk5_0
    | model_ub(esk4_0,esk5_0,esk6_0)
    | ~ lesseq(max(esk5_0,esk5_0),esk5_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(esk4_0,esk5_0,esk6_0)
    | model_ub(X1,X2,esk6_0)
    | ~ ub(X1,X2,esk5_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(esk4_0,esk5_0,esk6_0)
    | lesseq(summation(esk5_0),summation(max(esk4_0,esk5_0))) ),
    inference(spm,[status(thm)],[c_0_75,c_0_57]) ).

cnf(c_0_93,negated_conjecture,
    ( max(esk5_0,esk5_0) = esk5_0
    | model_ub(esk4_0,esk5_0,esk6_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(esk4_0,esk5_0,esk6_0)
    | model_ub(X1,X2,esk6_0)
    | ~ lesseq(X2,esk5_0)
    | ~ lesseq(X1,esk5_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(esk4_0,esk5_0,esk6_0)
    | lesseq(esk5_0,max(esk4_0,esk5_0)) ),
    inference(spm,[status(thm)],[c_0_77,c_0_92]) ).

cnf(c_0_97,negated_conjecture,
    ( model_ub(esk4_0,esk5_0,esk6_0)
    | model_max(esk5_0,esk5_0,sum(c,summation(esk5_0))) ),
    inference(spm,[status(thm)],[c_0_53,c_0_93]) ).

cnf(c_0_98,negated_conjecture,
    ( model_ub(esk4_0,esk5_0,esk6_0)
    | model_ub(X1,esk5_0,esk6_0)
    | ~ lesseq(X1,esk5_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(esk4_0,esk5_0,esk6_0)
    | lesseq(X1,max(esk4_0,esk5_0))
    | ~ lesseq(X1,esk5_0) ),
    inference(spm,[status(thm)],[c_0_51,c_0_96]) ).

cnf(c_0_101,negated_conjecture,
    ( model_ub(esk4_0,esk5_0,esk6_0)
    | lesseq(max(esk5_0,esk5_0),esk5_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,esk1_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,esk5_0),esk5_0,esk6_0)
    | model_ub(esk4_0,esk5_0,esk6_0)
    | ~ lesseq(X1,esk5_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(esk4_0,esk5_0,esk6_0)
    | lesseq(max(esk5_0,esk5_0),max(esk4_0,esk5_0)) ),
    inference(spm,[status(thm)],[c_0_100,c_0_101]) ).

cnf(c_0_107,plain,
    ( lesseq(sum(c,summation(esk1_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,esk1_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(esk5_0,esk5_0),esk5_0,esk6_0)
    | model_ub(esk4_0,esk5_0,esk6_0) ),
    inference(spm,[status(thm)],[c_0_104,c_0_43]) ).

cnf(c_0_112,negated_conjecture,
    ( max(esk5_0,esk5_0) = max(esk4_0,esk5_0)
    | model_ub(esk4_0,esk5_0,esk6_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(esk4_0,esk5_0,esk6_0)
    | model_ub(X1,esk5_0,esk6_0)
    | lesseq(esk5_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(esk1_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,esk1_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,esk1_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(esk4_0,esk5_0),esk5_0,esk6_0)
    | model_ub(esk4_0,esk5_0,esk6_0) ),
    inference(spm,[status(thm)],[c_0_111,c_0_112]) ).

cnf(c_0_119,negated_conjecture,
    ( model_ub(esk4_0,esk5_0,esk6_0)
    | lesseq(esk5_0,esk4_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(esk1_3(X3,X4,X2))) ),
    inference(spm,[status(thm)],[c_0_114,c_0_80]) ).

cnf(c_0_121,plain,
    ( lesseq(summation(X1),summation(esk1_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,esk1_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(esk4_0,esk5_0,esk6_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,esk1_3(esk4_0,esk5_0,esk6_0))
    | ~ lesseq(X2,esk4_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)),esk6_0)
    | ~ lesseq(X1,esk5_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,esk1_3(esk4_0,esk5_0,esk6_0))
    | ~ lesseq(X1,max(X2,esk4_0))
    | ~ lesseq(X2,esk4_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,esk6_0)
    | ~ lesseq(max(X1,X2),esk5_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,esk4_0),esk1_3(esk4_0,esk5_0,esk6_0))
    | ~ lesseq(X1,esk4_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,esk6_0)
    | lesseq(esk5_0,X1) ),
    inference(spm,[status(thm)],[c_0_131,c_0_132]) ).

cnf(c_0_136,negated_conjecture,
    ( lesseq(esk4_0,esk1_3(esk4_0,esk5_0,esk6_0))
    | ~ lesseq(X1,esk4_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,esk1_3(X4,X5,X3)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_107]) ).

cnf(c_0_138,negated_conjecture,
    ( model_ub(X1,X2,esk6_0)
    | lesseq(esk5_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(esk4_0,esk1_3(esk4_0,esk5_0,esk6_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,esk1_3(X4,X5,X3))
    | ~ lesseq(X1,esk1_3(X4,X5,X3)) ),
    inference(spm,[status(thm)],[c_0_137,c_0_37]) ).

cnf(c_0_141,negated_conjecture,
    ( model_ub(X1,esk4_0,esk6_0)
    | lesseq(esk5_0,esk1_3(esk4_0,esk5_0,esk6_0))
    | ~ lesseq(X1,esk1_3(esk4_0,esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_138,c_0_139]) ).

cnf(c_0_142,negated_conjecture,
    ( model_ub(X1,esk4_0,esk6_0)
    | ~ lesseq(X1,esk1_3(esk4_0,esk5_0,esk6_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(esk5_0,esk4_0,esk6_0)
    | lesseq(esk5_0,esk1_3(esk4_0,esk5_0,esk6_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,esk1_3(X2,X4,X3)) ),
    inference(spm,[status(thm)],[c_0_140,c_0_110]) ).

cnf(c_0_146,plain,
    ( model_ub(X1,X2,esk3_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(esk5_0,esk4_0,esk6_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(esk5_0,esk4_0,esk6_0)
    | model_ub(esk5_0,esk4_0,esk3_3(esk5_0,esk4_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_146,c_0_147]) ).

cnf(c_0_152,negated_conjecture,
    ( lesseq(summation(X1),summation(esk1_3(esk4_0,esk5_0,esk6_0)))
    | ~ lesseq(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_115,c_0_139]) ).

cnf(c_0_153,negated_conjecture,
    ( summation(esk1_3(esk4_0,esk5_0,esk6_0)) = summation(esk4_0)
    | ~ lesseq(esk1_3(esk4_0,esk5_0,esk6_0),esk4_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(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,X1)
    | ~ model_ub(esk4_0,esk5_0,X1) ),
    inference(spm,[status(thm)],[c_0_149,c_0_25]) ).

cnf(c_0_158,negated_conjecture,
    ( minsol_model_ub(esk5_0,esk4_0,esk6_0)
    | model_ub(esk4_0,esk5_0,esk3_3(esk5_0,esk4_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_150,c_0_151]) ).

cnf(c_0_159,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_ub(X4,X2,X3)
    | ~ lesseq(X1,esk1_3(X4,X2,X3)) ),
    inference(spm,[status(thm)],[c_0_140,c_0_116]) ).

cnf(c_0_160,negated_conjecture,
    model_ub(esk4_0,esk4_0,esk6_0),
    inference(spm,[status(thm)],[c_0_142,c_0_139]) ).

cnf(c_0_161,negated_conjecture,
    lesseq(summation(esk4_0),summation(esk1_3(esk4_0,esk5_0,esk6_0))),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]) ).

cnf(c_0_162,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_163,plain,
    ( lesseq(max(X1,X2),X1)
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_82,c_0_155]) ).

cnf(c_0_164,plain,
    ( lesseq(summation(X1),summation(max(X2,X1)))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_156,c_0_53]) ).

cnf(c_0_165,plain,
    ( minsol_model_ub(X2,X3,X1)
    | ~ lesseq(X1,esk3_3(X2,X3,X1))
    | ~ model_ub(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_166,negated_conjecture,
    ( minsol_model_ub(esk5_0,esk4_0,esk6_0)
    | minsol_model_max(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,esk3_3(esk5_0,esk4_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_157,c_0_158]) ).

cnf(c_0_167,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_ub(X4,X2,X3)
    | ~ lesseq(X1,X4) ),
    inference(spm,[status(thm)],[c_0_159,c_0_117]) ).

cnf(c_0_168,negated_conjecture,
    ( minsol_model_ub(esk4_0,esk4_0,esk6_0)
    | model_ub(esk4_0,esk4_0,esk3_3(esk4_0,esk4_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_146,c_0_160]) ).

cnf(c_0_169,negated_conjecture,
    lesseq(sum(c,summation(esk4_0)),esk6_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_161]),c_0_123])]) ).

cnf(c_0_170,plain,
    ( summation(X1) = summation(X2)
    | ~ lesseq(summation(X2),X3)
    | ~ lesseq(X3,summation(X1))
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_162,c_0_91]) ).

cnf(c_0_171,plain,
    ( lesseq(X1,X2)
    | lesseq(X2,X3)
    | lesseq(X3,X1) ),
    inference(spm,[status(thm)],[c_0_125,c_0_34]) ).

cnf(c_0_172,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_173,plain,
    ( summation(max(X1,X2)) = summation(X1)
    | ~ lesseq(X1,max(X1,X2))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_148,c_0_163]) ).

cnf(c_0_174,plain,
    ( lesseq(X1,max(X2,X1))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_77,c_0_164]) ).

cnf(c_0_175,negated_conjecture,
    ( minsol_model_ub(esk5_0,esk4_0,esk6_0)
    | minsol_model_max(esk4_0,esk5_0,esk6_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_147])]) ).

cnf(c_0_176,negated_conjecture,
    ( minsol_model_ub(esk4_0,esk4_0,esk6_0)
    | model_ub(X1,esk4_0,esk3_3(esk4_0,esk4_0,esk6_0))
    | ~ lesseq(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_167,c_0_168]) ).

cnf(c_0_177,negated_conjecture,
    ( model_max(esk4_0,X1,esk6_0)
    | ~ lesseq(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_54,c_0_169]) ).

cnf(c_0_178,plain,
    ( summation(X1) = summation(X2)
    | ~ lesseq(summation(X3),summation(X1))
    | ~ lesseq(X1,X2)
    | ~ lesseq(X2,X3) ),
    inference(spm,[status(thm)],[c_0_170,c_0_91]) ).

cnf(c_0_179,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_180,plain,
    ( lesseq(X1,X2)
    | lesseq(X3,X1)
    | lesseq(X4,X3)
    | ~ lesseq(X4,X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_171]) ).

cnf(c_0_181,plain,
    ( lesseq(summation(X1),summation(max(X1,X2)))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_172,c_0_53]) ).

cnf(c_0_182,plain,
    summation(max(X1,X1)) = summation(X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_43])]) ).

cnf(c_0_183,negated_conjecture,
    ( minsol_model_max(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,X1)
    | ~ model_ub(esk5_0,esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_149,c_0_175]) ).

cnf(c_0_184,negated_conjecture,
    ( minsol_model_ub(esk4_0,esk4_0,esk6_0)
    | model_ub(X1,esk4_0,esk3_3(esk4_0,esk4_0,esk6_0))
    | lesseq(esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_176,c_0_34]) ).

cnf(c_0_185,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_186,negated_conjecture,
    ( minsol_model_max(esk4_0,X1,esk6_0)
    | model_max(esk4_0,X1,esk2_3(esk4_0,X1,esk6_0))
    | ~ lesseq(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_61,c_0_177]) ).

cnf(c_0_187,negated_conjecture,
    ( lesseq(X1,esk6_0)
    | ~ lesseq(X1,sum(c,summation(esk4_0))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_169]) ).

cnf(c_0_188,plain,
    ( summation(X1) = summation(X2)
    | ~ lesseq(X1,X2)
    | ~ lesseq(X2,X3)
    | ~ lesseq(X3,X1) ),
    inference(spm,[status(thm)],[c_0_178,c_0_91]) ).

cnf(c_0_189,plain,
    ( lesseq(X1,X2)
    | lesseq(X2,X3)
    | ~ lesseq(X1,X4)
    | ~ lesseq(X4,X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_34]),c_0_180]) ).

cnf(c_0_190,plain,
    ( lesseq(summation(esk1_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_191,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_174]) ).

cnf(c_0_192,plain,
    ( lesseq(X1,max(X1,X2))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_77,c_0_181]) ).

cnf(c_0_193,plain,
    ( model_max(X1,X1,X2)
    | ~ lesseq(sum(c,summation(X1)),X2) ),
    inference(spm,[status(thm)],[c_0_48,c_0_182]) ).

cnf(c_0_194,negated_conjecture,
    ( model_max(X1,esk5_0,esk6_0)
    | ~ lesseq(X1,esk5_0) ),
    inference(spm,[status(thm)],[c_0_131,c_0_88]) ).

cnf(c_0_195,negated_conjecture,
    ( minsol_model_ub(esk4_0,esk4_0,esk6_0)
    | minsol_model_max(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,esk3_3(esk4_0,esk4_0,esk6_0))
    | lesseq(esk4_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_183,c_0_184]) ).

cnf(c_0_196,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_max(X4,X2,X3)
    | ~ lesseq(X1,X2)
    | ~ lesseq(X4,X2) ),
    inference(spm,[status(thm)],[c_0_185,c_0_44]) ).

cnf(c_0_197,negated_conjecture,
    ( minsol_model_max(esk4_0,esk4_0,esk6_0)
    | model_max(esk4_0,esk4_0,esk2_3(esk4_0,esk4_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_186,c_0_43]) ).

cnf(c_0_198,negated_conjecture,
    ( lesseq(sum(c,X1),esk6_0)
    | ~ lesseq(X1,summation(esk4_0)) ),
    inference(spm,[status(thm)],[c_0_187,c_0_80]) ).

cnf(c_0_199,plain,
    ( summation(max(X1,X2)) = summation(X2)
    | ~ lesseq(X3,max(X1,X2))
    | ~ lesseq(X2,X3)
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_188,c_0_88]) ).

cnf(c_0_200,plain,
    ( lesseq(X1,X2)
    | lesseq(X3,X1)
    | ~ model_ub(X3,X4,X5)
    | ~ lesseq(esk1_3(X3,X4,X5),X2) ),
    inference(spm,[status(thm)],[c_0_189,c_0_110]) ).

cnf(c_0_201,plain,
    ( lesseq(esk1_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_190]) ).

cnf(c_0_202,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_max(X1,X2,X3)
    | ~ lesseq(X1,X2)
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_191,c_0_192]) ).

cnf(c_0_203,plain,
    ( model_max(X1,X1,sum(c,X2))
    | ~ lesseq(summation(X1),X2) ),
    inference(spm,[status(thm)],[c_0_193,c_0_80]) ).

cnf(c_0_204,negated_conjecture,
    ( lesseq(sum(c,summation(esk5_0)),esk6_0)
    | ~ lesseq(X1,esk5_0) ),
    inference(spm,[status(thm)],[c_0_49,c_0_194]) ).

cnf(c_0_205,negated_conjecture,
    ( minsol_model_ub(esk4_0,esk4_0,esk6_0)
    | minsol_model_max(esk4_0,esk5_0,esk6_0)
    | lesseq(esk4_0,esk5_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_195]),c_0_160])]) ).

cnf(c_0_206,negated_conjecture,
    ( minsol_model_max(esk4_0,esk4_0,esk6_0)
    | model_ub(X1,esk4_0,esk2_3(esk4_0,esk4_0,esk6_0))
    | ~ lesseq(X1,esk4_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_197]),c_0_43])]) ).

cnf(c_0_207,negated_conjecture,
    ( model_max(X1,X2,esk6_0)
    | ~ lesseq(summation(max(X1,X2)),summation(esk4_0)) ),
    inference(spm,[status(thm)],[c_0_48,c_0_198]) ).

cnf(c_0_208,plain,
    ( summation(max(X1,X2)) = summation(X2)
    | ~ lesseq(X1,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_174]),c_0_43])]) ).

cnf(c_0_209,plain,
    ( lesseq(X1,X2)
    | lesseq(X2,X3)
    | ~ model_ub(X1,X4,sum(c,summation(X3))) ),
    inference(spm,[status(thm)],[c_0_200,c_0_201]) ).

cnf(c_0_210,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_202,c_0_203]),c_0_43])]) ).

cnf(c_0_211,negated_conjecture,
    lesseq(sum(c,summation(esk5_0)),esk6_0),
    inference(spm,[status(thm)],[c_0_204,c_0_43]) ).

cnf(c_0_212,negated_conjecture,
    ( minsol_model_max(esk4_0,esk5_0,esk6_0)
    | lesseq(esk4_0,esk5_0)
    | lesseq(esk6_0,X1)
    | ~ model_ub(esk4_0,esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_149,c_0_205]) ).

cnf(c_0_213,negated_conjecture,
    ( minsol_model_max(esk4_0,esk4_0,esk6_0)
    | model_ub(esk4_0,esk4_0,esk2_3(esk4_0,esk4_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_206,c_0_43]) ).

cnf(c_0_214,negated_conjecture,
    ( model_max(X1,X1,esk6_0)
    | ~ lesseq(summation(X1),summation(esk4_0)) ),
    inference(spm,[status(thm)],[c_0_207,c_0_182]) ).

cnf(c_0_215,plain,
    ( lesseq(X1,X2)
    | ~ lesseq(X1,max(X2,X3))
    | ~ lesseq(X3,X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_163]) ).

cnf(c_0_216,plain,
    ( lesseq(X1,max(X2,X3))
    | ~ lesseq(summation(X1),summation(X3))
    | ~ lesseq(X2,X3) ),
    inference(spm,[status(thm)],[c_0_77,c_0_208]) ).

cnf(c_0_217,plain,
    ( lesseq(X1,X2)
    | lesseq(X3,X1)
    | ~ lesseq(summation(X3),summation(X2)) ),
    inference(spm,[status(thm)],[c_0_209,c_0_210]) ).

cnf(c_0_218,negated_conjecture,
    ( lesseq(summation(X1),summation(esk6_0))
    | ~ lesseq(X1,sum(c,summation(esk5_0))) ),
    inference(spm,[status(thm)],[c_0_115,c_0_211]) ).

cnf(c_0_219,plain,
    model_max(X1,X1,sum(c,summation(X1))),
    inference(spm,[status(thm)],[c_0_53,c_0_182]) ).

cnf(c_0_220,negated_conjecture,
    ( minsol_model_max(esk4_0,esk4_0,esk6_0)
    | minsol_model_max(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,esk2_3(esk4_0,esk4_0,esk6_0))
    | lesseq(esk4_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_212,c_0_213]) ).

cnf(c_0_221,negated_conjecture,
    model_max(esk4_0,esk4_0,esk6_0),
    inference(spm,[status(thm)],[c_0_214,c_0_43]) ).

cnf(c_0_222,plain,
    ( lesseq(X1,X2)
    | ~ lesseq(summation(X1),summation(X3))
    | ~ lesseq(X3,X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_216]),c_0_217]) ).

cnf(c_0_223,negated_conjecture,
    lesseq(summation(sum(c,summation(esk5_0))),summation(esk6_0)),
    inference(spm,[status(thm)],[c_0_218,c_0_43]) ).

cnf(c_0_224,plain,
    lesseq(max(X1,X1),X1),
    inference(spm,[status(thm)],[c_0_82,c_0_219]) ).

cnf(c_0_225,negated_conjecture,
    ( minsol_model_max(esk4_0,esk5_0,esk6_0)
    | minsol_model_max(esk4_0,esk4_0,esk6_0)
    | lesseq(esk4_0,esk5_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_220]),c_0_221])]) ).

cnf(c_0_226,negated_conjecture,
    ( lesseq(sum(c,summation(esk5_0)),X1)
    | ~ lesseq(esk6_0,X1) ),
    inference(spm,[status(thm)],[c_0_222,c_0_223]) ).

cnf(c_0_227,plain,
    ( max(X1,X1) = X1
    | ~ lesseq(X1,max(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_69,c_0_224]) ).

cnf(c_0_228,negated_conjecture,
    ( minsol_model_max(esk4_0,esk4_0,esk6_0)
    | model_max(esk4_0,esk5_0,esk6_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_225]),c_0_194]) ).

cnf(c_0_229,negated_conjecture,
    ( model_max(esk5_0,esk5_0,X1)
    | ~ lesseq(esk6_0,X1) ),
    inference(spm,[status(thm)],[c_0_193,c_0_226]) ).

cnf(c_0_230,plain,
    max(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_174]),c_0_43])]) ).

cnf(c_0_231,negated_conjecture,
    ( model_max(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,X1)
    | ~ model_max(esk4_0,esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_228]) ).

cnf(c_0_232,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_ub(X1,X3,X2) ),
    inference(spm,[status(thm)],[c_0_145,c_0_110]) ).

cnf(c_0_233,negated_conjecture,
    ( lesseq(esk5_0,X1)
    | ~ lesseq(esk6_0,sum(c,summation(X1))) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_229]),c_0_230]) ).

cnf(c_0_234,negated_conjecture,
    ( model_max(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,sum(c,summation(esk4_0))) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_53]),c_0_182]) ).

cnf(c_0_235,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_max(X3,X4,X2)
    | ~ lesseq(X1,max(X3,X4)) ),
    inference(spm,[status(thm)],[c_0_232,c_0_185]) ).

cnf(c_0_236,negated_conjecture,
    model_max(esk4_0,esk5_0,esk6_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_177]) ).

cnf(c_0_237,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_max(X1,X3,X2)
    | ~ lesseq(X3,X1) ),
    inference(spm,[status(thm)],[c_0_235,c_0_192]) ).

cnf(c_0_238,negated_conjecture,
    ( minsol_model_max(esk4_0,esk5_0,esk6_0)
    | model_max(esk4_0,esk5_0,esk2_3(esk4_0,esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_61,c_0_236]) ).

cnf(c_0_239,negated_conjecture,
    ( minsol_model_max(esk4_0,esk5_0,esk6_0)
    | model_ub(esk4_0,esk4_0,esk2_3(esk4_0,esk5_0,esk6_0))
    | ~ lesseq(esk5_0,esk4_0) ),
    inference(spm,[status(thm)],[c_0_237,c_0_238]) ).

cnf(c_0_240,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_241,negated_conjecture,
    ( minsol_model_max(esk4_0,esk5_0,esk6_0)
    | model_ub(esk4_0,esk4_0,esk2_3(esk4_0,esk5_0,esk6_0))
    | lesseq(esk4_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_239,c_0_34]) ).

cnf(c_0_242,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_192]) ).

cnf(c_0_243,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_240,c_0_44]) ).

cnf(c_0_244,negated_conjecture,
    ( minsol_model_max(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,esk2_3(esk4_0,esk5_0,esk6_0))
    | lesseq(esk4_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_212,c_0_241]) ).

cnf(c_0_245,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_242,c_0_44]),c_0_243]) ).

cnf(c_0_246,negated_conjecture,
    ( minsol_model_max(esk4_0,esk5_0,esk6_0)
    | lesseq(esk4_0,esk5_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_244]),c_0_236])]) ).

cnf(c_0_247,negated_conjecture,
    ( minsol_model_max(esk4_0,esk5_0,esk6_0)
    | model_ub(X1,esk4_0,esk2_3(esk4_0,esk5_0,esk6_0))
    | ~ lesseq(X1,esk5_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_238]),c_0_246]) ).

cnf(c_0_248,plain,
    ( model_max(max(X1,X2),X3,X4)
    | ~ model_max(X1,X2,X4)
    | ~ lesseq(X3,max(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_54,c_0_21]) ).

cnf(c_0_249,negated_conjecture,
    ( minsol_model_max(esk4_0,esk5_0,esk6_0)
    | model_ub(esk5_0,esk4_0,esk2_3(esk4_0,esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_247,c_0_43]) ).

cnf(c_0_250,plain,
    ( model_max(X1,X2,X3)
    | ~ model_max(X1,X4,X3)
    | ~ lesseq(X2,X1)
    | ~ lesseq(X4,X1) ),
    inference(spm,[status(thm)],[c_0_248,c_0_27]) ).

cnf(c_0_251,negated_conjecture,
    ( minsol_model_max(esk4_0,esk5_0,esk6_0)
    | lesseq(esk6_0,esk2_3(esk4_0,esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_183,c_0_249]) ).

cnf(c_0_252,negated_conjecture,
    ( minsol_model_max(esk4_0,esk4_0,esk6_0)
    | model_max(esk4_0,X1,esk2_3(esk4_0,esk4_0,esk6_0))
    | ~ lesseq(X1,esk4_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_197]),c_0_43])]) ).

cnf(c_0_253,negated_conjecture,
    minsol_model_max(esk4_0,esk5_0,esk6_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_251]),c_0_236])]) ).

cnf(c_0_254,negated_conjecture,
    ( minsol_model_max(esk4_0,esk4_0,esk6_0)
    | lesseq(esk4_0,esk5_0)
    | lesseq(esk6_0,X1)
    | ~ model_max(esk4_0,esk5_0,X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_225]) ).

cnf(c_0_255,negated_conjecture,
    ( minsol_model_max(esk4_0,esk4_0,esk6_0)
    | model_max(esk4_0,X1,esk2_3(esk4_0,esk4_0,esk6_0))
    | lesseq(esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_252,c_0_34]) ).

cnf(c_0_256,negated_conjecture,
    ( ~ minsol_model_ub(esk4_0,esk5_0,esk6_0)
    | ~ minsol_model_max(esk4_0,esk5_0,esk6_0) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_257,negated_conjecture,
    ( lesseq(esk6_0,X1)
    | ~ model_max(esk4_0,esk5_0,X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_253]) ).

cnf(c_0_258,negated_conjecture,
    ( minsol_model_max(esk4_0,esk4_0,esk6_0)
    | lesseq(esk6_0,esk2_3(esk4_0,esk4_0,esk6_0))
    | lesseq(esk4_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_254,c_0_255]) ).

cnf(c_0_259,plain,
    ( lesseq(sum(c,summation(X1)),X2)
    | ~ model_ub(X3,X4,X2)
    | ~ lesseq(X1,esk1_3(X3,X4,X2)) ),
    inference(spm,[status(thm)],[c_0_120,c_0_91]) ).

cnf(c_0_260,negated_conjecture,
    ( minsol_model_ub(esk4_0,esk5_0,esk6_0)
    | model_ub(esk4_0,esk5_0,esk3_3(esk4_0,esk5_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_146,c_0_123]) ).

cnf(c_0_261,negated_conjecture,
    ~ minsol_model_ub(esk4_0,esk5_0,esk6_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_256,c_0_253])]) ).

cnf(c_0_262,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_263,negated_conjecture,
    lesseq(esk6_0,sum(c,summation(max(esk4_0,esk5_0)))),
    inference(spm,[status(thm)],[c_0_257,c_0_53]) ).

cnf(c_0_264,negated_conjecture,
    ( minsol_model_max(esk4_0,esk4_0,esk6_0)
    | lesseq(esk4_0,esk5_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_258]),c_0_221])]) ).

cnf(c_0_265,plain,
    ( lesseq(sum(c,summation(X1)),X2)
    | ~ model_ub(X3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_259,c_0_116]) ).

cnf(c_0_266,negated_conjecture,
    model_ub(esk4_0,esk5_0,esk3_3(esk4_0,esk5_0,esk6_0)),
    inference(sr,[status(thm)],[c_0_260,c_0_261]) ).

cnf(c_0_267,negated_conjecture,
    sum(c,summation(max(esk4_0,esk5_0))) = esk6_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_262,c_0_263]),c_0_236])]) ).

cnf(c_0_268,negated_conjecture,
    ( lesseq(esk4_0,esk5_0)
    | lesseq(esk6_0,X1)
    | ~ model_max(esk4_0,esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_264]) ).

cnf(c_0_269,negated_conjecture,
    lesseq(sum(c,summation(esk5_0)),esk3_3(esk4_0,esk5_0,esk6_0)),
    inference(spm,[status(thm)],[c_0_265,c_0_266]) ).

cnf(c_0_270,negated_conjecture,
    ( sum(c,summation(esk5_0)) = esk6_0
    | ~ lesseq(esk4_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_267,c_0_44]) ).

cnf(c_0_271,negated_conjecture,
    ( lesseq(esk6_0,sum(c,summation(esk4_0)))
    | lesseq(esk4_0,esk5_0) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_268,c_0_53]),c_0_182]) ).

cnf(c_0_272,negated_conjecture,
    ( lesseq(esk6_0,esk3_3(esk4_0,esk5_0,esk6_0))
    | ~ lesseq(esk4_0,esk5_0) ),
    inference(spm,[status(thm)],[c_0_269,c_0_270]) ).

cnf(c_0_273,negated_conjecture,
    ( sum(c,summation(esk4_0)) = esk6_0
    | lesseq(esk4_0,esk5_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_271]),c_0_169])]) ).

cnf(c_0_274,negated_conjecture,
    ~ lesseq(esk4_0,esk5_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_272]),c_0_123])]),c_0_261]) ).

cnf(c_0_275,negated_conjecture,
    sum(c,summation(esk4_0)) = esk6_0,
    inference(sr,[status(thm)],[c_0_273,c_0_274]) ).

cnf(c_0_276,negated_conjecture,
    lesseq(esk5_0,esk4_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_275]),c_0_43])]) ).

cnf(c_0_277,negated_conjecture,
    ( minsol_model_ub(esk4_0,esk4_0,esk6_0)
    | model_ub(esk5_0,esk4_0,esk3_3(esk4_0,esk4_0,esk6_0)) ),
    inference(spm,[status(thm)],[c_0_176,c_0_276]) ).

cnf(c_0_278,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_max(X3,X3,X2)
    | ~ lesseq(X1,X3) ),
    inference(spm,[status(thm)],[c_0_235,c_0_230]) ).

cnf(c_0_279,plain,
    ( model_max(esk1_3(X1,X2,X3),X4,X3)
    | ~ model_ub(X1,X2,X3)
    | ~ lesseq(X4,esk1_3(X1,X2,X3)) ),
    inference(spm,[status(thm)],[c_0_54,c_0_107]) ).

cnf(c_0_280,negated_conjecture,
    ( minsol_model_ub(esk4_0,esk4_0,esk6_0)
    | lesseq(esk6_0,esk3_3(esk4_0,esk4_0,esk6_0)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_277]),c_0_275]) ).

cnf(c_0_281,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_ub(X3,X4,X2)
    | ~ lesseq(X1,esk1_3(X3,X4,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_278,c_0_279]),c_0_43])]) ).

cnf(c_0_282,negated_conjecture,
    minsol_model_ub(esk4_0,esk4_0,esk6_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_280]),c_0_160])]) ).

cnf(c_0_283,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_ub(X3,X4,X2)
    | ~ lesseq(X1,X3) ),
    inference(spm,[status(thm)],[c_0_281,c_0_117]) ).

cnf(c_0_284,negated_conjecture,
    ( lesseq(esk6_0,X1)
    | ~ model_ub(esk4_0,esk4_0,X1) ),
    inference(spm,[status(thm)],[c_0_149,c_0_282]) ).

cnf(c_0_285,negated_conjecture,
    ( model_ub(X1,X1,esk3_3(esk4_0,esk5_0,esk6_0))
    | ~ lesseq(X1,esk4_0) ),
    inference(spm,[status(thm)],[c_0_283,c_0_266]) ).

cnf(c_0_286,negated_conjecture,
    lesseq(esk6_0,esk3_3(esk4_0,esk5_0,esk6_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_284,c_0_285]),c_0_43])]) ).

cnf(c_0_287,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_286]),c_0_123])]),c_0_261]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM862+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % 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   : Fri Aug 25 17:13:49 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.17/0.54  start to proof: theBenchmark
% 10.97/11.30  % Version  : CSE_E---1.5
% 10.97/11.30  % Problem  : theBenchmark.p
% 10.97/11.30  % Proof found
% 10.97/11.30  % SZS status Theorem for theBenchmark.p
% 10.97/11.30  % SZS output start Proof
% See solution above
% 10.97/11.32  % Total time : 10.609000 s
% 10.97/11.32  % SZS output end Proof
% 10.97/11.32  % Total time : 10.613000 s
%------------------------------------------------------------------------------