TSTP Solution File: NUM861+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : NUM861+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n016.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  : 600s
% DateTime : Mon Jul 18 09:37:16 EDT 2022

% Result   : Theorem 0.36s 24.54s
% Output   : CNFRefutation 0.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   46
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  166 (  16 unt;   0 def)
%            Number of atoms       :  446 (  30 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  470 ( 190   ~; 249   |;  19   &)
%                                         (   8 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :  298 (  28 sgn  89   !;   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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',max_is_ub_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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',minsol_model_max) ).

fof(model_max_4,axiom,
    ! [X1,X2,X4] :
      ( model_max(X1,X2,X4)
    <=> lesseq(sum(c,max(X1,X2)),X4) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',model_max_4) ).

fof(lesseq_ref,axiom,
    ! [X1] : lesseq(X1,X1),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',lesseq_ref) ).

fof(lesseq_antisymmetric,axiom,
    ! [X1,X2] :
      ( ( lesseq(X1,X2)
        & lesseq(X2,X1) )
     => X1 = X2 ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',lesseq_antisymmetric) ).

fof(max_2,axiom,
    ! [X1,X2] :
      ( max(X1,X2) = X2
      | ~ lesseq(X1,X2) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',max_2) ).

fof(lesseq_trans,axiom,
    ! [X1,X2,X3] :
      ( ( lesseq(X1,X2)
        & lesseq(X2,X3) )
     => lesseq(X1,X3) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',lesseq_trans) ).

fof(model_ub_4,axiom,
    ! [X1,X2,X4] :
      ( model_ub(X1,X2,X4)
    <=> ? [X3] :
          ( ub(X1,X2,X3)
          & lesseq(sum(c,X3),X4) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',model_ub_4) ).

fof(sum_monotone_1,axiom,
    ! [X1,X2,X3] :
      ( lesseq(X1,X2)
    <=> lesseq(sum(X3,X1),sum(X3,X2)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',sum_monotone_1) ).

fof(ub,axiom,
    ! [X1,X2,X3] :
      ( ub(X1,X2,X3)
    <=> ( lesseq(X1,X3)
        & lesseq(X2,X3) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',ub) ).

fof(max_1,axiom,
    ! [X1,X2] :
      ( max(X1,X2) = X1
      | ~ lesseq(X2,X1) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',max_1) ).

fof(lesseq_total,axiom,
    ! [X1,X2] :
      ( lesseq(X1,X2)
      | lesseq(X2,X1) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',lesseq_total) ).

fof(c_0_13,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_14,plain,
    ! [X5,X6,X7,X8,X5,X6,X7] :
      ( ( model_ub(X5,X6,X7)
        | ~ minsol_model_ub(X5,X6,X7) )
      & ( ~ model_ub(X5,X6,X8)
        | lesseq(X7,X8)
        | ~ minsol_model_ub(X5,X6,X7) )
      & ( model_ub(X5,X6,esk5_3(X5,X6,X7))
        | ~ model_ub(X5,X6,X7)
        | minsol_model_ub(X5,X6,X7) )
      & ( ~ lesseq(X7,esk5_3(X5,X6,X7))
        | ~ model_ub(X5,X6,X7)
        | minsol_model_ub(X5,X6,X7) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[minsol_model_ub])])])])])])]) ).

fof(c_0_15,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_13])])]) ).

fof(c_0_16,plain,
    ! [X5,X6,X7,X8,X5,X6,X7] :
      ( ( model_max(X5,X6,X7)
        | ~ minsol_model_max(X5,X6,X7) )
      & ( ~ model_max(X5,X6,X8)
        | lesseq(X7,X8)
        | ~ minsol_model_max(X5,X6,X7) )
      & ( model_max(X5,X6,esk4_3(X5,X6,X7))
        | ~ model_max(X5,X6,X7)
        | minsol_model_max(X5,X6,X7) )
      & ( ~ lesseq(X7,esk4_3(X5,X6,X7))
        | ~ model_max(X5,X6,X7)
        | minsol_model_max(X5,X6,X7) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[minsol_model_max])])])])])])]) ).

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

cnf(c_0_18,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | minsol_model_ub(esk1_0,esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_19,plain,
    ! [X5,X6,X7,X5,X6,X7] :
      ( ( ~ model_max(X5,X6,X7)
        | lesseq(sum(c,max(X5,X6)),X7) )
      & ( ~ lesseq(sum(c,max(X5,X6)),X7)
        | model_max(X5,X6,X7) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_max_4])])])]) ).

cnf(c_0_20,plain,
    ( model_max(X1,X2,X3)
    | ~ minsol_model_max(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_21,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_17,c_0_18]) ).

fof(c_0_22,plain,
    ! [X2] : lesseq(X2,X2),
    inference(variable_rename,[status(thm)],[lesseq_ref]) ).

fof(c_0_23,plain,
    ! [X3,X4] :
      ( ~ lesseq(X3,X4)
      | ~ lesseq(X4,X3)
      | X3 = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_antisymmetric])]) ).

cnf(c_0_24,plain,
    ( lesseq(sum(c,max(X1,X2)),X3)
    | ~ model_max(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_max(esk1_0,esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,plain,
    ( lesseq(X3,X4)
    | ~ minsol_model_max(X1,X2,X3)
    | ~ model_max(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_27,plain,
    ( model_max(X1,X2,X3)
    | ~ lesseq(sum(c,max(X1,X2)),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_28,plain,
    lesseq(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

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

cnf(c_0_30,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(sum(c,max(esk1_0,esk2_0)),esk3_0) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_31,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_26,c_0_21]) ).

cnf(c_0_32,plain,
    model_max(X1,X2,sum(c,max(X1,X2))),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_33,negated_conjecture,
    ( sum(c,max(esk1_0,esk2_0)) = esk3_0
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(esk3_0,sum(c,max(esk1_0,esk2_0))) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,sum(c,max(esk1_0,esk2_0))) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

fof(c_0_35,plain,
    ! [X3,X4] :
      ( max(X3,X4) = X4
      | ~ lesseq(X3,X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[max_2])]) ).

cnf(c_0_36,negated_conjecture,
    ( sum(c,max(esk1_0,esk2_0)) = esk3_0
    | model_ub(esk1_0,esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

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

fof(c_0_38,plain,
    ! [X4,X5,X6] :
      ( ~ lesseq(X4,X5)
      | ~ lesseq(X5,X6)
      | lesseq(X4,X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_trans])]) ).

fof(c_0_39,plain,
    ! [X5,X6,X7,X5,X6,X7,X9] :
      ( ( ub(X5,X6,esk6_3(X5,X6,X7))
        | ~ model_ub(X5,X6,X7) )
      & ( lesseq(sum(c,esk6_3(X5,X6,X7)),X7)
        | ~ model_ub(X5,X6,X7) )
      & ( ~ ub(X5,X6,X9)
        | ~ lesseq(sum(c,X9),X7)
        | model_ub(X5,X6,X7) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_ub_4])])])])])])]) ).

fof(c_0_40,plain,
    ! [X4,X5,X6,X4,X5,X6] :
      ( ( ~ lesseq(X4,X5)
        | lesseq(sum(X6,X4),sum(X6,X5)) )
      & ( ~ lesseq(sum(X6,X4),sum(X6,X5))
        | lesseq(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_monotone_1])])])]) ).

cnf(c_0_41,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_max(esk1_0,esk2_0,X1)
    | ~ lesseq(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_36]) ).

cnf(c_0_42,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,sum(c,esk2_0))
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_34,c_0_37]) ).

cnf(c_0_43,plain,
    ( lesseq(X1,X2)
    | ~ lesseq(X3,X2)
    | ~ lesseq(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_44,plain,
    ( lesseq(sum(c,esk6_3(X1,X2,X3)),X3)
    | ~ model_ub(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

fof(c_0_45,plain,
    ! [X4,X5,X6,X4,X5,X6] :
      ( ( lesseq(X4,X6)
        | ~ ub(X4,X5,X6) )
      & ( lesseq(X5,X6)
        | ~ ub(X4,X5,X6) )
      & ( ~ lesseq(X4,X6)
        | ~ lesseq(X5,X6)
        | ub(X4,X5,X6) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ub])])])])]) ).

cnf(c_0_46,plain,
    ( lesseq(sum(X1,X2),sum(X1,X3))
    | ~ lesseq(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_47,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_max(esk1_0,esk2_0,sum(c,esk2_0))
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_48,plain,
    ( lesseq(X1,X2)
    | ~ model_ub(X3,X4,X2)
    | ~ lesseq(X1,sum(c,esk6_3(X3,X4,X2))) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_49,plain,
    ( lesseq(X2,X3)
    | ~ ub(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_50,plain,
    ( ub(X1,X2,esk6_3(X1,X2,X3))
    | ~ model_ub(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_51,plain,
    ( model_ub(X1,X2,X3)
    | ~ lesseq(sum(c,X4),X3)
    | ~ ub(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_52,plain,
    ( sum(X1,X2) = sum(X1,X3)
    | ~ lesseq(sum(X1,X2),sum(X1,X3))
    | ~ lesseq(X3,X2) ),
    inference(spm,[status(thm)],[c_0_29,c_0_46]) ).

cnf(c_0_53,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(sum(c,max(esk1_0,esk2_0)),sum(c,esk2_0))
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_24,c_0_47]) ).

cnf(c_0_54,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(X1,esk3_0)
    | ~ lesseq(X1,sum(c,max(esk1_0,esk2_0))) ),
    inference(spm,[status(thm)],[c_0_43,c_0_30]) ).

cnf(c_0_55,plain,
    ( lesseq(sum(c,X1),X2)
    | ~ model_ub(X3,X4,X2)
    | ~ lesseq(X1,esk6_3(X3,X4,X2)) ),
    inference(spm,[status(thm)],[c_0_48,c_0_46]) ).

cnf(c_0_56,plain,
    ( lesseq(X1,esk6_3(X2,X1,X3))
    | ~ model_ub(X2,X1,X3) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

fof(c_0_57,plain,
    ! [X3,X4] :
      ( max(X3,X4) = X3
      | ~ lesseq(X4,X3) ),
    inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[max_1])]) ).

cnf(c_0_58,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_51,c_0_44]) ).

cnf(c_0_59,plain,
    ( ub(X1,X2,X3)
    | ~ lesseq(X2,X3)
    | ~ lesseq(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_60,negated_conjecture,
    ( sum(c,max(esk1_0,esk2_0)) = sum(c,esk2_0)
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(esk2_0,max(esk1_0,esk2_0))
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_61,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(sum(c,X1),esk3_0)
    | ~ lesseq(X1,max(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_54,c_0_46]) ).

cnf(c_0_62,plain,
    ( lesseq(sum(c,X1),X2)
    | ~ model_ub(X3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_63,plain,
    ( max(X2,X1) = X2
    | ~ lesseq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_57]) ).

fof(c_0_64,plain,
    ! [X3,X4] :
      ( lesseq(X3,X4)
      | lesseq(X4,X3) ),
    inference(variable_rename,[status(thm)],[lesseq_total]) ).

cnf(c_0_65,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_58,c_0_59]) ).

cnf(c_0_66,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,X2,esk3_0)
    | ~ ub(X1,X2,max(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_30]) ).

cnf(c_0_67,plain,
    ( lesseq(X1,X3)
    | ~ ub(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_68,plain,
    ( lesseq(X1,X2)
    | ~ lesseq(sum(X3,X1),sum(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_69,negated_conjecture,
    ( lesseq(sum(c,esk2_0),esk3_0)
    | ~ lesseq(esk2_0,max(esk1_0,esk2_0)) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_60]),c_0_61]),c_0_62]) ).

cnf(c_0_70,plain,
    ( model_max(X1,X2,X3)
    | ~ lesseq(sum(c,X1),X3)
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_63]) ).

cnf(c_0_71,plain,
    ( lesseq(X1,X2)
    | lesseq(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_72,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_ub(X4,X2,X3)
    | ~ lesseq(X1,esk6_3(X4,X2,X3)) ),
    inference(spm,[status(thm)],[c_0_65,c_0_56]) ).

cnf(c_0_73,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,X2,esk3_0)
    | ~ lesseq(X2,max(esk1_0,esk2_0))
    | ~ lesseq(X1,max(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_66,c_0_59]) ).

cnf(c_0_74,plain,
    ( lesseq(X1,esk6_3(X1,X2,X3))
    | ~ model_ub(X1,X2,X3) ),
    inference(spm,[status(thm)],[c_0_67,c_0_50]) ).

cnf(c_0_75,plain,
    ( minsol_model_max(X1,X2,X3)
    | model_max(X1,X2,esk4_3(X1,X2,X3))
    | ~ model_max(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_76,plain,
    ( lesseq(esk6_3(X1,X2,sum(c,X3)),X3)
    | ~ model_ub(X1,X2,sum(c,X3)) ),
    inference(spm,[status(thm)],[c_0_68,c_0_44]) ).

cnf(c_0_77,negated_conjecture,
    ( lesseq(sum(c,esk2_0),esk3_0)
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_69,c_0_63]) ).

cnf(c_0_78,plain,
    ( model_max(X1,X2,X3)
    | lesseq(X3,sum(c,X1))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_79,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_ub(X3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_72,c_0_56]) ).

cnf(c_0_80,negated_conjecture,
    ( model_ub(X1,max(esk1_0,esk2_0),esk3_0)
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(X1,max(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_73,c_0_28]) ).

cnf(c_0_81,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_ub(X2,X4,X3)
    | ~ lesseq(X1,esk6_3(X2,X4,X3)) ),
    inference(spm,[status(thm)],[c_0_65,c_0_74]) ).

cnf(c_0_82,plain,
    ( minsol_model_max(X1,X2,X3)
    | ~ model_max(X1,X2,X3)
    | ~ lesseq(X3,esk4_3(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_83,plain,
    ( minsol_model_max(X1,X2,X3)
    | lesseq(sum(c,max(X1,X2)),esk4_3(X1,X2,X3))
    | ~ model_max(X1,X2,X3) ),
    inference(spm,[status(thm)],[c_0_24,c_0_75]) ).

cnf(c_0_84,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(sum(c,X1),esk3_0)
    | ~ lesseq(esk2_0,esk1_0)
    | ~ lesseq(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_61,c_0_63]) ).

cnf(c_0_85,plain,
    ( lesseq(X1,X2)
    | ~ model_ub(X3,X4,sum(c,X2))
    | ~ lesseq(X1,esk6_3(X3,X4,sum(c,X2))) ),
    inference(spm,[status(thm)],[c_0_43,c_0_76]) ).

cnf(c_0_86,negated_conjecture,
    ( sum(c,esk2_0) = esk3_0
    | ~ lesseq(esk3_0,sum(c,esk2_0))
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_29,c_0_77]) ).

cnf(c_0_87,plain,
    ( model_max(X1,X1,X2)
    | lesseq(X2,sum(c,X1)) ),
    inference(spm,[status(thm)],[c_0_78,c_0_28]) ).

cnf(c_0_88,negated_conjecture,
    ( model_ub(max(esk1_0,esk2_0),max(esk1_0,esk2_0),esk3_0)
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(X1,max(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_89,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_ub(X1,X3,X2) ),
    inference(spm,[status(thm)],[c_0_81,c_0_74]) ).

cnf(c_0_90,plain,
    minsol_model_max(X1,X2,sum(c,max(X1,X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_32])]) ).

cnf(c_0_91,negated_conjecture,
    ( sum(c,X1) = esk3_0
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(esk3_0,sum(c,X1))
    | ~ lesseq(esk2_0,esk1_0)
    | ~ lesseq(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_29,c_0_84]) ).

cnf(c_0_92,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,sum(c,esk1_0))
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_34,c_0_63]) ).

cnf(c_0_93,plain,
    ( lesseq(X1,X2)
    | ~ model_ub(X3,X1,sum(c,X2)) ),
    inference(spm,[status(thm)],[c_0_85,c_0_56]) ).

cnf(c_0_94,negated_conjecture,
    ( sum(c,esk2_0) = esk3_0
    | model_max(esk2_0,esk2_0,esk3_0)
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_86,c_0_87]) ).

cnf(c_0_95,negated_conjecture,
    ( model_ub(esk1_0,esk1_0,esk3_0)
    | ~ lesseq(esk2_0,esk1_0)
    | ~ lesseq(X1,esk1_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_63]),c_0_89]) ).

cnf(c_0_96,plain,
    ( minsol_model_max(X1,X2,sum(c,X2))
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_90,c_0_37]) ).

cnf(c_0_97,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(max(esk1_0,esk2_0),X1)
    | ~ lesseq(esk3_0,sum(c,X1)) ),
    inference(spm,[status(thm)],[c_0_68,c_0_36]) ).

cnf(c_0_98,negated_conjecture,
    ( sum(c,esk1_0) = esk3_0
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_28])]) ).

cnf(c_0_99,plain,
    ( minsol_model_max(X1,X2,sum(c,X1))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_90,c_0_63]) ).

cnf(c_0_100,negated_conjecture,
    ( model_max(esk2_0,esk2_0,esk3_0)
    | lesseq(X1,esk2_0)
    | ~ model_ub(X2,X1,esk3_0)
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_93,c_0_94]) ).

cnf(c_0_101,negated_conjecture,
    ( model_ub(esk1_0,esk1_0,esk3_0)
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_95,c_0_28]) ).

cnf(c_0_102,plain,
    ( lesseq(sum(c,X1),X2)
    | ~ model_max(X3,X1,X2)
    | ~ lesseq(X3,X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_96]) ).

cnf(c_0_103,plain,
    ( sum(X1,X2) = sum(X1,X3)
    | ~ lesseq(X3,X2)
    | ~ lesseq(X2,X3) ),
    inference(spm,[status(thm)],[c_0_52,c_0_46]) ).

cnf(c_0_104,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(max(esk1_0,esk2_0),esk1_0)
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_28])]) ).

cnf(c_0_105,plain,
    ( lesseq(sum(c,X1),X2)
    | ~ model_max(X1,X3,X2)
    | ~ lesseq(X3,X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_99]) ).

cnf(c_0_106,negated_conjecture,
    ( model_max(esk2_0,esk2_0,esk3_0)
    | lesseq(esk1_0,esk2_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_71]) ).

cnf(c_0_107,negated_conjecture,
    ( lesseq(sum(c,esk2_0),esk3_0)
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_25]),c_0_62]) ).

cnf(c_0_108,negated_conjecture,
    ( sum(X1,max(esk1_0,esk2_0)) = sum(X1,esk1_0)
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(esk1_0,max(esk1_0,esk2_0))
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_103,c_0_104]) ).

cnf(c_0_109,plain,
    ( lesseq(sum(c,X1),X2)
    | ~ model_ub(X1,X3,X2) ),
    inference(spm,[status(thm)],[c_0_55,c_0_74]) ).

cnf(c_0_110,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(X1,max(esk1_0,esk2_0))
    | ~ lesseq(sum(c,X1),esk3_0) ),
    inference(spm,[status(thm)],[c_0_68,c_0_36]) ).

cnf(c_0_111,negated_conjecture,
    lesseq(sum(c,esk2_0),esk3_0),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_28])]),c_0_107]) ).

cnf(c_0_112,negated_conjecture,
    ( lesseq(sum(c,esk1_0),esk3_0)
    | ~ lesseq(esk1_0,max(esk1_0,esk2_0)) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_108]),c_0_61]),c_0_109]) ).

cnf(c_0_113,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk2_0,max(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_110,c_0_111]) ).

cnf(c_0_114,negated_conjecture,
    ( sum(c,X1) = esk3_0
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(sum(c,X1),esk3_0)
    | ~ lesseq(max(esk1_0,esk2_0),X1) ),
    inference(spm,[status(thm)],[c_0_52,c_0_36]) ).

cnf(c_0_115,negated_conjecture,
    ( lesseq(sum(c,esk1_0),esk3_0)
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_112,c_0_37]) ).

cnf(c_0_116,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,esk2_0,esk3_0)
    | ~ lesseq(X1,max(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_73,c_0_113]) ).

cnf(c_0_117,negated_conjecture,
    ( sum(c,esk2_0) = esk3_0
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_118,negated_conjecture,
    ( sum(c,esk1_0) = esk3_0
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(max(esk1_0,esk2_0),esk1_0)
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_114,c_0_115]) ).

cnf(c_0_119,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,esk2_0,esk3_0)
    | lesseq(max(esk1_0,esk2_0),X1) ),
    inference(spm,[status(thm)],[c_0_116,c_0_71]) ).

cnf(c_0_120,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk1_0,max(esk1_0,esk2_0))
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_98]),c_0_28])]) ).

cnf(c_0_121,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk2_0,X1)
    | ~ lesseq(esk3_0,sum(c,X1))
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_68,c_0_117]) ).

cnf(c_0_122,negated_conjecture,
    ( sum(c,esk1_0) = esk3_0
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_118,c_0_119]) ).

cnf(c_0_123,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_116,c_0_120]) ).

cnf(c_0_124,negated_conjecture,
    model_ub(esk1_0,esk2_0,esk3_0),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_28])]),c_0_71]),c_0_123]) ).

cnf(c_0_125,plain,
    ( lesseq(X3,X4)
    | ~ minsol_model_ub(X1,X2,X3)
    | ~ model_ub(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_126,plain,
    ( model_ub(X1,X2,sum(c,X3))
    | ~ ub(X1,X2,X3) ),
    inference(spm,[status(thm)],[c_0_51,c_0_28]) ).

cnf(c_0_127,negated_conjecture,
    lesseq(sum(c,esk1_0),esk3_0),
    inference(spm,[status(thm)],[c_0_109,c_0_124]) ).

cnf(c_0_128,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_125,c_0_18]) ).

cnf(c_0_129,plain,
    ( model_ub(X1,X2,sum(c,X3))
    | ~ lesseq(X2,X3)
    | ~ lesseq(X1,X3) ),
    inference(spm,[status(thm)],[c_0_126,c_0_59]) ).

cnf(c_0_130,negated_conjecture,
    ( sum(c,esk1_0) = esk3_0
    | ~ lesseq(esk3_0,sum(c,esk1_0)) ),
    inference(spm,[status(thm)],[c_0_29,c_0_127]) ).

cnf(c_0_131,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,sum(c,X1))
    | ~ lesseq(esk2_0,X1)
    | ~ lesseq(esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_128,c_0_129]) ).

cnf(c_0_132,negated_conjecture,
    ( sum(c,esk1_0) = esk3_0
    | minsol_model_max(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_28])]) ).

cnf(c_0_133,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | minsol_model_max(esk1_0,X1,esk3_0)
    | ~ lesseq(esk2_0,esk1_0)
    | ~ lesseq(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_99,c_0_132]) ).

cnf(c_0_134,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | minsol_model_max(esk1_0,X1,esk3_0)
    | lesseq(esk1_0,esk2_0)
    | ~ lesseq(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_133,c_0_71]) ).

cnf(c_0_135,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | minsol_model_max(esk1_0,X1,esk3_0)
    | lesseq(esk1_0,esk2_0)
    | lesseq(esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_134,c_0_71]) ).

cnf(c_0_136,plain,
    ( model_max(X1,X2,X3)
    | ~ lesseq(sum(c,X2),X3)
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_27,c_0_37]) ).

cnf(c_0_137,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk1_0,esk2_0) ),
    inference(ef,[status(thm)],[c_0_135]) ).

cnf(c_0_138,negated_conjecture,
    ( model_max(X1,esk2_0,esk3_0)
    | ~ lesseq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_136,c_0_111]) ).

cnf(c_0_139,negated_conjecture,
    model_max(esk1_0,esk2_0,esk3_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_137]),c_0_138]) ).

cnf(c_0_140,negated_conjecture,
    lesseq(sum(c,max(esk1_0,esk2_0)),esk3_0),
    inference(spm,[status(thm)],[c_0_24,c_0_139]) ).

cnf(c_0_141,negated_conjecture,
    ( sum(c,max(esk1_0,esk2_0)) = esk3_0
    | ~ lesseq(esk3_0,sum(c,max(esk1_0,esk2_0))) ),
    inference(spm,[status(thm)],[c_0_29,c_0_140]) ).

cnf(c_0_142,negated_conjecture,
    ( sum(c,max(esk1_0,esk2_0)) = esk3_0
    | minsol_model_max(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(esk2_0,max(esk1_0,esk2_0))
    | ~ lesseq(esk1_0,max(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_141,c_0_131]) ).

cnf(c_0_143,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(esk2_0,max(esk1_0,esk2_0))
    | ~ lesseq(esk1_0,max(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_90,c_0_142]) ).

cnf(c_0_144,negated_conjecture,
    minsol_model_max(esk1_0,esk2_0,esk3_0),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_37]),c_0_28])]),c_0_137]) ).

cnf(c_0_145,plain,
    ( minsol_model_ub(X1,X2,X3)
    | model_ub(X1,X2,esk5_3(X1,X2,X3))
    | ~ model_ub(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_146,negated_conjecture,
    ( lesseq(esk3_0,X1)
    | ~ model_max(esk1_0,esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_144]) ).

cnf(c_0_147,plain,
    ( model_max(X1,X2,sum(c,X1))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_70,c_0_28]) ).

cnf(c_0_148,plain,
    ( minsol_model_ub(X1,X2,X3)
    | ~ model_ub(X1,X2,X3)
    | ~ lesseq(X3,esk5_3(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_149,plain,
    ( minsol_model_ub(X1,X2,X3)
    | lesseq(sum(c,X1),esk5_3(X1,X2,X3))
    | ~ model_ub(X1,X2,X3) ),
    inference(spm,[status(thm)],[c_0_109,c_0_145]) ).

cnf(c_0_150,negated_conjecture,
    ( lesseq(esk3_0,sum(c,esk1_0))
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_146,c_0_147]) ).

cnf(c_0_151,negated_conjecture,
    ( ~ minsol_model_max(esk1_0,esk2_0,esk3_0)
    | ~ minsol_model_ub(esk1_0,esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_152,plain,
    ( minsol_model_ub(X1,X2,sum(c,X1))
    | ~ model_ub(X1,X2,sum(c,X1)) ),
    inference(spm,[status(thm)],[c_0_148,c_0_149]) ).

cnf(c_0_153,negated_conjecture,
    ( sum(c,esk1_0) = esk3_0
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_150]),c_0_127])]) ).

cnf(c_0_154,plain,
    ( model_max(X1,X2,sum(c,X2))
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_136,c_0_28]) ).

cnf(c_0_155,negated_conjecture,
    ~ minsol_model_ub(esk1_0,esk2_0,esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_144])]) ).

cnf(c_0_156,negated_conjecture,
    ( minsol_model_ub(esk1_0,X1,esk3_0)
    | ~ model_ub(esk1_0,X1,esk3_0)
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_152,c_0_153]) ).

cnf(c_0_157,negated_conjecture,
    ( lesseq(esk3_0,sum(c,esk2_0))
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_146,c_0_154]) ).

cnf(c_0_158,negated_conjecture,
    ~ lesseq(esk2_0,esk1_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_124])]) ).

cnf(c_0_159,plain,
    ( minsol_model_ub(X1,X2,X3)
    | lesseq(sum(c,X2),esk5_3(X1,X2,X3))
    | ~ model_ub(X1,X2,X3) ),
    inference(spm,[status(thm)],[c_0_62,c_0_145]) ).

cnf(c_0_160,negated_conjecture,
    ( sum(c,esk2_0) = esk3_0
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_157]),c_0_111])]) ).

cnf(c_0_161,negated_conjecture,
    lesseq(esk1_0,esk2_0),
    inference(spm,[status(thm)],[c_0_158,c_0_71]) ).

cnf(c_0_162,plain,
    ( minsol_model_ub(X1,X2,sum(c,X2))
    | ~ model_ub(X1,X2,sum(c,X2)) ),
    inference(spm,[status(thm)],[c_0_148,c_0_159]) ).

cnf(c_0_163,negated_conjecture,
    sum(c,esk2_0) = esk3_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_160,c_0_161])]) ).

cnf(c_0_164,negated_conjecture,
    ( minsol_model_ub(X1,esk2_0,esk3_0)
    | ~ model_ub(X1,esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[c_0_162,c_0_163]) ).

cnf(c_0_165,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_164]),c_0_124])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : NUM861+1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12  % Command  : run_ET %s %d
% 0.11/0.33  % Computer : n016.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Thu Jul  7 23:35:22 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.36/23.39  eprover: CPU time limit exceeded, terminating
% 0.36/23.40  eprover: CPU time limit exceeded, terminating
% 0.36/23.40  eprover: CPU time limit exceeded, terminating
% 0.36/23.41  eprover: CPU time limit exceeded, terminating
% 0.36/24.54  # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.36/24.54  
% 0.36/24.54  # Failure: Resource limit exceeded (time)
% 0.36/24.54  # OLD status Res
% 0.36/24.54  # Preprocessing time       : 0.016 s
% 0.36/24.54  # Running protocol protocol_eprover_773c90a94152ea2e8c9d3df9c4b1eb6152c40c03 for 23 seconds:
% 0.36/24.54  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,,100,1.0)
% 0.36/24.54  # Preprocessing time       : 0.016 s
% 0.36/24.54  
% 0.36/24.54  # Proof found!
% 0.36/24.54  # SZS status Theorem
% 0.36/24.54  # SZS output start CNFRefutation
% See solution above
% 0.36/24.54  # Proof object total steps             : 166
% 0.36/24.54  # Proof object clause steps            : 139
% 0.36/24.54  # Proof object formula steps           : 27
% 0.36/24.54  # Proof object conjectures             : 82
% 0.36/24.54  # Proof object clause conjectures      : 79
% 0.36/24.54  # Proof object formula conjectures     : 3
% 0.36/24.54  # Proof object initial clauses used    : 26
% 0.36/24.54  # Proof object initial formulas used   : 13
% 0.36/24.54  # Proof object generating inferences   : 111
% 0.36/24.54  # Proof object simplifying inferences  : 40
% 0.36/24.54  # Training examples: 0 positive, 0 negative
% 0.36/24.54  # Parsed axioms                        : 14
% 0.36/24.54  # Removed by relevancy pruning/SinE    : 1
% 0.36/24.54  # Initial clauses                      : 26
% 0.36/24.54  # Removed in clause preprocessing      : 0
% 0.36/24.54  # Initial clauses in saturation        : 26
% 0.36/24.54  # Processed clauses                    : 2830
% 0.36/24.54  # ...of these trivial                  : 16
% 0.36/24.54  # ...subsumed                          : 1588
% 0.36/24.54  # ...remaining for further processing  : 1226
% 0.36/24.54  # Other redundant clauses eliminated   : 0
% 0.36/24.54  # Clauses deleted for lack of memory   : 0
% 0.36/24.54  # Backward-subsumed                    : 445
% 0.36/24.54  # Backward-rewritten                   : 401
% 0.36/24.54  # Generated clauses                    : 34458
% 0.36/24.54  # ...of the previous two non-trivial   : 31374
% 0.36/24.54  # Contextual simplify-reflections      : 1600
% 0.36/24.54  # Paramodulations                      : 34438
% 0.36/24.54  # Factorizations                       : 20
% 0.36/24.54  # Equation resolutions                 : 0
% 0.36/24.54  # Current number of processed clauses  : 380
% 0.36/24.54  #    Positive orientable unit clauses  : 17
% 0.36/24.54  #    Positive unorientable unit clauses: 0
% 0.36/24.54  #    Negative unit clauses             : 2
% 0.36/24.54  #    Non-unit-clauses                  : 361
% 0.36/24.54  # Current number of unprocessed clauses: 7485
% 0.36/24.54  # ...number of literals in the above   : 28978
% 0.36/24.54  # Current number of archived formulas  : 0
% 0.36/24.54  # Current number of archived clauses   : 846
% 0.36/24.54  # Clause-clause subsumption calls (NU) : 211672
% 0.36/24.54  # Rec. Clause-clause subsumption calls : 61072
% 0.36/24.54  # Non-unit clause-clause subsumptions  : 3601
% 0.36/24.54  # Unit Clause-clause subsumption calls : 457
% 0.36/24.54  # Rewrite failures with RHS unbound    : 0
% 0.36/24.54  # BW rewrite match attempts            : 37
% 0.36/24.54  # BW rewrite match successes           : 14
% 0.36/24.54  # Condensation attempts                : 0
% 0.36/24.54  # Condensation successes               : 0
% 0.36/24.54  # Termbank termtop insertions          : 583336
% 0.36/24.54  
% 0.36/24.54  # -------------------------------------------------
% 0.36/24.54  # User time                : 0.737 s
% 0.36/24.54  # System time              : 0.006 s
% 0.36/24.54  # Total time               : 0.743 s
% 0.36/24.54  # Maximum resident set size: 15192 pages
% 0.36/46.42  eprover: CPU time limit exceeded, terminating
% 0.36/46.44  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.44  eprover: No such file or directory
% 0.36/46.44  eprover: CPU time limit exceeded, terminating
% 0.36/46.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.45  eprover: No such file or directory
% 0.36/46.45  eprover: CPU time limit exceeded, terminating
% 0.36/46.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.45  eprover: No such file or directory
% 0.36/46.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/46.45  eprover: No such file or directory
% 0.36/46.45  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.45  eprover: No such file or directory
% 0.36/46.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/46.46  eprover: No such file or directory
% 0.36/46.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.46  eprover: No such file or directory
% 0.36/46.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.46  eprover: No such file or directory
% 0.36/46.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/46.46  eprover: No such file or directory
% 0.36/46.46  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.46  eprover: No such file or directory
% 0.36/46.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.47  eprover: No such file or directory
% 0.36/46.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/46.47  eprover: No such file or directory
% 0.36/46.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.47  eprover: No such file or directory
% 0.36/46.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.47  eprover: No such file or directory
% 0.36/46.47  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/46.47  eprover: No such file or directory
% 0.36/46.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.48  eprover: No such file or directory
% 0.36/46.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/46.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.48  eprover: No such file or directory
% 0.36/46.48  eprover: No such file or directory
% 0.36/46.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.48  eprover: No such file or directory
% 0.36/46.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.48  eprover: No such file or directory
% 0.36/46.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/46.48  eprover: No such file or directory
% 0.36/46.48  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.48  eprover: No such file or directory
% 0.36/46.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.49  eprover: No such file or directory
% 0.36/46.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/46.49  eprover: No such file or directory
% 0.36/46.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.49  eprover: No such file or directory
% 0.36/46.49  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/46.49  eprover: No such file or directory
% 0.36/46.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.36/46.50  eprover: No such file or directory
% 0.36/46.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.50  eprover: No such file or directory
% 0.36/46.50  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.36/46.50  eprover: No such file or directory
%------------------------------------------------------------------------------