TSTP Solution File: NUM859+1 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM859+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n022.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 : Fri May  3 02:50:58 EDT 2024

% Result   : Theorem 56.53s 8.66s
% Output   : CNFRefutation 56.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  258 (  20 unt;   0 def)
%            Number of atoms       :  796 ( 169 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  953 ( 415   ~; 456   |;  57   &)
%                                         (  14 <=>;  10  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :  492 (   7 sgn 198   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] : lesseq(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_ref) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( ( lesseq(X1,X2)
        & lesseq(X0,X1) )
     => lesseq(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_trans) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( ( lesseq(X1,X0)
        & lesseq(X0,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_antisymmetric) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( lesseq(X1,X0)
      | lesseq(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lesseq_total) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( lesseq(X0,X1)
    <=> lesseq(summation(X0),summation(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',summation_monotone) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ lesseq(X1,X0)
      | max(X0,X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_1) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( ~ lesseq(X0,X1)
      | max(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_2) ).

fof(f9,axiom,
    ! [X0,X1,X2] :
      ( ub(X0,X1,X2)
    <=> ( lesseq(X1,X2)
        & lesseq(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ub) ).

fof(f10,axiom,
    ! [X0,X1,X3] :
      ( model_max(X0,X1,X3)
    <=> lesseq(max(X0,X1),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_max_2) ).

fof(f11,axiom,
    ! [X0,X1,X3] :
      ( model_ub(X0,X1,X3)
    <=> ? [X2] :
          ( lesseq(X2,X3)
          & ub(X0,X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',model_ub_2) ).

fof(f12,axiom,
    ! [X0,X1,X3] :
      ( minsol_model_max(X0,X1,X3)
    <=> ( ! [X2] :
            ( model_max(X0,X1,X2)
           => lesseq(X3,X2) )
        & model_max(X0,X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_max) ).

fof(f13,axiom,
    ! [X0,X1,X3] :
      ( minsol_model_ub(X0,X1,X3)
    <=> ( ! [X2] :
            ( model_ub(X0,X1,X2)
           => lesseq(X3,X2) )
        & model_ub(X0,X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',minsol_model_ub) ).

fof(f14,conjecture,
    ! [X0,X1,X2] :
      ( minsol_model_ub(X0,X1,X2)
    <=> minsol_model_max(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',max_is_ub_1) ).

fof(f15,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( minsol_model_ub(X0,X1,X2)
      <=> minsol_model_max(X0,X1,X2) ),
    inference(negated_conjecture,[],[f14]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( model_max(X0,X1,X2)
    <=> lesseq(max(X0,X1),X2) ),
    inference(rectify,[],[f10]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( model_ub(X0,X1,X2)
    <=> ? [X3] :
          ( lesseq(X3,X2)
          & ub(X0,X1,X3) ) ),
    inference(rectify,[],[f11]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( minsol_model_max(X0,X1,X2)
    <=> ( ! [X3] :
            ( model_max(X0,X1,X3)
           => lesseq(X2,X3) )
        & model_max(X0,X1,X2) ) ),
    inference(rectify,[],[f12]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( minsol_model_ub(X0,X1,X2)
    <=> ( ! [X3] :
            ( model_ub(X0,X1,X3)
           => lesseq(X2,X3) )
        & model_ub(X0,X1,X2) ) ),
    inference(rectify,[],[f13]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( lesseq(X0,X2)
      | ~ lesseq(X1,X2)
      | ~ lesseq(X0,X1) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( lesseq(X0,X2)
      | ~ lesseq(X1,X2)
      | ~ lesseq(X0,X1) ),
    inference(flattening,[],[f20]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ lesseq(X1,X0)
      | ~ lesseq(X0,X1) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ lesseq(X1,X0)
      | ~ lesseq(X0,X1) ),
    inference(flattening,[],[f22]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( minsol_model_max(X0,X1,X2)
    <=> ( ! [X3] :
            ( lesseq(X2,X3)
            | ~ model_max(X0,X1,X3) )
        & model_max(X0,X1,X2) ) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( minsol_model_ub(X0,X1,X2)
    <=> ( ! [X3] :
            ( lesseq(X2,X3)
            | ~ model_ub(X0,X1,X3) )
        & model_ub(X0,X1,X2) ) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f26,plain,
    ? [X0,X1,X2] :
      ( minsol_model_ub(X0,X1,X2)
    <~> minsol_model_max(X0,X1,X2) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( lesseq(X0,X1)
        | ~ lesseq(summation(X0),summation(X1)) )
      & ( lesseq(summation(X0),summation(X1))
        | ~ lesseq(X0,X1) ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( ub(X0,X1,X2)
        | ~ lesseq(X1,X2)
        | ~ lesseq(X0,X2) )
      & ( ( lesseq(X1,X2)
          & lesseq(X0,X2) )
        | ~ ub(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ( ub(X0,X1,X2)
        | ~ lesseq(X1,X2)
        | ~ lesseq(X0,X2) )
      & ( ( lesseq(X1,X2)
          & lesseq(X0,X2) )
        | ~ ub(X0,X1,X2) ) ),
    inference(flattening,[],[f29]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( model_max(X0,X1,X2)
        | ~ lesseq(max(X0,X1),X2) )
      & ( lesseq(max(X0,X1),X2)
        | ~ model_max(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ( model_ub(X0,X1,X2)
        | ! [X3] :
            ( ~ lesseq(X3,X2)
            | ~ ub(X0,X1,X3) ) )
      & ( ? [X3] :
            ( lesseq(X3,X2)
            & ub(X0,X1,X3) )
        | ~ model_ub(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ( model_ub(X0,X1,X2)
        | ! [X3] :
            ( ~ lesseq(X3,X2)
            | ~ ub(X0,X1,X3) ) )
      & ( ? [X4] :
            ( lesseq(X4,X2)
            & ub(X0,X1,X4) )
        | ~ model_ub(X0,X1,X2) ) ),
    inference(rectify,[],[f32]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( lesseq(X4,X2)
          & ub(X0,X1,X4) )
     => ( lesseq(sK0(X0,X1,X2),X2)
        & ub(X0,X1,sK0(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ( model_ub(X0,X1,X2)
        | ! [X3] :
            ( ~ lesseq(X3,X2)
            | ~ ub(X0,X1,X3) ) )
      & ( ( lesseq(sK0(X0,X1,X2),X2)
          & ub(X0,X1,sK0(X0,X1,X2)) )
        | ~ model_ub(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f33,f34]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ( minsol_model_max(X0,X1,X2)
        | ? [X3] :
            ( ~ lesseq(X2,X3)
            & model_max(X0,X1,X3) )
        | ~ model_max(X0,X1,X2) )
      & ( ( ! [X3] :
              ( lesseq(X2,X3)
              | ~ model_max(X0,X1,X3) )
          & model_max(X0,X1,X2) )
        | ~ minsol_model_max(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f24]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ( minsol_model_max(X0,X1,X2)
        | ? [X3] :
            ( ~ lesseq(X2,X3)
            & model_max(X0,X1,X3) )
        | ~ model_max(X0,X1,X2) )
      & ( ( ! [X3] :
              ( lesseq(X2,X3)
              | ~ model_max(X0,X1,X3) )
          & model_max(X0,X1,X2) )
        | ~ minsol_model_max(X0,X1,X2) ) ),
    inference(flattening,[],[f36]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ( minsol_model_max(X0,X1,X2)
        | ? [X3] :
            ( ~ lesseq(X2,X3)
            & model_max(X0,X1,X3) )
        | ~ model_max(X0,X1,X2) )
      & ( ( ! [X4] :
              ( lesseq(X2,X4)
              | ~ model_max(X0,X1,X4) )
          & model_max(X0,X1,X2) )
        | ~ minsol_model_max(X0,X1,X2) ) ),
    inference(rectify,[],[f37]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ lesseq(X2,X3)
          & model_max(X0,X1,X3) )
     => ( ~ lesseq(X2,sK1(X0,X1,X2))
        & model_max(X0,X1,sK1(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ( minsol_model_max(X0,X1,X2)
        | ( ~ lesseq(X2,sK1(X0,X1,X2))
          & model_max(X0,X1,sK1(X0,X1,X2)) )
        | ~ model_max(X0,X1,X2) )
      & ( ( ! [X4] :
              ( lesseq(X2,X4)
              | ~ model_max(X0,X1,X4) )
          & model_max(X0,X1,X2) )
        | ~ minsol_model_max(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f38,f39]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( ( minsol_model_ub(X0,X1,X2)
        | ? [X3] :
            ( ~ lesseq(X2,X3)
            & model_ub(X0,X1,X3) )
        | ~ model_ub(X0,X1,X2) )
      & ( ( ! [X3] :
              ( lesseq(X2,X3)
              | ~ model_ub(X0,X1,X3) )
          & model_ub(X0,X1,X2) )
        | ~ minsol_model_ub(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ( minsol_model_ub(X0,X1,X2)
        | ? [X3] :
            ( ~ lesseq(X2,X3)
            & model_ub(X0,X1,X3) )
        | ~ model_ub(X0,X1,X2) )
      & ( ( ! [X3] :
              ( lesseq(X2,X3)
              | ~ model_ub(X0,X1,X3) )
          & model_ub(X0,X1,X2) )
        | ~ minsol_model_ub(X0,X1,X2) ) ),
    inference(flattening,[],[f41]) ).

fof(f43,plain,
    ! [X0,X1,X2] :
      ( ( minsol_model_ub(X0,X1,X2)
        | ? [X3] :
            ( ~ lesseq(X2,X3)
            & model_ub(X0,X1,X3) )
        | ~ model_ub(X0,X1,X2) )
      & ( ( ! [X4] :
              ( lesseq(X2,X4)
              | ~ model_ub(X0,X1,X4) )
          & model_ub(X0,X1,X2) )
        | ~ minsol_model_ub(X0,X1,X2) ) ),
    inference(rectify,[],[f42]) ).

fof(f44,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ lesseq(X2,X3)
          & model_ub(X0,X1,X3) )
     => ( ~ lesseq(X2,sK2(X0,X1,X2))
        & model_ub(X0,X1,sK2(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( ( minsol_model_ub(X0,X1,X2)
        | ( ~ lesseq(X2,sK2(X0,X1,X2))
          & model_ub(X0,X1,sK2(X0,X1,X2)) )
        | ~ model_ub(X0,X1,X2) )
      & ( ( ! [X4] :
              ( lesseq(X2,X4)
              | ~ model_ub(X0,X1,X4) )
          & model_ub(X0,X1,X2) )
        | ~ minsol_model_ub(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f43,f44]) ).

fof(f46,plain,
    ? [X0,X1,X2] :
      ( ( ~ minsol_model_max(X0,X1,X2)
        | ~ minsol_model_ub(X0,X1,X2) )
      & ( minsol_model_max(X0,X1,X2)
        | minsol_model_ub(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f47,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ minsol_model_max(X0,X1,X2)
          | ~ minsol_model_ub(X0,X1,X2) )
        & ( minsol_model_max(X0,X1,X2)
          | minsol_model_ub(X0,X1,X2) ) )
   => ( ( ~ minsol_model_max(sK3,sK4,sK5)
        | ~ minsol_model_ub(sK3,sK4,sK5) )
      & ( minsol_model_max(sK3,sK4,sK5)
        | minsol_model_ub(sK3,sK4,sK5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ( ( ~ minsol_model_max(sK3,sK4,sK5)
      | ~ minsol_model_ub(sK3,sK4,sK5) )
    & ( minsol_model_max(sK3,sK4,sK5)
      | minsol_model_ub(sK3,sK4,sK5) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f46,f47]) ).

fof(f49,plain,
    ! [X0] : lesseq(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( lesseq(X0,X2)
      | ~ lesseq(X1,X2)
      | ~ lesseq(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ lesseq(X1,X0)
      | ~ lesseq(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( lesseq(X1,X0)
      | lesseq(X0,X1) ),
    inference(cnf_transformation,[],[f4]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( lesseq(X0,X1)
      | ~ lesseq(summation(X0),summation(X1)) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ lesseq(X1,X0)
      | max(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f7]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ lesseq(X0,X1)
      | max(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f8]) ).

fof(f59,plain,
    ! [X2,X0,X1] :
      ( lesseq(X0,X2)
      | ~ ub(X0,X1,X2) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( lesseq(X1,X2)
      | ~ ub(X0,X1,X2) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f61,plain,
    ! [X2,X0,X1] :
      ( ub(X0,X1,X2)
      | ~ lesseq(X1,X2)
      | ~ lesseq(X0,X2) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f62,plain,
    ! [X2,X0,X1] :
      ( lesseq(max(X0,X1),X2)
      | ~ model_max(X0,X1,X2) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f63,plain,
    ! [X2,X0,X1] :
      ( model_max(X0,X1,X2)
      | ~ lesseq(max(X0,X1),X2) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( ub(X0,X1,sK0(X0,X1,X2))
      | ~ model_ub(X0,X1,X2) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f65,plain,
    ! [X2,X0,X1] :
      ( lesseq(sK0(X0,X1,X2),X2)
      | ~ model_ub(X0,X1,X2) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f66,plain,
    ! [X2,X3,X0,X1] :
      ( model_ub(X0,X1,X2)
      | ~ lesseq(X3,X2)
      | ~ ub(X0,X1,X3) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f67,plain,
    ! [X2,X0,X1] :
      ( model_max(X0,X1,X2)
      | ~ minsol_model_max(X0,X1,X2) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f68,plain,
    ! [X2,X0,X1,X4] :
      ( lesseq(X2,X4)
      | ~ model_max(X0,X1,X4)
      | ~ minsol_model_max(X0,X1,X2) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f69,plain,
    ! [X2,X0,X1] :
      ( minsol_model_max(X0,X1,X2)
      | model_max(X0,X1,sK1(X0,X1,X2))
      | ~ model_max(X0,X1,X2) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f70,plain,
    ! [X2,X0,X1] :
      ( minsol_model_max(X0,X1,X2)
      | ~ lesseq(X2,sK1(X0,X1,X2))
      | ~ model_max(X0,X1,X2) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f71,plain,
    ! [X2,X0,X1] :
      ( model_ub(X0,X1,X2)
      | ~ minsol_model_ub(X0,X1,X2) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f72,plain,
    ! [X2,X0,X1,X4] :
      ( lesseq(X2,X4)
      | ~ model_ub(X0,X1,X4)
      | ~ minsol_model_ub(X0,X1,X2) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f73,plain,
    ! [X2,X0,X1] :
      ( minsol_model_ub(X0,X1,X2)
      | model_ub(X0,X1,sK2(X0,X1,X2))
      | ~ model_ub(X0,X1,X2) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f74,plain,
    ! [X2,X0,X1] :
      ( minsol_model_ub(X0,X1,X2)
      | ~ lesseq(X2,sK2(X0,X1,X2))
      | ~ model_ub(X0,X1,X2) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f75,plain,
    ( minsol_model_max(sK3,sK4,sK5)
    | minsol_model_ub(sK3,sK4,sK5) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f76,plain,
    ( ~ minsol_model_max(sK3,sK4,sK5)
    | ~ minsol_model_ub(sK3,sK4,sK5) ),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_49,plain,
    lesseq(X0,X0),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_50,plain,
    ( ~ lesseq(X0,X1)
    | ~ lesseq(X1,X2)
    | lesseq(X0,X2) ),
    inference(cnf_transformation,[],[f50]) ).

cnf(c_51,plain,
    ( ~ lesseq(X0,X1)
    | ~ lesseq(X1,X0)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_52,plain,
    ( lesseq(X0,X1)
    | lesseq(X1,X0) ),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_55,plain,
    ( ~ lesseq(summation(X0),summation(X1))
    | lesseq(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_57,plain,
    ( ~ lesseq(X0,X1)
    | max(X1,X0) = X1 ),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_58,plain,
    ( ~ lesseq(X0,X1)
    | max(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f58]) ).

cnf(c_59,plain,
    ( ~ lesseq(X0,X1)
    | ~ lesseq(X2,X1)
    | ub(X0,X2,X1) ),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_60,plain,
    ( ~ ub(X0,X1,X2)
    | lesseq(X1,X2) ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_61,plain,
    ( ~ ub(X0,X1,X2)
    | lesseq(X0,X2) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_62,plain,
    ( ~ lesseq(max(X0,X1),X2)
    | model_max(X0,X1,X2) ),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_63,plain,
    ( ~ model_max(X0,X1,X2)
    | lesseq(max(X0,X1),X2) ),
    inference(cnf_transformation,[],[f62]) ).

cnf(c_64,plain,
    ( ~ ub(X0,X1,X2)
    | ~ lesseq(X2,X3)
    | model_ub(X0,X1,X3) ),
    inference(cnf_transformation,[],[f66]) ).

cnf(c_65,plain,
    ( ~ model_ub(X0,X1,X2)
    | lesseq(sK0(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_66,plain,
    ( ~ model_ub(X0,X1,X2)
    | ub(X0,X1,sK0(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f64]) ).

cnf(c_67,plain,
    ( ~ lesseq(X0,sK1(X1,X2,X0))
    | ~ model_max(X1,X2,X0)
    | minsol_model_max(X1,X2,X0) ),
    inference(cnf_transformation,[],[f70]) ).

cnf(c_68,plain,
    ( ~ model_max(X0,X1,X2)
    | model_max(X0,X1,sK1(X0,X1,X2))
    | minsol_model_max(X0,X1,X2) ),
    inference(cnf_transformation,[],[f69]) ).

cnf(c_69,plain,
    ( ~ model_max(X0,X1,X2)
    | ~ minsol_model_max(X0,X1,X3)
    | lesseq(X3,X2) ),
    inference(cnf_transformation,[],[f68]) ).

cnf(c_70,plain,
    ( ~ minsol_model_max(X0,X1,X2)
    | model_max(X0,X1,X2) ),
    inference(cnf_transformation,[],[f67]) ).

cnf(c_71,plain,
    ( ~ lesseq(X0,sK2(X1,X2,X0))
    | ~ model_ub(X1,X2,X0)
    | minsol_model_ub(X1,X2,X0) ),
    inference(cnf_transformation,[],[f74]) ).

cnf(c_72,plain,
    ( ~ model_ub(X0,X1,X2)
    | model_ub(X0,X1,sK2(X0,X1,X2))
    | minsol_model_ub(X0,X1,X2) ),
    inference(cnf_transformation,[],[f73]) ).

cnf(c_73,plain,
    ( ~ model_ub(X0,X1,X2)
    | ~ minsol_model_ub(X0,X1,X3)
    | lesseq(X3,X2) ),
    inference(cnf_transformation,[],[f72]) ).

cnf(c_74,plain,
    ( ~ minsol_model_ub(X0,X1,X2)
    | model_ub(X0,X1,X2) ),
    inference(cnf_transformation,[],[f71]) ).

cnf(c_75,negated_conjecture,
    ( ~ minsol_model_max(sK3,sK4,sK5)
    | ~ minsol_model_ub(sK3,sK4,sK5) ),
    inference(cnf_transformation,[],[f76]) ).

cnf(c_76,negated_conjecture,
    ( minsol_model_max(sK3,sK4,sK5)
    | minsol_model_ub(sK3,sK4,sK5) ),
    inference(cnf_transformation,[],[f75]) ).

cnf(c_77,plain,
    lesseq(sK3,sK3),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_88,plain,
    ( ~ lesseq(sK3,sK3)
    | sK3 = sK3 ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_103,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_105,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_106,plain,
    ( X0 != X1
    | X2 != X3
    | ~ lesseq(X1,X3)
    | lesseq(X0,X2) ),
    theory(equality) ).

cnf(c_109,plain,
    ( X0 != X1
    | ~ model_ub(X2,X3,X1)
    | model_ub(X2,X3,X0) ),
    theory(equality) ).

cnf(c_110,plain,
    ( X0 != X1
    | X2 != X3
    | X4 != X5
    | ~ minsol_model_max(X1,X3,X5)
    | minsol_model_max(X0,X2,X4) ),
    theory(equality) ).

cnf(c_111,plain,
    ( X0 != X1
    | X2 != X3
    | X4 != X5
    | ~ minsol_model_ub(X1,X3,X5)
    | minsol_model_ub(X0,X2,X4) ),
    theory(equality) ).

cnf(c_119,plain,
    ( ~ lesseq(sK5,sK2(sK3,sK4,sK5))
    | ~ model_ub(sK3,sK4,sK5)
    | minsol_model_ub(sK3,sK4,sK5) ),
    inference(instantiation,[status(thm)],[c_71]) ).

cnf(c_120,plain,
    ( ~ model_ub(sK3,sK4,sK5)
    | model_ub(sK3,sK4,sK2(sK3,sK4,sK5))
    | minsol_model_ub(sK3,sK4,sK5) ),
    inference(instantiation,[status(thm)],[c_72]) ).

cnf(c_125,plain,
    ( ~ lesseq(max(X0,X1),max(X0,X1))
    | model_max(X0,X1,max(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_126,plain,
    lesseq(max(X0,X1),max(X0,X1)),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_131,plain,
    ( ~ lesseq(max(X0,X1),X2)
    | ~ lesseq(X2,X3)
    | lesseq(max(X0,X1),X3) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_143,plain,
    ( max(X0,X1) != X2
    | X3 != X4
    | ~ lesseq(X2,X4)
    | lesseq(max(X0,X1),X3) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_145,plain,
    ( ~ model_max(sK3,sK4,sK5)
    | lesseq(max(sK3,sK4),sK5) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_146,plain,
    ( ~ model_max(sK3,sK4,sK5)
    | model_max(sK3,sK4,sK1(sK3,sK4,sK5))
    | minsol_model_max(sK3,sK4,sK5) ),
    inference(instantiation,[status(thm)],[c_68]) ).

cnf(c_147,plain,
    ( ~ lesseq(sK5,sK1(sK3,sK4,sK5))
    | ~ model_max(sK3,sK4,sK5)
    | minsol_model_max(sK3,sK4,sK5) ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_154,plain,
    ( ~ lesseq(X0,sK5)
    | ~ lesseq(sK5,X0)
    | sK5 = X0 ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_155,plain,
    ( ~ lesseq(sK3,sK5)
    | ~ lesseq(sK5,sK3)
    | sK5 = sK3 ),
    inference(instantiation,[status(thm)],[c_154]) ).

cnf(c_157,plain,
    sK5 = sK5,
    inference(instantiation,[status(thm)],[c_103]) ).

cnf(c_159,plain,
    ( X0 != X1
    | sK5 != X1
    | sK5 = X0 ),
    inference(instantiation,[status(thm)],[c_105]) ).

cnf(c_161,plain,
    ( ~ lesseq(max(sK3,sK4),sK5)
    | model_max(sK3,sK4,sK5) ),
    inference(instantiation,[status(thm)],[c_62]) ).

cnf(c_178,plain,
    ( ~ lesseq(summation(sK5),summation(X0))
    | lesseq(sK5,X0) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_180,plain,
    ( X0 != X1
    | sK5 != X2
    | ~ lesseq(X2,X1)
    | lesseq(sK5,X0) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_181,plain,
    ( ~ lesseq(X0,X1)
    | ~ lesseq(sK5,X0)
    | lesseq(sK5,X1) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_184,plain,
    ( sK3 != sK3
    | sK5 != sK3
    | ~ lesseq(sK3,sK3)
    | lesseq(sK5,sK3) ),
    inference(instantiation,[status(thm)],[c_180]) ).

cnf(c_191,plain,
    ( ~ model_ub(X0,X1,X2)
    | ~ minsol_model_ub(X0,X1,sK5)
    | lesseq(sK5,X2) ),
    inference(instantiation,[status(thm)],[c_73]) ).

cnf(c_192,plain,
    ( ~ model_max(X0,X1,X2)
    | ~ minsol_model_max(X0,X1,sK5)
    | lesseq(sK5,X2) ),
    inference(instantiation,[status(thm)],[c_69]) ).

cnf(c_198,plain,
    sK4 = sK4,
    inference(instantiation,[status(thm)],[c_103]) ).

cnf(c_199,plain,
    ( X0 != X1
    | sK4 != X1
    | sK4 = X0 ),
    inference(instantiation,[status(thm)],[c_105]) ).

cnf(c_218,plain,
    ( max(sK3,sK4) != X0
    | sK5 != X1
    | ~ lesseq(X0,X1)
    | lesseq(max(sK3,sK4),sK5) ),
    inference(instantiation,[status(thm)],[c_143]) ).

cnf(c_237,plain,
    ( ~ lesseq(summation(sK5),summation(sK5))
    | lesseq(sK5,sK5) ),
    inference(instantiation,[status(thm)],[c_178]) ).

cnf(c_238,plain,
    lesseq(summation(sK5),summation(sK5)),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_276,plain,
    ( X0 != X1
    | sK5 != X1
    | X0 = sK5 ),
    inference(instantiation,[status(thm)],[c_105]) ).

cnf(c_316,plain,
    ( model_ub(sK3,sK4,sK5)
    | minsol_model_max(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_74,c_76]) ).

cnf(c_318,plain,
    ( ~ lesseq(summation(sK4),summation(X0))
    | lesseq(sK4,X0) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_320,plain,
    ( X0 != X1
    | sK4 != X2
    | ~ lesseq(X2,X1)
    | lesseq(sK4,X0) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_329,plain,
    ( lesseq(X0,sK4)
    | lesseq(sK4,X0) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_330,plain,
    ( lesseq(sK3,sK4)
    | lesseq(sK4,sK3) ),
    inference(instantiation,[status(thm)],[c_329]) ).

cnf(c_374,plain,
    ( model_max(sK3,sK4,sK5)
    | model_ub(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_70,c_316]) ).

cnf(c_391,plain,
    ( ~ model_ub(sK3,sK4,X0)
    | minsol_model_max(sK3,sK4,sK5)
    | lesseq(sK5,X0) ),
    inference(resolution,[status(thm)],[c_73,c_76]) ).

cnf(c_392,plain,
    ( ~ model_ub(sK3,sK4,sK3)
    | minsol_model_max(sK3,sK4,sK5)
    | lesseq(sK5,sK3) ),
    inference(instantiation,[status(thm)],[c_391]) ).

cnf(c_397,plain,
    ( X0 != sK4
    | sK4 != sK4
    | sK4 = X0 ),
    inference(instantiation,[status(thm)],[c_199]) ).

cnf(c_403,plain,
    ( X0 != X1
    | sK5 != sK5
    | ~ lesseq(sK5,X1)
    | lesseq(sK5,X0) ),
    inference(instantiation,[status(thm)],[c_180]) ).

cnf(c_415,plain,
    ( ~ model_ub(sK3,sK4,X0)
    | ~ minsol_model_ub(sK3,sK4,sK5)
    | lesseq(sK5,X0) ),
    inference(instantiation,[status(thm)],[c_191]) ).

cnf(c_500,plain,
    ( ~ ub(sK3,sK4,X0)
    | ~ lesseq(X0,X1)
    | model_ub(sK3,sK4,X1) ),
    inference(instantiation,[status(thm)],[c_64]) ).

cnf(c_501,plain,
    ( ~ ub(sK3,sK4,sK3)
    | ~ lesseq(sK3,sK3)
    | model_ub(sK3,sK4,sK3) ),
    inference(instantiation,[status(thm)],[c_500]) ).

cnf(c_504,plain,
    ( X0 != X1
    | ~ model_ub(sK3,sK4,X1)
    | model_ub(sK3,sK4,X0) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_511,plain,
    ( ~ model_ub(sK3,sK4,X0)
    | lesseq(sK5,sK2(sK3,sK4,X0))
    | minsol_model_ub(sK3,sK4,X0)
    | minsol_model_max(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_72,c_391]) ).

cnf(c_527,plain,
    ( ~ lesseq(max(X0,X1),sK5)
    | ~ lesseq(sK5,max(X0,X1))
    | sK5 = max(X0,X1) ),
    inference(instantiation,[status(thm)],[c_154]) ).

cnf(c_567,plain,
    ( X0 != sK3
    | X1 != sK4
    | X2 != sK5
    | minsol_model_max(X0,X1,X2)
    | model_ub(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_110,c_316]) ).

cnf(c_579,plain,
    ( X0 != sK3
    | X1 != sK4
    | X2 != sK5
    | model_max(X0,X1,X2)
    | model_ub(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_567,c_70]) ).

cnf(c_585,plain,
    ( ~ lesseq(X0,sK1(sK3,sK4,sK5))
    | ~ lesseq(sK5,X0)
    | lesseq(sK5,sK1(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_181]) ).

cnf(c_618,plain,
    ( ~ lesseq(sK4,sK5)
    | ~ lesseq(sK5,sK4)
    | sK5 = sK4 ),
    inference(instantiation,[status(thm)],[c_154]) ).

cnf(c_728,plain,
    ( ~ lesseq(summation(sK4),summation(sK4))
    | lesseq(sK4,sK4) ),
    inference(instantiation,[status(thm)],[c_318]) ).

cnf(c_729,plain,
    lesseq(summation(sK4),summation(sK4)),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_780,plain,
    ( max(X0,sK4) != sK4
    | sK4 != sK4
    | sK4 = max(X0,sK4) ),
    inference(instantiation,[status(thm)],[c_397]) ).

cnf(c_781,plain,
    ( ~ lesseq(X0,sK4)
    | max(X0,sK4) = sK4 ),
    inference(instantiation,[status(thm)],[c_58]) ).

cnf(c_782,plain,
    ( max(sK3,sK4) != sK4
    | sK4 != sK4
    | sK4 = max(sK3,sK4) ),
    inference(instantiation,[status(thm)],[c_780]) ).

cnf(c_783,plain,
    ( ~ lesseq(sK3,sK4)
    | max(sK3,sK4) = sK4 ),
    inference(instantiation,[status(thm)],[c_781]) ).

cnf(c_809,plain,
    ( ~ model_max(sK3,sK4,X0)
    | model_ub(sK3,sK4,sK5)
    | lesseq(sK5,X0) ),
    inference(resolution,[status(thm)],[c_69,c_316]) ).

cnf(c_873,plain,
    ( ~ lesseq(X0,X1)
    | ~ lesseq(sK4,X1)
    | ub(X0,sK4,X1) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_874,plain,
    ( ~ lesseq(sK3,sK3)
    | ~ lesseq(sK4,sK3)
    | ub(sK3,sK4,sK3) ),
    inference(instantiation,[status(thm)],[c_873]) ).

cnf(c_898,plain,
    ( lesseq(summation(X0),summation(X1))
    | lesseq(X1,X0) ),
    inference(resolution,[status(thm)],[c_55,c_52]) ).

cnf(c_1001,plain,
    model_max(X0,X1,max(X0,X1)),
    inference(resolution,[status(thm)],[c_62,c_49]) ).

cnf(c_1235,plain,
    ( X0 != X1
    | sK4 != X2
    | ~ lesseq(X1,X2)
    | lesseq(X0,sK4) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_1321,plain,
    ( X0 != sK5
    | sK5 != sK5
    | ~ lesseq(sK5,sK5)
    | lesseq(sK5,X0) ),
    inference(instantiation,[status(thm)],[c_403]) ).

cnf(c_1378,plain,
    ( ~ model_max(X0,sK4,X1)
    | ~ minsol_model_max(X0,sK4,sK5)
    | lesseq(sK5,X1) ),
    inference(instantiation,[status(thm)],[c_192]) ).

cnf(c_1519,plain,
    ( sK4 != X0
    | sK5 != X0
    | sK5 = sK4 ),
    inference(instantiation,[status(thm)],[c_159]) ).

cnf(c_1520,plain,
    ( sK4 != sK4
    | sK5 != sK4
    | sK4 = sK5 ),
    inference(instantiation,[status(thm)],[c_397]) ).

cnf(c_1626,plain,
    ( ~ lesseq(max(sK3,sK4),max(sK3,sK4))
    | model_max(sK3,sK4,max(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_125]) ).

cnf(c_1681,plain,
    ( sK2(sK3,sK4,sK5) != X0
    | sK5 != X1
    | ~ lesseq(X1,X0)
    | lesseq(sK5,sK2(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_180]) ).

cnf(c_1737,plain,
    ( ~ lesseq(max(sK3,sK4),sK5)
    | ~ lesseq(sK5,max(sK3,sK4))
    | sK5 = max(sK3,sK4) ),
    inference(instantiation,[status(thm)],[c_527]) ).

cnf(c_1756,plain,
    ( ~ model_max(sK3,sK4,X0)
    | lesseq(max(sK3,sK4),X0) ),
    inference(instantiation,[status(thm)],[c_63]) ).

cnf(c_1764,plain,
    ( ~ lesseq(max(sK3,sK4),X0)
    | ~ lesseq(X0,X1)
    | lesseq(max(sK3,sK4),X1) ),
    inference(instantiation,[status(thm)],[c_131]) ).

cnf(c_1890,plain,
    ( ~ lesseq(sK4,sK3)
    | max(sK3,sK4) = sK3 ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_1935,plain,
    ( max(sK3,sK4) != X0
    | sK5 != X0
    | max(sK3,sK4) = sK5 ),
    inference(instantiation,[status(thm)],[c_276]) ).

cnf(c_1937,plain,
    ( max(sK3,sK4) != sK3
    | sK5 != sK3
    | max(sK3,sK4) = sK5 ),
    inference(instantiation,[status(thm)],[c_1935]) ).

cnf(c_2200,plain,
    ( ~ lesseq(X0,X1)
    | lesseq(X0,X2)
    | lesseq(X2,X1) ),
    inference(resolution,[status(thm)],[c_50,c_52]) ).

cnf(c_2203,plain,
    ( ~ lesseq(X0,max(X1,X2))
    | ~ model_max(X1,X2,X3)
    | lesseq(X0,X3) ),
    inference(resolution,[status(thm)],[c_50,c_63]) ).

cnf(c_2279,plain,
    ( X0 != X1
    | sK4 != max(X2,sK4)
    | ~ lesseq(max(X2,sK4),X1)
    | lesseq(sK4,X0) ),
    inference(instantiation,[status(thm)],[c_320]) ).

cnf(c_2280,plain,
    ( sK3 != sK3
    | sK4 != max(sK3,sK4)
    | ~ lesseq(max(sK3,sK4),sK3)
    | lesseq(sK4,sK3) ),
    inference(instantiation,[status(thm)],[c_2279]) ).

cnf(c_2295,plain,
    ( max(sK3,sK4) != sK4
    | sK5 != X0
    | ~ lesseq(sK4,X0)
    | lesseq(max(sK3,sK4),sK5) ),
    inference(instantiation,[status(thm)],[c_218]) ).

cnf(c_2330,plain,
    ( ~ lesseq(X0,sK0(X1,X2,X3))
    | ~ model_ub(X1,X2,X3)
    | lesseq(X0,X3) ),
    inference(resolution,[status(thm)],[c_65,c_50]) ).

cnf(c_2797,plain,
    ( ~ lesseq(X0,sK4)
    | ~ lesseq(sK4,sK4)
    | ub(X0,sK4,sK4) ),
    inference(instantiation,[status(thm)],[c_873]) ).

cnf(c_2798,plain,
    ( ~ lesseq(sK3,sK4)
    | ~ lesseq(sK4,sK4)
    | ub(sK3,sK4,sK4) ),
    inference(instantiation,[status(thm)],[c_2797]) ).

cnf(c_3554,plain,
    ( ~ ub(sK3,sK4,X0)
    | ~ lesseq(X0,sK4)
    | model_ub(sK3,sK4,sK4) ),
    inference(instantiation,[status(thm)],[c_500]) ).

cnf(c_4093,plain,
    ( ~ model_ub(sK3,sK4,sK4)
    | ~ minsol_model_ub(sK3,sK4,sK5)
    | lesseq(sK5,sK4) ),
    inference(instantiation,[status(thm)],[c_415]) ).

cnf(c_4241,plain,
    lesseq(max(sK3,sK4),max(sK3,sK4)),
    inference(instantiation,[status(thm)],[c_126]) ).

cnf(c_4742,plain,
    ( ~ model_ub(X0,X1,X2)
    | lesseq(X1,sK0(X0,X1,X2)) ),
    inference(resolution,[status(thm)],[c_66,c_60]) ).

cnf(c_4743,plain,
    ( ~ model_ub(X0,X1,X2)
    | lesseq(X0,sK0(X0,X1,X2)) ),
    inference(resolution,[status(thm)],[c_66,c_61]) ).

cnf(c_5180,plain,
    ( max(X0,sK4) != X1
    | X2 != X1
    | X2 = max(X0,sK4) ),
    inference(instantiation,[status(thm)],[c_105]) ).

cnf(c_5181,plain,
    ( max(sK3,sK4) != sK3
    | sK3 != sK3
    | sK3 = max(sK3,sK4) ),
    inference(instantiation,[status(thm)],[c_5180]) ).

cnf(c_6040,plain,
    ( max(sK3,sK4) != X0
    | sK5 != sK5
    | ~ lesseq(X0,sK5)
    | lesseq(max(sK3,sK4),sK5) ),
    inference(instantiation,[status(thm)],[c_218]) ).

cnf(c_6041,plain,
    ( max(sK3,sK4) != sK3
    | sK5 != sK5
    | ~ lesseq(sK3,sK5)
    | lesseq(max(sK3,sK4),sK5) ),
    inference(instantiation,[status(thm)],[c_6040]) ).

cnf(c_6622,plain,
    ( max(sK3,sK4) != sK4
    | sK5 != sK5
    | ~ lesseq(sK4,sK5)
    | lesseq(max(sK3,sK4),sK5) ),
    inference(instantiation,[status(thm)],[c_2295]) ).

cnf(c_7164,plain,
    ( ~ lesseq(X0,X1)
    | ~ lesseq(X1,X3)
    | ~ lesseq(X2,X1)
    | model_ub(X0,X2,X3) ),
    inference(resolution,[status(thm)],[c_64,c_59]) ).

cnf(c_7396,plain,
    ( X0 != sK5
    | model_ub(sK3,sK4,X0)
    | model_max(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_109,c_374]) ).

cnf(c_7409,plain,
    ( X0 != sK5
    | model_max(sK3,sK4,sK5)
    | minsol_model_max(sK3,sK4,sK5)
    | lesseq(sK5,X0) ),
    inference(resolution,[status(thm)],[c_7396,c_391]) ).

cnf(c_7412,plain,
    ( X0 != sK5
    | lesseq(sK5,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_7409,c_157,c_237,c_238,c_1321]) ).

cnf(c_7424,plain,
    ( ~ lesseq(X0,sK5)
    | lesseq(sK5,max(sK5,X0)) ),
    inference(resolution,[status(thm)],[c_7412,c_57]) ).

cnf(c_7688,plain,
    ( sK5 != X0
    | ~ model_ub(sK3,sK4,X0)
    | model_ub(sK3,sK4,sK5) ),
    inference(instantiation,[status(thm)],[c_504]) ).

cnf(c_7689,plain,
    ( sK5 != sK3
    | ~ model_ub(sK3,sK4,sK3)
    | model_ub(sK3,sK4,sK5) ),
    inference(instantiation,[status(thm)],[c_7688]) ).

cnf(c_7893,plain,
    ( sK4 != max(sK3,sK4)
    | sK5 != max(sK3,sK4)
    | sK5 = sK4 ),
    inference(instantiation,[status(thm)],[c_1519]) ).

cnf(c_7899,plain,
    ( X0 != max(sK3,sK4)
    | sK5 != max(sK3,sK4)
    | sK5 = X0 ),
    inference(instantiation,[status(thm)],[c_159]) ).

cnf(c_7902,plain,
    ( sK3 != max(sK3,sK4)
    | sK5 != max(sK3,sK4)
    | sK5 = sK3 ),
    inference(instantiation,[status(thm)],[c_7899]) ).

cnf(c_8266,plain,
    ( ~ model_max(X0,sK4,max(X0,sK4))
    | ~ minsol_model_max(X0,sK4,sK5)
    | lesseq(sK5,max(X0,sK4)) ),
    inference(instantiation,[status(thm)],[c_1378]) ).

cnf(c_8268,plain,
    ( ~ model_max(sK3,sK4,max(sK3,sK4))
    | ~ minsol_model_max(sK3,sK4,sK5)
    | lesseq(sK5,max(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_8266]) ).

cnf(c_8624,plain,
    ( max(sK3,sK4) != sK5
    | sK5 != sK5
    | ~ lesseq(sK5,sK5)
    | lesseq(sK5,max(sK3,sK4)) ),
    inference(instantiation,[status(thm)],[c_1321]) ).

cnf(c_8774,plain,
    ( ~ model_max(sK3,sK4,sK1(sK3,sK4,sK5))
    | lesseq(max(sK3,sK4),sK1(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_1756]) ).

cnf(c_9123,plain,
    ( X0 != sK3
    | X1 != sK4
    | X2 != sK5
    | minsol_model_ub(X0,X1,X2)
    | minsol_model_max(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_111,c_76]) ).

cnf(c_9210,plain,
    ( ~ lesseq(max(X0,X1),sK1(sK3,sK4,sK5))
    | ~ lesseq(sK5,max(X0,X1))
    | lesseq(sK5,sK1(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_585]) ).

cnf(c_9234,plain,
    ( lesseq(sK5,max(sK3,sK4))
    | model_ub(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_1001,c_809]) ).

cnf(c_9268,plain,
    ( X0 != sK3
    | X1 != sK4
    | X2 != sK5
    | ~ model_ub(X0,X1,X3)
    | minsol_model_max(sK3,sK4,sK5)
    | lesseq(X2,X3) ),
    inference(resolution,[status(thm)],[c_9123,c_73]) ).

cnf(c_9269,plain,
    ( X0 != sK3
    | X1 != sK4
    | X2 != sK5
    | model_ub(X0,X1,X2)
    | minsol_model_max(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_9123,c_74]) ).

cnf(c_9323,plain,
    ( X0 != sK3
    | X1 != sK4
    | X2 != sK5
    | model_ub(X0,X1,X2)
    | model_max(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_9269,c_70]) ).

cnf(c_9510,plain,
    ( ~ lesseq(max(sK3,sK4),sK5)
    | ~ lesseq(sK5,X0)
    | lesseq(max(sK3,sK4),X0) ),
    inference(instantiation,[status(thm)],[c_1764]) ).

cnf(c_9511,plain,
    ( ~ lesseq(max(sK3,sK4),sK5)
    | ~ lesseq(sK5,sK3)
    | lesseq(max(sK3,sK4),sK3) ),
    inference(instantiation,[status(thm)],[c_9510]) ).

cnf(c_10382,plain,
    ( sK5 != sK4
    | ~ model_ub(sK3,sK4,sK4)
    | model_ub(sK3,sK4,sK5) ),
    inference(instantiation,[status(thm)],[c_7688]) ).

cnf(c_10390,plain,
    ( max(sK3,sK4) != sK4
    | sK5 != sK4
    | max(sK3,sK4) = sK5 ),
    inference(instantiation,[status(thm)],[c_1935]) ).

cnf(c_10453,plain,
    ( X0 != X1
    | sK4 != sK5
    | ~ lesseq(X1,sK5)
    | lesseq(X0,sK4) ),
    inference(instantiation,[status(thm)],[c_1235]) ).

cnf(c_10456,plain,
    ( sK3 != sK3
    | sK4 != sK5
    | ~ lesseq(sK3,sK5)
    | lesseq(sK3,sK4) ),
    inference(instantiation,[status(thm)],[c_10453]) ).

cnf(c_10615,plain,
    ( ~ ub(sK3,sK4,sK4)
    | ~ lesseq(sK4,sK4)
    | model_ub(sK3,sK4,sK4) ),
    inference(instantiation,[status(thm)],[c_3554]) ).

cnf(c_11780,plain,
    ( lesseq(summation(X0),X1)
    | lesseq(X1,summation(X2))
    | lesseq(X2,X0) ),
    inference(resolution,[status(thm)],[c_2200,c_898]) ).

cnf(c_12207,plain,
    ( ~ model_ub(X0,X1,sK2(X2,X3,X4))
    | lesseq(sK0(X0,X1,sK2(X2,X3,X4)),sK2(X2,X3,X4)) ),
    inference(instantiation,[status(thm)],[c_65]) ).

cnf(c_13454,plain,
    sK2(X0,X1,X2) = sK2(X0,X1,X2),
    inference(instantiation,[status(thm)],[c_103]) ).

cnf(c_14346,plain,
    ( ~ model_max(sK5,X0,X1)
    | ~ lesseq(X0,sK5)
    | lesseq(sK5,X1) ),
    inference(resolution,[status(thm)],[c_2203,c_7424]) ).

cnf(c_14415,plain,
    ( X0 != sK4
    | X1 != sK5
    | sK5 != sK3
    | ~ lesseq(X0,sK5)
    | model_ub(sK3,sK4,sK5)
    | lesseq(sK5,X1) ),
    inference(resolution,[status(thm)],[c_14346,c_579]) ).

cnf(c_15739,plain,
    ( model_ub(sK3,sK4,sK5)
    | sK5 != sK3 ),
    inference(global_subsumption_just,[status(thm)],[c_14415,c_77,c_88,c_145,c_184,c_198,c_330,c_374,c_501,c_728,c_729,c_782,c_783,c_874,c_1737,c_1890,c_2280,c_2798,c_5181,c_7689,c_7893,c_7902,c_9234,c_9511,c_10382,c_10615]) ).

cnf(c_15740,plain,
    ( sK5 != sK3
    | model_ub(sK3,sK4,sK5) ),
    inference(renaming,[status(thm)],[c_15739]) ).

cnf(c_15741,plain,
    model_ub(sK3,sK4,sK5),
    inference(global_subsumption_just,[status(thm)],[c_15740,c_77,c_88,c_145,c_198,c_330,c_374,c_728,c_729,c_782,c_783,c_1737,c_1890,c_2798,c_5181,c_7893,c_7902,c_9234,c_10382,c_10615,c_15740]) ).

cnf(c_16177,plain,
    ( ~ model_ub(X0,X1,X2)
    | lesseq(X1,X2) ),
    inference(resolution,[status(thm)],[c_2330,c_4742]) ).

cnf(c_16178,plain,
    ( ~ model_ub(X0,X1,X2)
    | lesseq(X0,X2) ),
    inference(resolution,[status(thm)],[c_2330,c_4743]) ).

cnf(c_19960,plain,
    ( ~ lesseq(sK2(sK3,sK4,X0),X1)
    | ~ lesseq(X2,sK2(sK3,sK4,X0))
    | ~ model_ub(sK3,sK4,X0)
    | model_ub(X2,sK5,X1)
    | minsol_model_ub(sK3,sK4,X0)
    | minsol_model_max(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_7164,c_511]) ).

cnf(c_21117,plain,
    ( ~ lesseq(sK2(sK3,sK4,X0),X1)
    | ~ model_ub(sK3,sK4,X0)
    | model_ub(sK5,sK5,X1)
    | minsol_model_ub(sK3,sK4,X0)
    | minsol_model_max(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_19960,c_511]) ).

cnf(c_28204,plain,
    ( X0 != sK4
    | X1 != sK5
    | X2 != sK3
    | model_max(sK3,sK4,sK5)
    | lesseq(X0,X1) ),
    inference(resolution,[status(thm)],[c_16177,c_9323]) ).

cnf(c_28208,plain,
    lesseq(sK4,sK5),
    inference(resolution,[status(thm)],[c_16177,c_15741]) ).

cnf(c_28957,plain,
    lesseq(sK3,sK5),
    inference(resolution,[status(thm)],[c_16178,c_15741]) ).

cnf(c_30941,plain,
    model_max(sK3,sK4,sK5),
    inference(global_subsumption_just,[status(thm)],[c_28204,c_157,c_161,c_330,c_783,c_1890,c_6041,c_6622,c_28208,c_28957]) ).

cnf(c_32221,plain,
    ( ~ model_ub(sK3,sK4,sK2(sK3,sK4,sK5))
    | lesseq(sK0(sK3,sK4,sK2(sK3,sK4,sK5)),sK2(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_12207]) ).

cnf(c_32624,plain,
    ( ~ model_ub(sK3,sK4,X0)
    | lesseq(X1,summation(sK2(sK3,sK4,X0)))
    | lesseq(summation(X2),X1)
    | model_ub(sK5,sK5,X2)
    | minsol_model_ub(sK3,sK4,X0)
    | minsol_model_max(sK3,sK4,sK5) ),
    inference(resolution,[status(thm)],[c_11780,c_21117]) ).

cnf(c_34410,plain,
    ( X0 != sK5
    | sK5 != sK3
    | sK5 != sK4
    | ~ model_ub(sK3,sK4,X1)
    | lesseq(X2,summation(sK2(sK3,sK4,X1)))
    | lesseq(summation(X3),X2)
    | minsol_model_ub(sK3,sK4,X1)
    | minsol_model_max(sK3,sK4,sK5)
    | lesseq(X0,X3) ),
    inference(resolution,[status(thm)],[c_32624,c_9268]) ).

cnf(c_34809,plain,
    ( ~ lesseq(max(sK3,sK4),sK1(sK3,sK4,sK5))
    | ~ lesseq(sK5,max(sK3,sK4))
    | lesseq(sK5,sK1(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_9210]) ).

cnf(c_35657,plain,
    ( minsol_model_max(sK3,sK4,sK5)
    | sK5 != sK4 ),
    inference(global_subsumption_just,[status(thm)],[c_34410,c_77,c_76,c_88,c_146,c_147,c_155,c_157,c_198,c_237,c_238,c_330,c_392,c_501,c_618,c_728,c_729,c_783,c_874,c_1520,c_1890,c_1937,c_2798,c_4093,c_8624,c_8774,c_10390,c_10456,c_10615,c_28208,c_28957,c_30941,c_34809]) ).

cnf(c_35658,plain,
    ( sK5 != sK4
    | minsol_model_max(sK3,sK4,sK5) ),
    inference(renaming,[status(thm)],[c_35657]) ).

cnf(c_35659,plain,
    minsol_model_max(sK3,sK4,sK5),
    inference(global_subsumption_just,[status(thm)],[c_35658,c_77,c_76,c_146,c_147,c_155,c_157,c_237,c_238,c_330,c_392,c_501,c_618,c_728,c_729,c_874,c_1890,c_1937,c_2798,c_4093,c_8624,c_8774,c_10615,c_28208,c_28957,c_30941,c_34809,c_35658]) ).

cnf(c_37526,plain,
    ( sK2(sK3,sK4,sK5) != sK2(sK3,sK4,sK5)
    | sK5 != X0
    | ~ lesseq(X0,sK2(sK3,sK4,sK5))
    | lesseq(sK5,sK2(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_1681]) ).

cnf(c_37527,plain,
    sK2(sK3,sK4,sK5) = sK2(sK3,sK4,sK5),
    inference(instantiation,[status(thm)],[c_13454]) ).

cnf(c_37528,plain,
    ( sK2(sK3,sK4,sK5) != sK2(sK3,sK4,sK5)
    | sK5 != sK3
    | ~ lesseq(sK3,sK2(sK3,sK4,sK5))
    | lesseq(sK5,sK2(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_37526]) ).

cnf(c_43084,plain,
    ( sK2(sK3,sK4,sK5) != X0
    | sK5 != X1
    | ~ lesseq(X1,X0)
    | lesseq(sK5,sK2(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_106]) ).

cnf(c_43135,plain,
    ( ~ lesseq(X0,sK2(sK3,sK4,sK5))
    | ~ lesseq(X1,X0)
    | lesseq(X1,sK2(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_43176,plain,
    ( sK2(sK3,sK4,sK5) != sK2(sK3,sK4,sK5)
    | sK5 != X0
    | ~ lesseq(X0,sK2(sK3,sK4,sK5))
    | lesseq(sK5,sK2(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_43084]) ).

cnf(c_44161,plain,
    ( ~ lesseq(sK0(sK3,sK4,sK2(sK3,sK4,sK5)),sK2(sK3,sK4,sK5))
    | ~ lesseq(X0,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
    | lesseq(X0,sK2(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_43135]) ).

cnf(c_44165,plain,
    ( ~ lesseq(sK0(sK3,sK4,sK2(sK3,sK4,sK5)),sK2(sK3,sK4,sK5))
    | ~ lesseq(sK3,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
    | lesseq(sK3,sK2(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_44161]) ).

cnf(c_48773,plain,
    ( ~ ub(X0,X1,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
    | lesseq(X0,sK0(sK3,sK4,sK2(sK3,sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_48777,plain,
    ( ~ ub(X0,X1,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
    | lesseq(X1,sK0(sK3,sK4,sK2(sK3,sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_48799,plain,
    ( ~ lesseq(sK0(sK3,sK4,sK2(sK3,sK4,sK5)),sK2(sK3,sK4,sK5))
    | ~ lesseq(sK4,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
    | lesseq(sK4,sK2(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_44161]) ).

cnf(c_49227,plain,
    ( ~ model_ub(sK3,sK4,sK2(sK3,sK4,sK5))
    | ub(sK3,sK4,sK0(sK3,sK4,sK2(sK3,sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_66]) ).

cnf(c_55967,plain,
    ( sK2(sK3,sK4,sK5) != sK2(sK3,sK4,sK5)
    | sK5 != sK4
    | ~ lesseq(sK4,sK2(sK3,sK4,sK5))
    | lesseq(sK5,sK2(sK3,sK4,sK5)) ),
    inference(instantiation,[status(thm)],[c_43176]) ).

cnf(c_60042,plain,
    ( ~ ub(sK3,sK4,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
    | lesseq(sK3,sK0(sK3,sK4,sK2(sK3,sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_48773]) ).

cnf(c_60047,plain,
    ( ~ ub(sK3,sK4,sK0(sK3,sK4,sK2(sK3,sK4,sK5)))
    | lesseq(sK4,sK0(sK3,sK4,sK2(sK3,sK4,sK5))) ),
    inference(instantiation,[status(thm)],[c_48777]) ).

cnf(c_60048,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_60047,c_60042,c_55967,c_49227,c_48799,c_44165,c_37527,c_37528,c_35659,c_32221,c_30941,c_15741,c_8268,c_7902,c_7893,c_5181,c_4241,c_1890,c_1737,c_1626,c_783,c_782,c_330,c_198,c_145,c_120,c_119,c_88,c_75,c_77]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : NUM859+1 : TPTP v8.1.2. Released v4.1.0.
% 0.09/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n022.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Thu May  2 19:19:27 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.16/0.41  Running first-order theorem proving
% 0.16/0.41  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 56.53/8.66  % SZS status Started for theBenchmark.p
% 56.53/8.66  % SZS status Theorem for theBenchmark.p
% 56.53/8.66  
% 56.53/8.66  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 56.53/8.66  
% 56.53/8.66  ------  iProver source info
% 56.53/8.66  
% 56.53/8.66  git: date: 2024-05-02 19:28:25 +0000
% 56.53/8.66  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 56.53/8.66  git: non_committed_changes: false
% 56.53/8.66  
% 56.53/8.66  ------ Parsing...
% 56.53/8.66  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 56.53/8.66  
% 56.53/8.66  ------ Preprocessing... sf_s  rm: 1 0s  sf_e 
% 56.53/8.66  
% 56.53/8.66  ------ Preprocessing...
% 56.53/8.66  
% 56.53/8.66  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 56.53/8.66  ------ Proving...
% 56.53/8.66  ------ Problem Properties 
% 56.53/8.66  
% 56.53/8.66  
% 56.53/8.66  clauses                                 28
% 56.53/8.66  conjectures                             2
% 56.53/8.66  EPR                                     14
% 56.53/8.66  Horn                                    24
% 56.53/8.66  unary                                   1
% 56.53/8.66  binary                                  17
% 56.53/8.66  lits                                    65
% 56.53/8.66  lits eq                                 3
% 56.53/8.66  fd_pure                                 0
% 56.53/8.66  fd_pseudo                               0
% 56.53/8.66  fd_cond                                 0
% 56.53/8.66  fd_pseudo_cond                          1
% 56.53/8.66  AC symbols                              0
% 56.53/8.66  
% 56.53/8.66  ------ Input Options Time Limit: Unbounded
% 56.53/8.66  
% 56.53/8.66  
% 56.53/8.66  ------ 
% 56.53/8.66  Current options:
% 56.53/8.66  ------ 
% 56.53/8.66  
% 56.53/8.66  
% 56.53/8.66  
% 56.53/8.66  
% 56.53/8.66  ------ Proving...
% 56.53/8.66  
% 56.53/8.66  
% 56.53/8.66  % SZS status Theorem for theBenchmark.p
% 56.53/8.66  
% 56.53/8.66  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 56.53/8.66  
% 56.53/8.67  
%------------------------------------------------------------------------------