TSTP Solution File: SET802+4 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET802+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n023.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 15:09:55 EDT 2023

% Result   : Theorem 3.52s 1.13s
% Output   : CNFRefutation 3.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   10
% Syntax   : Number of formulae    :  110 (   2 unt;   0 def)
%            Number of atoms       :  478 (  29 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  607 ( 239   ~; 241   |;  95   &)
%                                         (  13 <=>;  18  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-4 aty)
%            Number of variables   :  268 (   6 sgn; 149   !;  33   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f15,axiom,
    ! [X5,X3,X7] :
      ( lower_bound(X7,X5,X3)
    <=> ! [X2] :
          ( member(X2,X3)
         => apply(X5,X7,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_bound) ).

fof(f17,axiom,
    ! [X5,X3,X7] :
      ( least(X7,X5,X3)
    <=> ( ! [X2] :
            ( member(X2,X3)
           => apply(X5,X7,X2) )
        & member(X7,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',least) ).

fof(f21,axiom,
    ! [X0,X2,X5,X3] :
      ( greatest_lower_bound(X0,X2,X5,X3)
    <=> ( ! [X7] :
            ( ( lower_bound(X7,X5,X2)
              & member(X7,X3) )
           => apply(X5,X7,X0) )
        & lower_bound(X0,X5,X2)
        & member(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',greatest_lower_bound) ).

fof(f22,conjecture,
    ! [X5,X3] :
      ( order(X5,X3)
     => ! [X2] :
          ( subset(X2,X3)
         => ! [X7] :
              ( least(X7,X5,X2)
            <=> ( greatest_lower_bound(X7,X2,X5,X3)
                & member(X7,X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV14) ).

fof(f23,negated_conjecture,
    ~ ! [X5,X3] :
        ( order(X5,X3)
       => ! [X2] :
            ( subset(X2,X3)
           => ! [X7] :
                ( least(X7,X5,X2)
              <=> ( greatest_lower_bound(X7,X2,X5,X3)
                  & member(X7,X2) ) ) ) ),
    inference(negated_conjecture,[],[f22]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( lower_bound(X2,X0,X1)
    <=> ! [X3] :
          ( member(X3,X1)
         => apply(X0,X2,X3) ) ),
    inference(rectify,[],[f15]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( least(X2,X0,X1)
    <=> ( ! [X3] :
            ( member(X3,X1)
           => apply(X0,X2,X3) )
        & member(X2,X1) ) ),
    inference(rectify,[],[f17]) ).

fof(f42,plain,
    ! [X0,X1,X2,X3] :
      ( greatest_lower_bound(X0,X1,X2,X3)
    <=> ( ! [X4] :
            ( ( lower_bound(X4,X2,X1)
              & member(X4,X3) )
           => apply(X2,X4,X0) )
        & lower_bound(X0,X2,X1)
        & member(X0,X1) ) ),
    inference(rectify,[],[f21]) ).

fof(f43,plain,
    ~ ! [X0,X1] :
        ( order(X0,X1)
       => ! [X2] :
            ( subset(X2,X1)
           => ! [X3] :
                ( least(X3,X0,X2)
              <=> ( greatest_lower_bound(X3,X2,X0,X1)
                  & member(X3,X2) ) ) ) ),
    inference(rectify,[],[f23]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( lower_bound(X2,X0,X1)
    <=> ! [X3] :
          ( apply(X0,X2,X3)
          | ~ member(X3,X1) ) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( least(X2,X0,X1)
    <=> ( ! [X3] :
            ( apply(X0,X2,X3)
            | ~ member(X3,X1) )
        & member(X2,X1) ) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f51,plain,
    ! [X0,X1,X2,X3] :
      ( greatest_lower_bound(X0,X1,X2,X3)
    <=> ( ! [X4] :
            ( apply(X2,X4,X0)
            | ~ lower_bound(X4,X2,X1)
            | ~ member(X4,X3) )
        & lower_bound(X0,X2,X1)
        & member(X0,X1) ) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f52,plain,
    ! [X0,X1,X2,X3] :
      ( greatest_lower_bound(X0,X1,X2,X3)
    <=> ( ! [X4] :
            ( apply(X2,X4,X0)
            | ~ lower_bound(X4,X2,X1)
            | ~ member(X4,X3) )
        & lower_bound(X0,X2,X1)
        & member(X0,X1) ) ),
    inference(flattening,[],[f51]) ).

fof(f53,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( least(X3,X0,X2)
            <~> ( greatest_lower_bound(X3,X2,X0,X1)
                & member(X3,X2) ) )
          & subset(X2,X1) )
      & order(X0,X1) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( ( lower_bound(X2,X0,X1)
        | ? [X3] :
            ( ~ apply(X0,X2,X3)
            & member(X3,X1) ) )
      & ( ! [X3] :
            ( apply(X0,X2,X3)
            | ~ member(X3,X1) )
        | ~ lower_bound(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( ( lower_bound(X2,X0,X1)
        | ? [X3] :
            ( ~ apply(X0,X2,X3)
            & member(X3,X1) ) )
      & ( ! [X4] :
            ( apply(X0,X2,X4)
            | ~ member(X4,X1) )
        | ~ lower_bound(X2,X0,X1) ) ),
    inference(rectify,[],[f76]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ apply(X0,X2,X3)
          & member(X3,X1) )
     => ( ~ apply(X0,X2,sK3(X0,X1,X2))
        & member(sK3(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( ( lower_bound(X2,X0,X1)
        | ( ~ apply(X0,X2,sK3(X0,X1,X2))
          & member(sK3(X0,X1,X2),X1) ) )
      & ( ! [X4] :
            ( apply(X0,X2,X4)
            | ~ member(X4,X1) )
        | ~ lower_bound(X2,X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f77,f78]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( ( least(X2,X0,X1)
        | ? [X3] :
            ( ~ apply(X0,X2,X3)
            & member(X3,X1) )
        | ~ member(X2,X1) )
      & ( ( ! [X3] :
              ( apply(X0,X2,X3)
              | ~ member(X3,X1) )
          & member(X2,X1) )
        | ~ least(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( ( least(X2,X0,X1)
        | ? [X3] :
            ( ~ apply(X0,X2,X3)
            & member(X3,X1) )
        | ~ member(X2,X1) )
      & ( ( ! [X3] :
              ( apply(X0,X2,X3)
              | ~ member(X3,X1) )
          & member(X2,X1) )
        | ~ least(X2,X0,X1) ) ),
    inference(flattening,[],[f80]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( ( least(X2,X0,X1)
        | ? [X3] :
            ( ~ apply(X0,X2,X3)
            & member(X3,X1) )
        | ~ member(X2,X1) )
      & ( ( ! [X4] :
              ( apply(X0,X2,X4)
              | ~ member(X4,X1) )
          & member(X2,X1) )
        | ~ least(X2,X0,X1) ) ),
    inference(rectify,[],[f81]) ).

fof(f83,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ apply(X0,X2,X3)
          & member(X3,X1) )
     => ( ~ apply(X0,X2,sK4(X0,X1,X2))
        & member(sK4(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f84,plain,
    ! [X0,X1,X2] :
      ( ( least(X2,X0,X1)
        | ( ~ apply(X0,X2,sK4(X0,X1,X2))
          & member(sK4(X0,X1,X2),X1) )
        | ~ member(X2,X1) )
      & ( ( ! [X4] :
              ( apply(X0,X2,X4)
              | ~ member(X4,X1) )
          & member(X2,X1) )
        | ~ least(X2,X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f82,f83]) ).

fof(f85,plain,
    ! [X0,X1,X2,X3] :
      ( ( greatest_lower_bound(X0,X1,X2,X3)
        | ? [X4] :
            ( ~ apply(X2,X4,X0)
            & lower_bound(X4,X2,X1)
            & member(X4,X3) )
        | ~ lower_bound(X0,X2,X1)
        | ~ member(X0,X1) )
      & ( ( ! [X4] :
              ( apply(X2,X4,X0)
              | ~ lower_bound(X4,X2,X1)
              | ~ member(X4,X3) )
          & lower_bound(X0,X2,X1)
          & member(X0,X1) )
        | ~ greatest_lower_bound(X0,X1,X2,X3) ) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f86,plain,
    ! [X0,X1,X2,X3] :
      ( ( greatest_lower_bound(X0,X1,X2,X3)
        | ? [X4] :
            ( ~ apply(X2,X4,X0)
            & lower_bound(X4,X2,X1)
            & member(X4,X3) )
        | ~ lower_bound(X0,X2,X1)
        | ~ member(X0,X1) )
      & ( ( ! [X4] :
              ( apply(X2,X4,X0)
              | ~ lower_bound(X4,X2,X1)
              | ~ member(X4,X3) )
          & lower_bound(X0,X2,X1)
          & member(X0,X1) )
        | ~ greatest_lower_bound(X0,X1,X2,X3) ) ),
    inference(flattening,[],[f85]) ).

fof(f87,plain,
    ! [X0,X1,X2,X3] :
      ( ( greatest_lower_bound(X0,X1,X2,X3)
        | ? [X4] :
            ( ~ apply(X2,X4,X0)
            & lower_bound(X4,X2,X1)
            & member(X4,X3) )
        | ~ lower_bound(X0,X2,X1)
        | ~ member(X0,X1) )
      & ( ( ! [X5] :
              ( apply(X2,X5,X0)
              | ~ lower_bound(X5,X2,X1)
              | ~ member(X5,X3) )
          & lower_bound(X0,X2,X1)
          & member(X0,X1) )
        | ~ greatest_lower_bound(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f86]) ).

fof(f88,plain,
    ! [X0,X1,X2,X3] :
      ( ? [X4] :
          ( ~ apply(X2,X4,X0)
          & lower_bound(X4,X2,X1)
          & member(X4,X3) )
     => ( ~ apply(X2,sK5(X0,X1,X2,X3),X0)
        & lower_bound(sK5(X0,X1,X2,X3),X2,X1)
        & member(sK5(X0,X1,X2,X3),X3) ) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ! [X0,X1,X2,X3] :
      ( ( greatest_lower_bound(X0,X1,X2,X3)
        | ( ~ apply(X2,sK5(X0,X1,X2,X3),X0)
          & lower_bound(sK5(X0,X1,X2,X3),X2,X1)
          & member(sK5(X0,X1,X2,X3),X3) )
        | ~ lower_bound(X0,X2,X1)
        | ~ member(X0,X1) )
      & ( ( ! [X5] :
              ( apply(X2,X5,X0)
              | ~ lower_bound(X5,X2,X1)
              | ~ member(X5,X3) )
          & lower_bound(X0,X2,X1)
          & member(X0,X1) )
        | ~ greatest_lower_bound(X0,X1,X2,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f87,f88]) ).

fof(f90,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ( ~ greatest_lower_bound(X3,X2,X0,X1)
                | ~ member(X3,X2)
                | ~ least(X3,X0,X2) )
              & ( ( greatest_lower_bound(X3,X2,X0,X1)
                  & member(X3,X2) )
                | least(X3,X0,X2) ) )
          & subset(X2,X1) )
      & order(X0,X1) ),
    inference(nnf_transformation,[],[f53]) ).

fof(f91,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ? [X3] :
              ( ( ~ greatest_lower_bound(X3,X2,X0,X1)
                | ~ member(X3,X2)
                | ~ least(X3,X0,X2) )
              & ( ( greatest_lower_bound(X3,X2,X0,X1)
                  & member(X3,X2) )
                | least(X3,X0,X2) ) )
          & subset(X2,X1) )
      & order(X0,X1) ),
    inference(flattening,[],[f90]) ).

fof(f92,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ greatest_lower_bound(X3,X2,X0,X1)
                  | ~ member(X3,X2)
                  | ~ least(X3,X0,X2) )
                & ( ( greatest_lower_bound(X3,X2,X0,X1)
                    & member(X3,X2) )
                  | least(X3,X0,X2) ) )
            & subset(X2,X1) )
        & order(X0,X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ greatest_lower_bound(X3,X2,sK6,sK7)
                | ~ member(X3,X2)
                | ~ least(X3,sK6,X2) )
              & ( ( greatest_lower_bound(X3,X2,sK6,sK7)
                  & member(X3,X2) )
                | least(X3,sK6,X2) ) )
          & subset(X2,sK7) )
      & order(sK6,sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f93,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ greatest_lower_bound(X3,X2,sK6,sK7)
              | ~ member(X3,X2)
              | ~ least(X3,sK6,X2) )
            & ( ( greatest_lower_bound(X3,X2,sK6,sK7)
                & member(X3,X2) )
              | least(X3,sK6,X2) ) )
        & subset(X2,sK7) )
   => ( ? [X3] :
          ( ( ~ greatest_lower_bound(X3,sK8,sK6,sK7)
            | ~ member(X3,sK8)
            | ~ least(X3,sK6,sK8) )
          & ( ( greatest_lower_bound(X3,sK8,sK6,sK7)
              & member(X3,sK8) )
            | least(X3,sK6,sK8) ) )
      & subset(sK8,sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ( ? [X3] :
        ( ( ~ greatest_lower_bound(X3,sK8,sK6,sK7)
          | ~ member(X3,sK8)
          | ~ least(X3,sK6,sK8) )
        & ( ( greatest_lower_bound(X3,sK8,sK6,sK7)
            & member(X3,sK8) )
          | least(X3,sK6,sK8) ) )
   => ( ( ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
        | ~ member(sK9,sK8)
        | ~ least(sK9,sK6,sK8) )
      & ( ( greatest_lower_bound(sK9,sK8,sK6,sK7)
          & member(sK9,sK8) )
        | least(sK9,sK6,sK8) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f95,plain,
    ( ( ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
      | ~ member(sK9,sK8)
      | ~ least(sK9,sK6,sK8) )
    & ( ( greatest_lower_bound(sK9,sK8,sK6,sK7)
        & member(sK9,sK8) )
      | least(sK9,sK6,sK8) )
    & subset(sK8,sK7)
    & order(sK6,sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f91,f94,f93,f92]) ).

fof(f125,plain,
    ! [X2,X0,X1,X4] :
      ( apply(X0,X2,X4)
      | ~ member(X4,X1)
      | ~ lower_bound(X2,X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f126,plain,
    ! [X2,X0,X1] :
      ( lower_bound(X2,X0,X1)
      | member(sK3(X0,X1,X2),X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f127,plain,
    ! [X2,X0,X1] :
      ( lower_bound(X2,X0,X1)
      | ~ apply(X0,X2,sK3(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f128,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ least(X2,X0,X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f129,plain,
    ! [X2,X0,X1,X4] :
      ( apply(X0,X2,X4)
      | ~ member(X4,X1)
      | ~ least(X2,X0,X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f130,plain,
    ! [X2,X0,X1] :
      ( least(X2,X0,X1)
      | member(sK4(X0,X1,X2),X1)
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f131,plain,
    ! [X2,X0,X1] :
      ( least(X2,X0,X1)
      | ~ apply(X0,X2,sK4(X0,X1,X2))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f133,plain,
    ! [X2,X3,X0,X1] :
      ( lower_bound(X0,X2,X1)
      | ~ greatest_lower_bound(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f136,plain,
    ! [X2,X3,X0,X1] :
      ( greatest_lower_bound(X0,X1,X2,X3)
      | lower_bound(sK5(X0,X1,X2,X3),X2,X1)
      | ~ lower_bound(X0,X2,X1)
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f137,plain,
    ! [X2,X3,X0,X1] :
      ( greatest_lower_bound(X0,X1,X2,X3)
      | ~ apply(X2,sK5(X0,X1,X2,X3),X0)
      | ~ lower_bound(X0,X2,X1)
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f140,plain,
    ( member(sK9,sK8)
    | least(sK9,sK6,sK8) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f141,plain,
    ( greatest_lower_bound(sK9,sK8,sK6,sK7)
    | least(sK9,sK6,sK8) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f142,plain,
    ( ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
    | ~ member(sK9,sK8)
    | ~ least(sK9,sK6,sK8) ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_78,plain,
    ( ~ apply(X0,X1,sK3(X0,X2,X1))
    | lower_bound(X1,X0,X2) ),
    inference(cnf_transformation,[],[f127]) ).

cnf(c_79,plain,
    ( member(sK3(X0,X1,X2),X1)
    | lower_bound(X2,X0,X1) ),
    inference(cnf_transformation,[],[f126]) ).

cnf(c_80,plain,
    ( ~ lower_bound(X0,X1,X2)
    | ~ member(X3,X2)
    | apply(X1,X0,X3) ),
    inference(cnf_transformation,[],[f125]) ).

cnf(c_81,plain,
    ( ~ apply(X0,X1,sK4(X0,X2,X1))
    | ~ member(X1,X2)
    | least(X1,X0,X2) ),
    inference(cnf_transformation,[],[f131]) ).

cnf(c_82,plain,
    ( ~ member(X0,X1)
    | member(sK4(X2,X1,X0),X1)
    | least(X0,X2,X1) ),
    inference(cnf_transformation,[],[f130]) ).

cnf(c_83,plain,
    ( ~ least(X0,X1,X2)
    | ~ member(X3,X2)
    | apply(X1,X0,X3) ),
    inference(cnf_transformation,[],[f129]) ).

cnf(c_84,plain,
    ( ~ least(X0,X1,X2)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f128]) ).

cnf(c_85,plain,
    ( ~ apply(X0,sK5(X1,X2,X0,X3),X1)
    | ~ lower_bound(X1,X0,X2)
    | ~ member(X1,X2)
    | greatest_lower_bound(X1,X2,X0,X3) ),
    inference(cnf_transformation,[],[f137]) ).

cnf(c_86,plain,
    ( ~ lower_bound(X0,X1,X2)
    | ~ member(X0,X2)
    | lower_bound(sK5(X0,X2,X1,X3),X1,X2)
    | greatest_lower_bound(X0,X2,X1,X3) ),
    inference(cnf_transformation,[],[f136]) ).

cnf(c_89,plain,
    ( ~ greatest_lower_bound(X0,X1,X2,X3)
    | lower_bound(X0,X2,X1) ),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_91,negated_conjecture,
    ( ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
    | ~ least(sK9,sK6,sK8)
    | ~ member(sK9,sK8) ),
    inference(cnf_transformation,[],[f142]) ).

cnf(c_92,negated_conjecture,
    ( greatest_lower_bound(sK9,sK8,sK6,sK7)
    | least(sK9,sK6,sK8) ),
    inference(cnf_transformation,[],[f141]) ).

cnf(c_93,negated_conjecture,
    ( least(sK9,sK6,sK8)
    | member(sK9,sK8) ),
    inference(cnf_transformation,[],[f140]) ).

cnf(c_155,plain,
    ( member(X0,X2)
    | ~ least(X0,X1,X2) ),
    inference(prop_impl_just,[status(thm)],[c_84]) ).

cnf(c_156,plain,
    ( ~ least(X0,X1,X2)
    | member(X0,X2) ),
    inference(renaming,[status(thm)],[c_155]) ).

cnf(c_187,plain,
    ( ~ greatest_lower_bound(X0,X1,X2,X3)
    | lower_bound(X0,X2,X1) ),
    inference(prop_impl_just,[status(thm)],[c_89]) ).

cnf(c_189,plain,
    ( greatest_lower_bound(sK9,sK8,sK6,sK7)
    | least(sK9,sK6,sK8) ),
    inference(prop_impl_just,[status(thm)],[c_92]) ).

cnf(c_191,plain,
    ( member(sK9,sK8)
    | least(sK9,sK6,sK8) ),
    inference(prop_impl_just,[status(thm)],[c_93]) ).

cnf(c_192,plain,
    ( least(sK9,sK6,sK8)
    | member(sK9,sK8) ),
    inference(renaming,[status(thm)],[c_191]) ).

cnf(c_313,plain,
    member(sK9,sK8),
    inference(forward_subsumption_resolution,[status(thm)],[c_192,c_156]) ).

cnf(c_317,plain,
    ( ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
    | ~ least(sK9,sK6,sK8) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_91,c_313]) ).

cnf(c_923,plain,
    ( X0 != sK6
    | X1 != sK9
    | X2 != sK8
    | ~ apply(X0,X1,sK4(X0,X2,X1))
    | ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
    | ~ member(X1,X2) ),
    inference(resolution_lifted,[status(thm)],[c_81,c_317]) ).

cnf(c_924,plain,
    ( ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
    | ~ member(sK9,sK8) ),
    inference(unflattening,[status(thm)],[c_923]) ).

cnf(c_925,plain,
    ( ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
    | ~ apply(sK6,sK9,sK4(sK6,sK8,sK9)) ),
    inference(global_subsumption_just,[status(thm)],[c_924,c_313,c_924]) ).

cnf(c_926,plain,
    ( ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | ~ greatest_lower_bound(sK9,sK8,sK6,sK7) ),
    inference(renaming,[status(thm)],[c_925]) ).

cnf(c_950,plain,
    ( X0 != sK9
    | X1 != sK8
    | X2 != sK6
    | ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
    | ~ member(X0,X1)
    | member(sK4(X2,X1,X0),X1) ),
    inference(resolution_lifted,[status(thm)],[c_82,c_317]) ).

cnf(c_951,plain,
    ( ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
    | ~ member(sK9,sK8)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(unflattening,[status(thm)],[c_950]) ).

cnf(c_952,plain,
    ( ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(global_subsumption_just,[status(thm)],[c_951,c_313,c_951]) ).

cnf(c_962,plain,
    ( X0 != sK9
    | X1 != sK6
    | X2 != sK8
    | ~ member(X3,X2)
    | greatest_lower_bound(sK9,sK8,sK6,sK7)
    | apply(X1,X0,X3) ),
    inference(resolution_lifted,[status(thm)],[c_83,c_189]) ).

cnf(c_963,plain,
    ( ~ member(X0,sK8)
    | greatest_lower_bound(sK9,sK8,sK6,sK7)
    | apply(sK6,sK9,X0) ),
    inference(unflattening,[status(thm)],[c_962]) ).

cnf(c_1017,plain,
    ( X0 != sK6
    | X1 != sK9
    | X2 != sK8
    | X3 != sK7
    | ~ apply(X0,sK5(X1,X2,X0,X3),X1)
    | ~ lower_bound(X1,X0,X2)
    | ~ member(X1,X2)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(resolution_lifted,[status(thm)],[c_85,c_952]) ).

cnf(c_1018,plain,
    ( ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9)
    | ~ lower_bound(sK9,sK6,sK8)
    | ~ member(sK9,sK8)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(unflattening,[status(thm)],[c_1017]) ).

cnf(c_1019,plain,
    ( ~ lower_bound(sK9,sK6,sK8)
    | ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(global_subsumption_just,[status(thm)],[c_1018,c_313,c_1018]) ).

cnf(c_1020,plain,
    ( ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9)
    | ~ lower_bound(sK9,sK6,sK8)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(renaming,[status(thm)],[c_1019]) ).

cnf(c_1030,plain,
    ( X0 != sK6
    | X1 != sK9
    | X2 != sK8
    | X3 != sK7
    | ~ apply(X0,sK5(X1,X2,X0,X3),X1)
    | ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | ~ lower_bound(X1,X0,X2)
    | ~ member(X1,X2) ),
    inference(resolution_lifted,[status(thm)],[c_85,c_926]) ).

cnf(c_1031,plain,
    ( ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9)
    | ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | ~ lower_bound(sK9,sK6,sK8)
    | ~ member(sK9,sK8) ),
    inference(unflattening,[status(thm)],[c_1030]) ).

cnf(c_1032,plain,
    ( ~ lower_bound(sK9,sK6,sK8)
    | ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9) ),
    inference(global_subsumption_just,[status(thm)],[c_1031,c_313,c_1031]) ).

cnf(c_1033,plain,
    ( ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9)
    | ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | ~ lower_bound(sK9,sK6,sK8) ),
    inference(renaming,[status(thm)],[c_1032]) ).

cnf(c_1081,plain,
    ( X0 != sK9
    | X1 != sK6
    | X2 != sK8
    | X3 != sK7
    | ~ lower_bound(X0,X1,X2)
    | ~ member(X0,X2)
    | lower_bound(sK5(X0,X2,X1,X3),X1,X2)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(resolution_lifted,[status(thm)],[c_86,c_952]) ).

cnf(c_1082,plain,
    ( ~ lower_bound(sK9,sK6,sK8)
    | ~ member(sK9,sK8)
    | lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(unflattening,[status(thm)],[c_1081]) ).

cnf(c_1083,plain,
    ( ~ lower_bound(sK9,sK6,sK8)
    | lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(global_subsumption_just,[status(thm)],[c_1082,c_313,c_1082]) ).

cnf(c_1094,plain,
    ( X0 != sK9
    | X1 != sK6
    | X2 != sK8
    | X3 != sK7
    | ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | ~ lower_bound(X0,X1,X2)
    | ~ member(X0,X2)
    | lower_bound(sK5(X0,X2,X1,X3),X1,X2) ),
    inference(resolution_lifted,[status(thm)],[c_86,c_926]) ).

cnf(c_1095,plain,
    ( ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | ~ lower_bound(sK9,sK6,sK8)
    | ~ member(sK9,sK8)
    | lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8) ),
    inference(unflattening,[status(thm)],[c_1094]) ).

cnf(c_1096,plain,
    ( ~ lower_bound(sK9,sK6,sK8)
    | ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8) ),
    inference(global_subsumption_just,[status(thm)],[c_1095,c_313,c_1095]) ).

cnf(c_1097,plain,
    ( ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | ~ lower_bound(sK9,sK6,sK8)
    | lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8) ),
    inference(renaming,[status(thm)],[c_1096]) ).

cnf(c_1109,plain,
    ( X0 != sK9
    | X1 != sK8
    | X2 != sK6
    | X3 != sK7
    | ~ member(X4,sK8)
    | lower_bound(X0,X2,X1)
    | apply(sK6,sK9,X4) ),
    inference(resolution_lifted,[status(thm)],[c_187,c_963]) ).

cnf(c_1110,plain,
    ( ~ member(X0,sK8)
    | apply(sK6,sK9,X0)
    | lower_bound(sK9,sK6,sK8) ),
    inference(unflattening,[status(thm)],[c_1109]) ).

cnf(c_1118,plain,
    ( ~ member(X0,sK8)
    | apply(sK6,sK9,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1110,c_80]) ).

cnf(c_1213,plain,
    ( ~ member(X0,sK8)
    | apply(sK6,sK9,X0) ),
    inference(prop_impl_just,[status(thm)],[c_1118]) ).

cnf(c_3373,plain,
    ( ~ member(sK3(sK6,X0,sK9),sK8)
    | lower_bound(sK9,sK6,X0) ),
    inference(superposition,[status(thm)],[c_1213,c_78]) ).

cnf(c_3376,plain,
    ( ~ member(sK3(sK6,sK8,sK9),sK8)
    | lower_bound(sK9,sK6,sK8) ),
    inference(instantiation,[status(thm)],[c_3373]) ).

cnf(c_3701,plain,
    ( ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | ~ lower_bound(sK9,sK6,sK8)
    | ~ member(X0,sK8)
    | apply(sK6,sK5(sK9,sK8,sK6,sK7),X0) ),
    inference(superposition,[status(thm)],[c_1097,c_80]) ).

cnf(c_3702,plain,
    ( ~ lower_bound(sK9,sK6,sK8)
    | ~ member(X0,sK8)
    | apply(sK6,sK5(sK9,sK8,sK6,sK7),X0)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(superposition,[status(thm)],[c_1083,c_80]) ).

cnf(c_3860,plain,
    ( member(sK3(sK6,sK8,sK9),sK8)
    | lower_bound(sK9,sK6,sK8) ),
    inference(instantiation,[status(thm)],[c_79]) ).

cnf(c_4306,plain,
    ( ~ member(sK4(sK6,sK8,sK9),sK8)
    | apply(sK6,sK9,sK4(sK6,sK8,sK9)) ),
    inference(instantiation,[status(thm)],[c_1213]) ).

cnf(c_5097,plain,
    ( ~ member(X0,sK8)
    | apply(sK6,sK5(sK9,sK8,sK6,sK7),X0)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(global_subsumption_just,[status(thm)],[c_3702,c_3376,c_3702,c_3701,c_3860,c_4306]) ).

cnf(c_5100,plain,
    ( apply(sK6,sK5(sK9,sK8,sK6,sK7),X0)
    | ~ member(X0,sK8) ),
    inference(global_subsumption_just,[status(thm)],[c_5097,c_3376,c_3702,c_3701,c_3860,c_4306]) ).

cnf(c_5101,plain,
    ( ~ member(X0,sK8)
    | apply(sK6,sK5(sK9,sK8,sK6,sK7),X0) ),
    inference(renaming,[status(thm)],[c_5100]) ).

cnf(c_5110,plain,
    ( ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | ~ lower_bound(sK9,sK6,sK8)
    | ~ member(sK9,sK8) ),
    inference(superposition,[status(thm)],[c_5101,c_1033]) ).

cnf(c_5111,plain,
    ( ~ lower_bound(sK9,sK6,sK8)
    | ~ member(sK9,sK8)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(superposition,[status(thm)],[c_5101,c_1020]) ).

cnf(c_5114,plain,
    ( ~ lower_bound(sK9,sK6,sK8)
    | member(sK4(sK6,sK8,sK9),sK8) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5111,c_313]) ).

cnf(c_5117,plain,
    ( ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
    | ~ lower_bound(sK9,sK6,sK8) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_5110,c_313]) ).

cnf(c_5388,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_5117,c_5114,c_4306,c_3860,c_3376]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET802+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n023.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
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Aug 26 16:34:11 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.46  Running first-order theorem proving
% 0.18/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.52/1.13  % SZS status Started for theBenchmark.p
% 3.52/1.13  % SZS status Theorem for theBenchmark.p
% 3.52/1.13  
% 3.52/1.13  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.52/1.13  
% 3.52/1.13  ------  iProver source info
% 3.52/1.13  
% 3.52/1.13  git: date: 2023-05-31 18:12:56 +0000
% 3.52/1.13  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.52/1.13  git: non_committed_changes: false
% 3.52/1.13  git: last_make_outside_of_git: false
% 3.52/1.13  
% 3.52/1.13  ------ Parsing...
% 3.52/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.52/1.13  
% 3.52/1.13  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e 
% 3.52/1.13  
% 3.52/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.52/1.13  
% 3.52/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.52/1.13  ------ Proving...
% 3.52/1.13  ------ Problem Properties 
% 3.52/1.13  
% 3.52/1.13  
% 3.52/1.13  clauses                                 43
% 3.52/1.13  conjectures                             1
% 3.52/1.13  EPR                                     9
% 3.52/1.13  Horn                                    34
% 3.52/1.13  unary                                   6
% 3.52/1.13  binary                                  19
% 3.52/1.13  lits                                    105
% 3.52/1.13  lits eq                                 4
% 3.52/1.13  fd_pure                                 0
% 3.52/1.13  fd_pseudo                               0
% 3.52/1.13  fd_cond                                 0
% 3.52/1.13  fd_pseudo_cond                          3
% 3.52/1.13  AC symbols                              0
% 3.52/1.13  
% 3.52/1.13  ------ Schedule dynamic 5 is on 
% 3.52/1.13  
% 3.52/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.52/1.13  
% 3.52/1.13  
% 3.52/1.13  ------ 
% 3.52/1.13  Current options:
% 3.52/1.13  ------ 
% 3.52/1.13  
% 3.52/1.13  
% 3.52/1.13  
% 3.52/1.13  
% 3.52/1.13  ------ Proving...
% 3.52/1.13  
% 3.52/1.13  
% 3.52/1.13  % SZS status Theorem for theBenchmark.p
% 3.52/1.13  
% 3.52/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.52/1.13  
% 3.52/1.13  
%------------------------------------------------------------------------------