TSTP Solution File: SEU304+2 by iProver---3.8

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%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU304+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n007.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 17:05:38 EDT 2023

% Result   : Theorem 23.31s 4.10s
% Output   : CNFRefutation 23.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  105 (  24 unt;   0 def)
%            Number of atoms       :  423 (  74 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  534 ( 216   ~; 218   |;  73   &)
%                                         (   6 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-3 aty)
%            Number of variables   :  185 (   0 sgn;  84   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f20,axiom,
    ! [X0,X1,X2] :
      ( ( element(X2,the_carrier(X0))
        & element(X1,the_carrier(X0))
        & meet_semilatt_str(X0)
        & meet_commutative(X0)
        & ~ empty_carrier(X0) )
     => meet_commut(X0,X1,X2) = meet_commut(X0,X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_lattices) ).

fof(f58,axiom,
    ! [X0] :
      ( ( join_semilatt_str(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( below(X0,X1,X2)
              <=> join(X0,X1,X2) = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_lattices) ).

fof(f87,axiom,
    ! [X0] :
      ( ( latt_str(X0)
        & ~ empty_carrier(X0) )
     => ( meet_absorbing(X0)
      <=> ! [X1] :
            ( element(X1,the_carrier(X0))
           => ! [X2] :
                ( element(X2,the_carrier(X0))
               => join(X0,meet(X0,X1,X2),X2) = X2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattices) ).

fof(f110,axiom,
    ! [X0,X1,X2] :
      ( ( element(X2,the_carrier(X0))
        & element(X1,the_carrier(X0))
        & meet_semilatt_str(X0)
        & ~ empty_carrier(X0) )
     => element(meet(X0,X1,X2),the_carrier(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_lattices) ).

fof(f141,axiom,
    ! [X0] :
      ( latt_str(X0)
     => ( join_semilatt_str(X0)
        & meet_semilatt_str(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_lattices) ).

fof(f245,axiom,
    ! [X0,X1,X2] :
      ( ( element(X2,the_carrier(X0))
        & element(X1,the_carrier(X0))
        & meet_semilatt_str(X0)
        & meet_commutative(X0)
        & ~ empty_carrier(X0) )
     => meet_commut(X0,X1,X2) = meet(X0,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_lattices) ).

fof(f339,conjecture,
    ! [X0] :
      ( ( latt_str(X0)
        & meet_absorbing(X0)
        & meet_commutative(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => below(X0,meet_commut(X0,X1,X2),X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_lattices) ).

fof(f340,negated_conjecture,
    ~ ! [X0] :
        ( ( latt_str(X0)
          & meet_absorbing(X0)
          & meet_commutative(X0)
          & ~ empty_carrier(X0) )
       => ! [X1] :
            ( element(X1,the_carrier(X0))
           => ! [X2] :
                ( element(X2,the_carrier(X0))
               => below(X0,meet_commut(X0,X1,X2),X1) ) ) ),
    inference(negated_conjecture,[],[f339]) ).

fof(f503,plain,
    ! [X0,X1,X2] :
      ( meet_commut(X0,X1,X2) = meet_commut(X0,X2,X1)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ meet_semilatt_str(X0)
      | ~ meet_commutative(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f504,plain,
    ! [X0,X1,X2] :
      ( meet_commut(X0,X1,X2) = meet_commut(X0,X2,X1)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ meet_semilatt_str(X0)
      | ~ meet_commutative(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f503]) ).

fof(f540,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( below(X0,X1,X2)
              <=> join(X0,X1,X2) = X2 )
              | ~ element(X2,the_carrier(X0)) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ join_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f541,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( below(X0,X1,X2)
              <=> join(X0,X1,X2) = X2 )
              | ~ element(X2,the_carrier(X0)) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ join_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f540]) ).

fof(f567,plain,
    ! [X0] :
      ( ( meet_absorbing(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( join(X0,meet(X0,X1,X2),X2) = X2
                | ~ element(X2,the_carrier(X0)) )
            | ~ element(X1,the_carrier(X0)) ) )
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f87]) ).

fof(f568,plain,
    ! [X0] :
      ( ( meet_absorbing(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( join(X0,meet(X0,X1,X2),X2) = X2
                | ~ element(X2,the_carrier(X0)) )
            | ~ element(X1,the_carrier(X0)) ) )
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f567]) ).

fof(f584,plain,
    ! [X0,X1,X2] :
      ( element(meet(X0,X1,X2),the_carrier(X0))
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ meet_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f110]) ).

fof(f585,plain,
    ! [X0,X1,X2] :
      ( element(meet(X0,X1,X2),the_carrier(X0))
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ meet_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f584]) ).

fof(f604,plain,
    ! [X0] :
      ( ( join_semilatt_str(X0)
        & meet_semilatt_str(X0) )
      | ~ latt_str(X0) ),
    inference(ennf_transformation,[],[f141]) ).

fof(f680,plain,
    ! [X0,X1,X2] :
      ( meet_commut(X0,X1,X2) = meet(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ meet_semilatt_str(X0)
      | ~ meet_commutative(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f245]) ).

fof(f681,plain,
    ! [X0,X1,X2] :
      ( meet_commut(X0,X1,X2) = meet(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ meet_semilatt_str(X0)
      | ~ meet_commutative(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f680]) ).

fof(f812,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ below(X0,meet_commut(X0,X1,X2),X1)
              & element(X2,the_carrier(X0)) )
          & element(X1,the_carrier(X0)) )
      & latt_str(X0)
      & meet_absorbing(X0)
      & meet_commutative(X0)
      & ~ empty_carrier(X0) ),
    inference(ennf_transformation,[],[f340]) ).

fof(f813,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ below(X0,meet_commut(X0,X1,X2),X1)
              & element(X2,the_carrier(X0)) )
          & element(X1,the_carrier(X0)) )
      & latt_str(X0)
      & meet_absorbing(X0)
      & meet_commutative(X0)
      & ~ empty_carrier(X0) ),
    inference(flattening,[],[f812]) ).

fof(f1133,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( below(X0,X1,X2)
                  | join(X0,X1,X2) != X2 )
                & ( join(X0,X1,X2) = X2
                  | ~ below(X0,X1,X2) ) )
              | ~ element(X2,the_carrier(X0)) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ join_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(nnf_transformation,[],[f541]) ).

fof(f1226,plain,
    ! [X0] :
      ( ( ( meet_absorbing(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( join(X0,meet(X0,X1,X2),X2) != X2
                  & element(X2,the_carrier(X0)) )
              & element(X1,the_carrier(X0)) ) )
        & ( ! [X1] :
              ( ! [X2] :
                  ( join(X0,meet(X0,X1,X2),X2) = X2
                  | ~ element(X2,the_carrier(X0)) )
              | ~ element(X1,the_carrier(X0)) )
          | ~ meet_absorbing(X0) ) )
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(nnf_transformation,[],[f568]) ).

fof(f1227,plain,
    ! [X0] :
      ( ( ( meet_absorbing(X0)
          | ? [X1] :
              ( ? [X2] :
                  ( join(X0,meet(X0,X1,X2),X2) != X2
                  & element(X2,the_carrier(X0)) )
              & element(X1,the_carrier(X0)) ) )
        & ( ! [X3] :
              ( ! [X4] :
                  ( join(X0,meet(X0,X3,X4),X4) = X4
                  | ~ element(X4,the_carrier(X0)) )
              | ~ element(X3,the_carrier(X0)) )
          | ~ meet_absorbing(X0) ) )
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(rectify,[],[f1226]) ).

fof(f1228,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( join(X0,meet(X0,X1,X2),X2) != X2
              & element(X2,the_carrier(X0)) )
          & element(X1,the_carrier(X0)) )
     => ( ? [X2] :
            ( join(X0,meet(X0,sK120(X0),X2),X2) != X2
            & element(X2,the_carrier(X0)) )
        & element(sK120(X0),the_carrier(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f1229,plain,
    ! [X0] :
      ( ? [X2] :
          ( join(X0,meet(X0,sK120(X0),X2),X2) != X2
          & element(X2,the_carrier(X0)) )
     => ( sK121(X0) != join(X0,meet(X0,sK120(X0),sK121(X0)),sK121(X0))
        & element(sK121(X0),the_carrier(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f1230,plain,
    ! [X0] :
      ( ( ( meet_absorbing(X0)
          | ( sK121(X0) != join(X0,meet(X0,sK120(X0),sK121(X0)),sK121(X0))
            & element(sK121(X0),the_carrier(X0))
            & element(sK120(X0),the_carrier(X0)) ) )
        & ( ! [X3] :
              ( ! [X4] :
                  ( join(X0,meet(X0,X3,X4),X4) = X4
                  | ~ element(X4,the_carrier(X0)) )
              | ~ element(X3,the_carrier(X0)) )
          | ~ meet_absorbing(X0) ) )
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK120,sK121])],[f1227,f1229,f1228]) ).

fof(f1650,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ~ below(X0,meet_commut(X0,X1,X2),X1)
                & element(X2,the_carrier(X0)) )
            & element(X1,the_carrier(X0)) )
        & latt_str(X0)
        & meet_absorbing(X0)
        & meet_commutative(X0)
        & ~ empty_carrier(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ~ below(sK334,meet_commut(sK334,X1,X2),X1)
              & element(X2,the_carrier(sK334)) )
          & element(X1,the_carrier(sK334)) )
      & latt_str(sK334)
      & meet_absorbing(sK334)
      & meet_commutative(sK334)
      & ~ empty_carrier(sK334) ) ),
    introduced(choice_axiom,[]) ).

fof(f1651,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ~ below(sK334,meet_commut(sK334,X1,X2),X1)
            & element(X2,the_carrier(sK334)) )
        & element(X1,the_carrier(sK334)) )
   => ( ? [X2] :
          ( ~ below(sK334,meet_commut(sK334,sK335,X2),sK335)
          & element(X2,the_carrier(sK334)) )
      & element(sK335,the_carrier(sK334)) ) ),
    introduced(choice_axiom,[]) ).

fof(f1652,plain,
    ( ? [X2] :
        ( ~ below(sK334,meet_commut(sK334,sK335,X2),sK335)
        & element(X2,the_carrier(sK334)) )
   => ( ~ below(sK334,meet_commut(sK334,sK335,sK336),sK335)
      & element(sK336,the_carrier(sK334)) ) ),
    introduced(choice_axiom,[]) ).

fof(f1653,plain,
    ( ~ below(sK334,meet_commut(sK334,sK335,sK336),sK335)
    & element(sK336,the_carrier(sK334))
    & element(sK335,the_carrier(sK334))
    & latt_str(sK334)
    & meet_absorbing(sK334)
    & meet_commutative(sK334)
    & ~ empty_carrier(sK334) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK334,sK335,sK336])],[f813,f1652,f1651,f1650]) ).

fof(f1761,plain,
    ! [X2,X0,X1] :
      ( meet_commut(X0,X1,X2) = meet_commut(X0,X2,X1)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ meet_semilatt_str(X0)
      | ~ meet_commutative(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f504]) ).

fof(f1924,plain,
    ! [X2,X0,X1] :
      ( below(X0,X1,X2)
      | join(X0,X1,X2) != X2
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ join_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f1133]) ).

fof(f2051,plain,
    ! [X3,X0,X4] :
      ( join(X0,meet(X0,X3,X4),X4) = X4
      | ~ element(X4,the_carrier(X0))
      | ~ element(X3,the_carrier(X0))
      | ~ meet_absorbing(X0)
      | ~ latt_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f1230]) ).

fof(f2082,plain,
    ! [X2,X0,X1] :
      ( element(meet(X0,X1,X2),the_carrier(X0))
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ meet_semilatt_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f585]) ).

fof(f2100,plain,
    ! [X0] :
      ( meet_semilatt_str(X0)
      | ~ latt_str(X0) ),
    inference(cnf_transformation,[],[f604]) ).

fof(f2101,plain,
    ! [X0] :
      ( join_semilatt_str(X0)
      | ~ latt_str(X0) ),
    inference(cnf_transformation,[],[f604]) ).

fof(f2318,plain,
    ! [X2,X0,X1] :
      ( meet_commut(X0,X1,X2) = meet(X0,X1,X2)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0))
      | ~ meet_semilatt_str(X0)
      | ~ meet_commutative(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f681]) ).

fof(f2725,plain,
    ~ empty_carrier(sK334),
    inference(cnf_transformation,[],[f1653]) ).

fof(f2726,plain,
    meet_commutative(sK334),
    inference(cnf_transformation,[],[f1653]) ).

fof(f2727,plain,
    meet_absorbing(sK334),
    inference(cnf_transformation,[],[f1653]) ).

fof(f2728,plain,
    latt_str(sK334),
    inference(cnf_transformation,[],[f1653]) ).

fof(f2729,plain,
    element(sK335,the_carrier(sK334)),
    inference(cnf_transformation,[],[f1653]) ).

fof(f2730,plain,
    element(sK336,the_carrier(sK334)),
    inference(cnf_transformation,[],[f1653]) ).

fof(f2731,plain,
    ~ below(sK334,meet_commut(sK334,sK335,sK336),sK335),
    inference(cnf_transformation,[],[f1653]) ).

cnf(c_79,plain,
    ( ~ element(X0,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ meet_semilatt_str(X1)
    | ~ meet_commutative(X1)
    | meet_commut(X1,X0,X2) = meet_commut(X1,X2,X0)
    | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f1761]) ).

cnf(c_240,plain,
    ( join(X0,X1,X2) != X2
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ join_semilatt_str(X0)
    | below(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f1924]) ).

cnf(c_370,plain,
    ( ~ element(X0,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ meet_absorbing(X1)
    | ~ latt_str(X1)
    | join(X1,meet(X1,X2,X0),X0) = X0
    | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f2051]) ).

cnf(c_398,plain,
    ( ~ element(X0,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ meet_semilatt_str(X1)
    | element(meet(X1,X0,X2),the_carrier(X1))
    | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f2082]) ).

cnf(c_416,plain,
    ( ~ latt_str(X0)
    | join_semilatt_str(X0) ),
    inference(cnf_transformation,[],[f2101]) ).

cnf(c_417,plain,
    ( ~ latt_str(X0)
    | meet_semilatt_str(X0) ),
    inference(cnf_transformation,[],[f2100]) ).

cnf(c_634,plain,
    ( ~ element(X0,the_carrier(X1))
    | ~ element(X2,the_carrier(X1))
    | ~ meet_semilatt_str(X1)
    | ~ meet_commutative(X1)
    | meet_commut(X1,X0,X2) = meet(X1,X0,X2)
    | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f2318]) ).

cnf(c_1041,negated_conjecture,
    ~ below(sK334,meet_commut(sK334,sK335,sK336),sK335),
    inference(cnf_transformation,[],[f2731]) ).

cnf(c_1042,negated_conjecture,
    element(sK336,the_carrier(sK334)),
    inference(cnf_transformation,[],[f2730]) ).

cnf(c_1043,negated_conjecture,
    element(sK335,the_carrier(sK334)),
    inference(cnf_transformation,[],[f2729]) ).

cnf(c_1044,negated_conjecture,
    latt_str(sK334),
    inference(cnf_transformation,[],[f2728]) ).

cnf(c_1045,negated_conjecture,
    meet_absorbing(sK334),
    inference(cnf_transformation,[],[f2727]) ).

cnf(c_1046,negated_conjecture,
    meet_commutative(sK334),
    inference(cnf_transformation,[],[f2726]) ).

cnf(c_1047,negated_conjecture,
    ~ empty_carrier(sK334),
    inference(cnf_transformation,[],[f2725]) ).

cnf(c_2471,plain,
    ( join_semilatt_str(X0)
    | ~ latt_str(X0) ),
    inference(prop_impl_just,[status(thm)],[c_416]) ).

cnf(c_2472,plain,
    ( ~ latt_str(X0)
    | join_semilatt_str(X0) ),
    inference(renaming,[status(thm)],[c_2471]) ).

cnf(c_2519,plain,
    ( ~ latt_str(X0)
    | meet_semilatt_str(X0) ),
    inference(prop_impl_just,[status(thm)],[c_417]) ).

cnf(c_18563,plain,
    ( X0 != sK334
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ meet_semilatt_str(X0)
    | meet_commut(X0,X1,X2) = meet(X0,X1,X2)
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_634,c_1046]) ).

cnf(c_18564,plain,
    ( ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | ~ meet_semilatt_str(sK334)
    | meet_commut(sK334,X0,X1) = meet(sK334,X0,X1)
    | empty_carrier(sK334) ),
    inference(unflattening,[status(thm)],[c_18563]) ).

cnf(c_18566,plain,
    ( meet_commut(sK334,X0,X1) = meet(sK334,X0,X1)
    | ~ meet_semilatt_str(sK334)
    | ~ element(X1,the_carrier(sK334))
    | ~ element(X0,the_carrier(sK334)) ),
    inference(global_subsumption_just,[status(thm)],[c_18564,c_1047,c_18564]) ).

cnf(c_18567,plain,
    ( ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | ~ meet_semilatt_str(sK334)
    | meet_commut(sK334,X0,X1) = meet(sK334,X0,X1) ),
    inference(renaming,[status(thm)],[c_18566]) ).

cnf(c_18599,plain,
    ( X0 != sK334
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ meet_semilatt_str(X0)
    | meet_commut(X0,X1,X2) = meet_commut(X0,X2,X1)
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_79,c_1046]) ).

cnf(c_18600,plain,
    ( ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | ~ meet_semilatt_str(sK334)
    | meet_commut(sK334,X0,X1) = meet_commut(sK334,X1,X0)
    | empty_carrier(sK334) ),
    inference(unflattening,[status(thm)],[c_18599]) ).

cnf(c_18602,plain,
    ( meet_commut(sK334,X0,X1) = meet_commut(sK334,X1,X0)
    | ~ meet_semilatt_str(sK334)
    | ~ element(X1,the_carrier(sK334))
    | ~ element(X0,the_carrier(sK334)) ),
    inference(global_subsumption_just,[status(thm)],[c_18600,c_1047,c_18600]) ).

cnf(c_18603,plain,
    ( ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | ~ meet_semilatt_str(sK334)
    | meet_commut(sK334,X0,X1) = meet_commut(sK334,X1,X0) ),
    inference(renaming,[status(thm)],[c_18602]) ).

cnf(c_18631,plain,
    ( join(X0,X1,X2) != X2
    | meet_commut(sK334,sK335,sK336) != X1
    | X0 != sK334
    | X2 != sK335
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ join_semilatt_str(X0)
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_240,c_1041]) ).

cnf(c_18632,plain,
    ( join(sK334,meet_commut(sK334,sK335,sK336),sK335) != sK335
    | ~ element(meet_commut(sK334,sK335,sK336),the_carrier(sK334))
    | ~ element(sK335,the_carrier(sK334))
    | ~ join_semilatt_str(sK334)
    | empty_carrier(sK334) ),
    inference(unflattening,[status(thm)],[c_18631]) ).

cnf(c_18633,plain,
    ( ~ join_semilatt_str(sK334)
    | join(sK334,meet_commut(sK334,sK335,sK336),sK335) != sK335
    | ~ element(meet_commut(sK334,sK335,sK336),the_carrier(sK334)) ),
    inference(global_subsumption_just,[status(thm)],[c_18632,c_1047,c_1043,c_18632]) ).

cnf(c_18634,plain,
    ( join(sK334,meet_commut(sK334,sK335,sK336),sK335) != sK335
    | ~ element(meet_commut(sK334,sK335,sK336),the_carrier(sK334))
    | ~ join_semilatt_str(sK334) ),
    inference(renaming,[status(thm)],[c_18633]) ).

cnf(c_18989,plain,
    ( X0 != sK334
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ latt_str(X0)
    | join(X0,meet(X0,X2,X1),X1) = X1
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_370,c_1045]) ).

cnf(c_18990,plain,
    ( ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | ~ latt_str(sK334)
    | join(sK334,meet(sK334,X1,X0),X0) = X0
    | empty_carrier(sK334) ),
    inference(unflattening,[status(thm)],[c_18989]) ).

cnf(c_18992,plain,
    ( join(sK334,meet(sK334,X1,X0),X0) = X0
    | ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334)) ),
    inference(global_subsumption_just,[status(thm)],[c_18990,c_1044,c_1047,c_18990]) ).

cnf(c_18993,plain,
    ( ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | join(sK334,meet(sK334,X1,X0),X0) = X0 ),
    inference(renaming,[status(thm)],[c_18992]) ).

cnf(c_19187,plain,
    ( X0 != sK334
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | ~ meet_absorbing(X0)
    | join(X0,meet(X0,X2,X1),X1) = X1
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_370,c_1044]) ).

cnf(c_19188,plain,
    ( ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | ~ meet_absorbing(sK334)
    | join(sK334,meet(sK334,X1,X0),X0) = X0
    | empty_carrier(sK334) ),
    inference(unflattening,[status(thm)],[c_19187]) ).

cnf(c_19189,plain,
    ( join(sK334,meet(sK334,X1,X0),X0) = X0
    | ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334)) ),
    inference(global_subsumption_just,[status(thm)],[c_19188,c_18993]) ).

cnf(c_19190,plain,
    ( ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | join(sK334,meet(sK334,X1,X0),X0) = X0 ),
    inference(renaming,[status(thm)],[c_19189]) ).

cnf(c_19243,plain,
    ( X0 != sK334
    | meet_semilatt_str(X0) ),
    inference(resolution_lifted,[status(thm)],[c_2519,c_1044]) ).

cnf(c_19244,plain,
    meet_semilatt_str(sK334),
    inference(unflattening,[status(thm)],[c_19243]) ).

cnf(c_19248,plain,
    ( X0 != sK334
    | join_semilatt_str(X0) ),
    inference(resolution_lifted,[status(thm)],[c_2472,c_1044]) ).

cnf(c_19249,plain,
    join_semilatt_str(sK334),
    inference(unflattening,[status(thm)],[c_19248]) ).

cnf(c_19279,plain,
    ( ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | meet_commut(sK334,X0,X1) = meet(sK334,X0,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_18567,c_19244]) ).

cnf(c_19280,plain,
    ( ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | meet_commut(sK334,X0,X1) = meet_commut(sK334,X1,X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_18603,c_19244]) ).

cnf(c_19554,plain,
    ( X0 != sK334
    | ~ element(X1,the_carrier(X0))
    | ~ element(X2,the_carrier(X0))
    | element(meet(X0,X1,X2),the_carrier(X0))
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_398,c_19244]) ).

cnf(c_19555,plain,
    ( ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | element(meet(sK334,X0,X1),the_carrier(sK334))
    | empty_carrier(sK334) ),
    inference(unflattening,[status(thm)],[c_19554]) ).

cnf(c_19557,plain,
    ( element(meet(sK334,X0,X1),the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | ~ element(X0,the_carrier(sK334)) ),
    inference(global_subsumption_just,[status(thm)],[c_19555,c_1047,c_19555]) ).

cnf(c_19558,plain,
    ( ~ element(X0,the_carrier(sK334))
    | ~ element(X1,the_carrier(sK334))
    | element(meet(sK334,X0,X1),the_carrier(sK334)) ),
    inference(renaming,[status(thm)],[c_19557]) ).

cnf(c_138050,plain,
    ( ~ element(X0,the_carrier(sK334))
    | join(sK334,meet(sK334,sK336,X0),X0) = X0 ),
    inference(superposition,[status(thm)],[c_1042,c_19190]) ).

cnf(c_138063,plain,
    join(sK334,meet(sK334,sK336,sK335),sK335) = sK335,
    inference(superposition,[status(thm)],[c_1043,c_138050]) ).

cnf(c_138152,plain,
    ( ~ element(X0,the_carrier(sK334))
    | meet_commut(sK334,X0,sK336) = meet(sK334,X0,sK336) ),
    inference(superposition,[status(thm)],[c_1042,c_19279]) ).

cnf(c_138153,plain,
    ( ~ element(X0,the_carrier(sK334))
    | meet_commut(sK334,X0,sK335) = meet(sK334,X0,sK335) ),
    inference(superposition,[status(thm)],[c_1043,c_19279]) ).

cnf(c_138183,plain,
    meet_commut(sK334,sK335,sK336) = meet(sK334,sK335,sK336),
    inference(superposition,[status(thm)],[c_1043,c_138152]) ).

cnf(c_138220,plain,
    ( ~ element(sK335,the_carrier(sK334))
    | ~ element(sK336,the_carrier(sK334))
    | element(meet_commut(sK334,sK335,sK336),the_carrier(sK334)) ),
    inference(superposition,[status(thm)],[c_138183,c_19558]) ).

cnf(c_138221,plain,
    element(meet_commut(sK334,sK335,sK336),the_carrier(sK334)),
    inference(forward_subsumption_resolution,[status(thm)],[c_138220,c_1042,c_1043]) ).

cnf(c_138237,plain,
    meet_commut(sK334,sK336,sK335) = meet(sK334,sK336,sK335),
    inference(superposition,[status(thm)],[c_1042,c_138153]) ).

cnf(c_138253,plain,
    join(sK334,meet_commut(sK334,sK336,sK335),sK335) = sK335,
    inference(demodulation,[status(thm)],[c_138063,c_138237]) ).

cnf(c_138598,plain,
    ( ~ element(X0,the_carrier(sK334))
    | meet_commut(sK334,X0,sK336) = meet_commut(sK334,sK336,X0) ),
    inference(superposition,[status(thm)],[c_1042,c_19280]) ).

cnf(c_138677,plain,
    meet_commut(sK334,sK335,sK336) = meet_commut(sK334,sK336,sK335),
    inference(superposition,[status(thm)],[c_1043,c_138598]) ).

cnf(c_138711,plain,
    join(sK334,meet_commut(sK334,sK335,sK336),sK335) = sK335,
    inference(demodulation,[status(thm)],[c_138253,c_138677]) ).

cnf(c_138723,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_138711,c_138221,c_19249,c_18634]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU304+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.11/0.33  % Computer : n007.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  : 300
% 0.11/0.33  % DateTime : Wed Aug 23 19:34:25 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.17/0.45  Running first-order theorem proving
% 0.17/0.45  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 23.31/4.10  % SZS status Started for theBenchmark.p
% 23.31/4.10  % SZS status Theorem for theBenchmark.p
% 23.31/4.10  
% 23.31/4.10  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 23.31/4.10  
% 23.31/4.10  ------  iProver source info
% 23.31/4.10  
% 23.31/4.10  git: date: 2023-05-31 18:12:56 +0000
% 23.31/4.10  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 23.31/4.10  git: non_committed_changes: false
% 23.31/4.10  git: last_make_outside_of_git: false
% 23.31/4.10  
% 23.31/4.10  ------ Parsing...
% 23.31/4.10  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 23.31/4.10  
% 23.31/4.10  ------ Preprocessing... sup_sim: 95  sf_s  rm: 21 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e  sup_sim: 0  sf_s  rm: 18 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 18 0s  sf_e  pe_s  pe_e 
% 23.31/4.10  
% 23.31/4.10  ------ Preprocessing... gs_s  sp: 15 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 23.31/4.10  
% 23.31/4.10  ------ Preprocessing... sf_s  rm: 3 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 23.31/4.10  ------ Proving...
% 23.31/4.10  ------ Problem Properties 
% 23.31/4.10  
% 23.31/4.10  
% 23.31/4.10  clauses                                 1109
% 23.31/4.10  conjectures                             4
% 23.31/4.10  EPR                                     173
% 23.31/4.10  Horn                                    820
% 23.31/4.10  unary                                   161
% 23.31/4.10  binary                                  334
% 23.31/4.10  lits                                    3272
% 23.31/4.10  lits eq                                 478
% 23.31/4.10  fd_pure                                 0
% 23.31/4.10  fd_pseudo                               0
% 23.31/4.10  fd_cond                                 44
% 23.31/4.10  fd_pseudo_cond                          115
% 23.31/4.10  AC symbols                              0
% 23.31/4.10  
% 23.31/4.10  ------ Schedule dynamic 5 is on 
% 23.31/4.10  
% 23.31/4.10  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 23.31/4.10  
% 23.31/4.10  
% 23.31/4.10  ------ 
% 23.31/4.10  Current options:
% 23.31/4.10  ------ 
% 23.31/4.10  
% 23.31/4.10  
% 23.31/4.10  
% 23.31/4.10  
% 23.31/4.10  ------ Proving...
% 23.31/4.10  
% 23.31/4.10  
% 23.31/4.10  % SZS status Theorem for theBenchmark.p
% 23.31/4.10  
% 23.31/4.10  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 23.31/4.11  
% 23.31/4.11  
%------------------------------------------------------------------------------