TSTP Solution File: SEU310+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU310+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n020.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 03:05:26 EDT 2024

% Result   : Theorem 3.93s 1.18s
% Output   : CNFRefutation 3.93s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ! [X0,X1] :
      ( ( element(X1,powerset(powerset(the_carrier(X0))))
        & top_str(X0)
        & topological_space(X0) )
     => ? [X2] :
        ! [X3] :
          ( in(X3,X2)
        <=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
            & in(X3,powerset(the_carrier(X0))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).

fof(f2,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( element(X1,powerset(powerset(the_carrier(X0))))
          & top_str(X0)
          & topological_space(X0) )
       => ? [X2] :
          ! [X3] :
            ( in(X3,X2)
          <=> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
              & in(X3,powerset(the_carrier(X0))) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f37,axiom,
    ! [X0,X1] :
      ( ( element(X1,powerset(powerset(the_carrier(X0))))
        & top_str(X0)
        & topological_space(X0) )
     => ( ! [X2,X3,X4] :
            ( ( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
              & X2 = X4
              & in(set_difference(cast_as_carrier_subset(X0),X3),X1)
              & X2 = X3 )
           => X3 = X4 )
       => ? [X2] :
          ! [X3] :
            ( in(X3,X2)
          <=> ? [X4] :
                ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
                & X3 = X4
                & in(X4,powerset(the_carrier(X0))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e2_37_1_1__pre_topc__1) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ( element(X1,powerset(powerset(the_carrier(X0))))
        & top_str(X0)
        & topological_space(X0) )
     => ( ! [X2,X3,X4] :
            ( ( in(set_difference(cast_as_carrier_subset(X0),X4),X1)
              & X2 = X4
              & in(set_difference(cast_as_carrier_subset(X0),X3),X1)
              & X2 = X3 )
           => X3 = X4 )
       => ? [X5] :
          ! [X6] :
            ( in(X6,X5)
          <=> ? [X7] :
                ( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
                & X6 = X7
                & in(X7,powerset(the_carrier(X0))) ) ) ) ),
    inference(rectify,[],[f37]) ).

fof(f56,plain,
    ? [X0,X1] :
      ( ! [X2] :
        ? [X3] :
          ( in(X3,X2)
        <~> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
            & in(X3,powerset(the_carrier(X0))) ) )
      & element(X1,powerset(powerset(the_carrier(X0))))
      & top_str(X0)
      & topological_space(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f57,plain,
    ? [X0,X1] :
      ( ! [X2] :
        ? [X3] :
          ( in(X3,X2)
        <~> ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
            & in(X3,powerset(the_carrier(X0))) ) )
      & element(X1,powerset(powerset(the_carrier(X0))))
      & top_str(X0)
      & topological_space(X0) ),
    inference(flattening,[],[f56]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( ? [X5] :
        ! [X6] :
          ( in(X6,X5)
        <=> ? [X7] :
              ( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
              & X6 = X7
              & in(X7,powerset(the_carrier(X0))) ) )
      | ? [X2,X3,X4] :
          ( X3 != X4
          & in(set_difference(cast_as_carrier_subset(X0),X4),X1)
          & X2 = X4
          & in(set_difference(cast_as_carrier_subset(X0),X3),X1)
          & X2 = X3 )
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ? [X5] :
        ! [X6] :
          ( in(X6,X5)
        <=> ? [X7] :
              ( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
              & X6 = X7
              & in(X7,powerset(the_carrier(X0))) ) )
      | ? [X2,X3,X4] :
          ( X3 != X4
          & in(set_difference(cast_as_carrier_subset(X0),X4),X1)
          & X2 = X4
          & in(set_difference(cast_as_carrier_subset(X0),X3),X1)
          & X2 = X3 )
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(flattening,[],[f79]) ).

fof(f81,plain,
    ! [X1,X0] :
      ( ? [X2,X3,X4] :
          ( X3 != X4
          & in(set_difference(cast_as_carrier_subset(X0),X4),X1)
          & X2 = X4
          & in(set_difference(cast_as_carrier_subset(X0),X3),X1)
          & X2 = X3 )
      | ~ sP0(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ? [X5] :
        ! [X6] :
          ( in(X6,X5)
        <=> ? [X7] :
              ( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
              & X6 = X7
              & in(X7,powerset(the_carrier(X0))) ) )
      | sP0(X1,X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(definition_folding,[],[f80,f81]) ).

fof(f83,plain,
    ? [X0,X1] :
      ( ! [X2] :
        ? [X3] :
          ( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
            | ~ in(X3,powerset(the_carrier(X0)))
            | ~ in(X3,X2) )
          & ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
              & in(X3,powerset(the_carrier(X0))) )
            | in(X3,X2) ) )
      & element(X1,powerset(powerset(the_carrier(X0))))
      & top_str(X0)
      & topological_space(X0) ),
    inference(nnf_transformation,[],[f57]) ).

fof(f84,plain,
    ? [X0,X1] :
      ( ! [X2] :
        ? [X3] :
          ( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
            | ~ in(X3,powerset(the_carrier(X0)))
            | ~ in(X3,X2) )
          & ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
              & in(X3,powerset(the_carrier(X0))) )
            | in(X3,X2) ) )
      & element(X1,powerset(powerset(the_carrier(X0))))
      & top_str(X0)
      & topological_space(X0) ),
    inference(flattening,[],[f83]) ).

fof(f85,plain,
    ( ? [X0,X1] :
        ( ! [X2] :
          ? [X3] :
            ( ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
              | ~ in(X3,powerset(the_carrier(X0)))
              | ~ in(X3,X2) )
            & ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
                & in(X3,powerset(the_carrier(X0))) )
              | in(X3,X2) ) )
        & element(X1,powerset(powerset(the_carrier(X0))))
        & top_str(X0)
        & topological_space(X0) )
   => ( ! [X2] :
        ? [X3] :
          ( ( ~ in(set_difference(cast_as_carrier_subset(sK1),X3),sK2)
            | ~ in(X3,powerset(the_carrier(sK1)))
            | ~ in(X3,X2) )
          & ( ( in(set_difference(cast_as_carrier_subset(sK1),X3),sK2)
              & in(X3,powerset(the_carrier(sK1))) )
            | in(X3,X2) ) )
      & element(sK2,powerset(powerset(the_carrier(sK1))))
      & top_str(sK1)
      & topological_space(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X2] :
      ( ? [X3] :
          ( ( ~ in(set_difference(cast_as_carrier_subset(sK1),X3),sK2)
            | ~ in(X3,powerset(the_carrier(sK1)))
            | ~ in(X3,X2) )
          & ( ( in(set_difference(cast_as_carrier_subset(sK1),X3),sK2)
              & in(X3,powerset(the_carrier(sK1))) )
            | in(X3,X2) ) )
     => ( ( ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
          | ~ in(sK3(X2),powerset(the_carrier(sK1)))
          | ~ in(sK3(X2),X2) )
        & ( ( in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
            & in(sK3(X2),powerset(the_carrier(sK1))) )
          | in(sK3(X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ( ! [X2] :
        ( ( ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
          | ~ in(sK3(X2),powerset(the_carrier(sK1)))
          | ~ in(sK3(X2),X2) )
        & ( ( in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
            & in(sK3(X2),powerset(the_carrier(sK1))) )
          | in(sK3(X2),X2) ) )
    & element(sK2,powerset(powerset(the_carrier(sK1))))
    & top_str(sK1)
    & topological_space(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f84,f86,f85]) ).

fof(f96,plain,
    ! [X1,X0] :
      ( ? [X2,X3,X4] :
          ( X3 != X4
          & in(set_difference(cast_as_carrier_subset(X0),X4),X1)
          & X2 = X4
          & in(set_difference(cast_as_carrier_subset(X0),X3),X1)
          & X2 = X3 )
      | ~ sP0(X1,X0) ),
    inference(nnf_transformation,[],[f81]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ? [X2,X3,X4] :
          ( X3 != X4
          & in(set_difference(cast_as_carrier_subset(X1),X4),X0)
          & X2 = X4
          & in(set_difference(cast_as_carrier_subset(X1),X3),X0)
          & X2 = X3 )
      | ~ sP0(X0,X1) ),
    inference(rectify,[],[f96]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ? [X2,X3,X4] :
          ( X3 != X4
          & in(set_difference(cast_as_carrier_subset(X1),X4),X0)
          & X2 = X4
          & in(set_difference(cast_as_carrier_subset(X1),X3),X0)
          & X2 = X3 )
     => ( sK9(X0,X1) != sK10(X0,X1)
        & in(set_difference(cast_as_carrier_subset(X1),sK10(X0,X1)),X0)
        & sK8(X0,X1) = sK10(X0,X1)
        & in(set_difference(cast_as_carrier_subset(X1),sK9(X0,X1)),X0)
        & sK8(X0,X1) = sK9(X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ( sK9(X0,X1) != sK10(X0,X1)
        & in(set_difference(cast_as_carrier_subset(X1),sK10(X0,X1)),X0)
        & sK8(X0,X1) = sK10(X0,X1)
        & in(set_difference(cast_as_carrier_subset(X1),sK9(X0,X1)),X0)
        & sK8(X0,X1) = sK9(X0,X1) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f97,f98]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ? [X5] :
        ! [X6] :
          ( ( in(X6,X5)
            | ! [X7] :
                ( ~ in(set_difference(cast_as_carrier_subset(X0),X6),X1)
                | X6 != X7
                | ~ in(X7,powerset(the_carrier(X0))) ) )
          & ( ? [X7] :
                ( in(set_difference(cast_as_carrier_subset(X0),X6),X1)
                & X6 = X7
                & in(X7,powerset(the_carrier(X0))) )
            | ~ in(X6,X5) ) )
      | sP0(X1,X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(nnf_transformation,[],[f82]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( in(X3,X2)
            | ! [X4] :
                ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
                | X3 != X4
                | ~ in(X4,powerset(the_carrier(X0))) ) )
          & ( ? [X5] :
                ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
                & X3 = X5
                & in(X5,powerset(the_carrier(X0))) )
            | ~ in(X3,X2) ) )
      | sP0(X1,X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(rectify,[],[f100]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ? [X2] :
        ! [X3] :
          ( ( in(X3,X2)
            | ! [X4] :
                ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
                | X3 != X4
                | ~ in(X4,powerset(the_carrier(X0))) ) )
          & ( ? [X5] :
                ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
                & X3 = X5
                & in(X5,powerset(the_carrier(X0))) )
            | ~ in(X3,X2) ) )
     => ! [X3] :
          ( ( in(X3,sK11(X0,X1))
            | ! [X4] :
                ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
                | X3 != X4
                | ~ in(X4,powerset(the_carrier(X0))) ) )
          & ( ? [X5] :
                ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
                & X3 = X5
                & in(X5,powerset(the_carrier(X0))) )
            | ~ in(X3,sK11(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ! [X0,X1,X3] :
      ( ? [X5] :
          ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
          & X3 = X5
          & in(X5,powerset(the_carrier(X0))) )
     => ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
        & sK12(X0,X1,X3) = X3
        & in(sK12(X0,X1,X3),powerset(the_carrier(X0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ! [X3] :
          ( ( in(X3,sK11(X0,X1))
            | ! [X4] :
                ( ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
                | X3 != X4
                | ~ in(X4,powerset(the_carrier(X0))) ) )
          & ( ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
              & sK12(X0,X1,X3) = X3
              & in(sK12(X0,X1,X3),powerset(the_carrier(X0))) )
            | ~ in(X3,sK11(X0,X1)) ) )
      | sP0(X1,X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f101,f103,f102]) ).

fof(f105,plain,
    topological_space(sK1),
    inference(cnf_transformation,[],[f87]) ).

fof(f106,plain,
    top_str(sK1),
    inference(cnf_transformation,[],[f87]) ).

fof(f107,plain,
    element(sK2,powerset(powerset(the_carrier(sK1)))),
    inference(cnf_transformation,[],[f87]) ).

fof(f108,plain,
    ! [X2] :
      ( in(sK3(X2),powerset(the_carrier(sK1)))
      | in(sK3(X2),X2) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f109,plain,
    ! [X2] :
      ( in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
      | in(sK3(X2),X2) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f110,plain,
    ! [X2] :
      ( ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X2)),sK2)
      | ~ in(sK3(X2),powerset(the_carrier(sK1)))
      | ~ in(sK3(X2),X2) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( sK8(X0,X1) = sK9(X0,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( sK8(X0,X1) = sK10(X0,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f169,plain,
    ! [X0,X1] :
      ( sK9(X0,X1) != sK10(X0,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f170,plain,
    ! [X3,X0,X1] :
      ( in(sK12(X0,X1,X3),powerset(the_carrier(X0)))
      | ~ in(X3,sK11(X0,X1))
      | sP0(X1,X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f171,plain,
    ! [X3,X0,X1] :
      ( sK12(X0,X1,X3) = X3
      | ~ in(X3,sK11(X0,X1))
      | sP0(X1,X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f172,plain,
    ! [X3,X0,X1] :
      ( in(set_difference(cast_as_carrier_subset(X0),X3),X1)
      | ~ in(X3,sK11(X0,X1))
      | sP0(X1,X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f173,plain,
    ! [X3,X0,X1,X4] :
      ( in(X3,sK11(X0,X1))
      | ~ in(set_difference(cast_as_carrier_subset(X0),X3),X1)
      | X3 != X4
      | ~ in(X4,powerset(the_carrier(X0)))
      | sP0(X1,X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f174,plain,
    ! [X0,X1,X4] :
      ( in(X4,sK11(X0,X1))
      | ~ in(set_difference(cast_as_carrier_subset(X0),X4),X1)
      | ~ in(X4,powerset(the_carrier(X0)))
      | sP0(X1,X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(equality_resolution,[],[f173]) ).

cnf(c_49,negated_conjecture,
    ( ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(X0)),sK2)
    | ~ in(sK3(X0),powerset(the_carrier(sK1)))
    | ~ in(sK3(X0),X0) ),
    inference(cnf_transformation,[],[f110]) ).

cnf(c_50,negated_conjecture,
    ( in(set_difference(cast_as_carrier_subset(sK1),sK3(X0)),sK2)
    | in(sK3(X0),X0) ),
    inference(cnf_transformation,[],[f109]) ).

cnf(c_51,negated_conjecture,
    ( in(sK3(X0),powerset(the_carrier(sK1)))
    | in(sK3(X0),X0) ),
    inference(cnf_transformation,[],[f108]) ).

cnf(c_52,negated_conjecture,
    element(sK2,powerset(powerset(the_carrier(sK1)))),
    inference(cnf_transformation,[],[f107]) ).

cnf(c_53,negated_conjecture,
    top_str(sK1),
    inference(cnf_transformation,[],[f106]) ).

cnf(c_54,negated_conjecture,
    topological_space(sK1),
    inference(cnf_transformation,[],[f105]) ).

cnf(c_109,plain,
    ( sK9(X0,X1) != sK10(X0,X1)
    | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f169]) ).

cnf(c_111,plain,
    ( ~ sP0(X0,X1)
    | sK10(X0,X1) = sK8(X0,X1) ),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_113,plain,
    ( ~ sP0(X0,X1)
    | sK9(X0,X1) = sK8(X0,X1) ),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_114,plain,
    ( ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2)
    | ~ element(X2,powerset(powerset(the_carrier(X0))))
    | ~ in(X1,powerset(the_carrier(X0)))
    | ~ top_str(X0)
    | ~ topological_space(X0)
    | in(X1,sK11(X0,X2))
    | sP0(X2,X0) ),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_115,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ in(X2,sK11(X1,X0))
    | ~ top_str(X1)
    | ~ topological_space(X1)
    | in(set_difference(cast_as_carrier_subset(X1),X2),X0)
    | sP0(X0,X1) ),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_116,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ in(X2,sK11(X1,X0))
    | ~ top_str(X1)
    | ~ topological_space(X1)
    | sK12(X1,X0,X2) = X2
    | sP0(X0,X1) ),
    inference(cnf_transformation,[],[f171]) ).

cnf(c_117,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ in(X2,sK11(X1,X0))
    | ~ top_str(X1)
    | ~ topological_space(X1)
    | in(sK12(X1,X0,X2),powerset(the_carrier(X1)))
    | sP0(X0,X1) ),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_811,plain,
    ( X0 != sK1
    | ~ element(X1,powerset(powerset(the_carrier(X0))))
    | ~ in(X2,sK11(X0,X1))
    | ~ top_str(X0)
    | in(sK12(X0,X1,X2),powerset(the_carrier(X0)))
    | sP0(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_54,c_117]) ).

cnf(c_812,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(sK1))))
    | ~ in(X1,sK11(sK1,X0))
    | ~ top_str(sK1)
    | in(sK12(sK1,X0,X1),powerset(the_carrier(sK1)))
    | sP0(X0,sK1) ),
    inference(unflattening,[status(thm)],[c_811]) ).

cnf(c_814,plain,
    ( ~ in(X1,sK11(sK1,X0))
    | ~ element(X0,powerset(powerset(the_carrier(sK1))))
    | in(sK12(sK1,X0,X1),powerset(the_carrier(sK1)))
    | sP0(X0,sK1) ),
    inference(global_subsumption_just,[status(thm)],[c_812,c_53,c_812]) ).

cnf(c_815,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(sK1))))
    | ~ in(X1,sK11(sK1,X0))
    | in(sK12(sK1,X0,X1),powerset(the_carrier(sK1)))
    | sP0(X0,sK1) ),
    inference(renaming,[status(thm)],[c_814]) ).

cnf(c_829,plain,
    ( X0 != sK1
    | ~ element(X1,powerset(powerset(the_carrier(X0))))
    | ~ in(X2,sK11(X0,X1))
    | ~ top_str(X0)
    | sK12(X0,X1,X2) = X2
    | sP0(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_54,c_116]) ).

cnf(c_830,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(sK1))))
    | ~ in(X1,sK11(sK1,X0))
    | ~ top_str(sK1)
    | sK12(sK1,X0,X1) = X1
    | sP0(X0,sK1) ),
    inference(unflattening,[status(thm)],[c_829]) ).

cnf(c_832,plain,
    ( ~ in(X1,sK11(sK1,X0))
    | ~ element(X0,powerset(powerset(the_carrier(sK1))))
    | sK12(sK1,X0,X1) = X1
    | sP0(X0,sK1) ),
    inference(global_subsumption_just,[status(thm)],[c_830,c_53,c_830]) ).

cnf(c_833,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(sK1))))
    | ~ in(X1,sK11(sK1,X0))
    | sK12(sK1,X0,X1) = X1
    | sP0(X0,sK1) ),
    inference(renaming,[status(thm)],[c_832]) ).

cnf(c_847,plain,
    ( X0 != sK1
    | ~ element(X1,powerset(powerset(the_carrier(X0))))
    | ~ in(X2,sK11(X0,X1))
    | ~ top_str(X0)
    | in(set_difference(cast_as_carrier_subset(X0),X2),X1)
    | sP0(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_54,c_115]) ).

cnf(c_848,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(sK1))))
    | ~ in(X1,sK11(sK1,X0))
    | ~ top_str(sK1)
    | in(set_difference(cast_as_carrier_subset(sK1),X1),X0)
    | sP0(X0,sK1) ),
    inference(unflattening,[status(thm)],[c_847]) ).

cnf(c_850,plain,
    ( ~ in(X1,sK11(sK1,X0))
    | ~ element(X0,powerset(powerset(the_carrier(sK1))))
    | in(set_difference(cast_as_carrier_subset(sK1),X1),X0)
    | sP0(X0,sK1) ),
    inference(global_subsumption_just,[status(thm)],[c_848,c_53,c_848]) ).

cnf(c_851,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(sK1))))
    | ~ in(X1,sK11(sK1,X0))
    | in(set_difference(cast_as_carrier_subset(sK1),X1),X0)
    | sP0(X0,sK1) ),
    inference(renaming,[status(thm)],[c_850]) ).

cnf(c_865,plain,
    ( X0 != sK1
    | ~ in(set_difference(cast_as_carrier_subset(X0),X1),X2)
    | ~ element(X2,powerset(powerset(the_carrier(X0))))
    | ~ in(X1,powerset(the_carrier(X0)))
    | ~ top_str(X0)
    | in(X1,sK11(X0,X2))
    | sP0(X2,X0) ),
    inference(resolution_lifted,[status(thm)],[c_54,c_114]) ).

cnf(c_866,plain,
    ( ~ in(set_difference(cast_as_carrier_subset(sK1),X0),X1)
    | ~ element(X1,powerset(powerset(the_carrier(sK1))))
    | ~ in(X0,powerset(the_carrier(sK1)))
    | ~ top_str(sK1)
    | in(X0,sK11(sK1,X1))
    | sP0(X1,sK1) ),
    inference(unflattening,[status(thm)],[c_865]) ).

cnf(c_868,plain,
    ( ~ in(X0,powerset(the_carrier(sK1)))
    | ~ element(X1,powerset(powerset(the_carrier(sK1))))
    | ~ in(set_difference(cast_as_carrier_subset(sK1),X0),X1)
    | in(X0,sK11(sK1,X1))
    | sP0(X1,sK1) ),
    inference(global_subsumption_just,[status(thm)],[c_866,c_53,c_866]) ).

cnf(c_869,plain,
    ( ~ in(set_difference(cast_as_carrier_subset(sK1),X0),X1)
    | ~ element(X1,powerset(powerset(the_carrier(sK1))))
    | ~ in(X0,powerset(the_carrier(sK1)))
    | in(X0,sK11(sK1,X1))
    | sP0(X1,sK1) ),
    inference(renaming,[status(thm)],[c_868]) ).

cnf(c_2663,plain,
    the_carrier(sK1) = sP0_iProver_def,
    definition ).

cnf(c_2664,plain,
    powerset(sP0_iProver_def) = sP1_iProver_def,
    definition ).

cnf(c_2665,plain,
    powerset(sP1_iProver_def) = sP2_iProver_def,
    definition ).

cnf(c_2666,plain,
    cast_as_carrier_subset(sK1) = sP3_iProver_def,
    definition ).

cnf(c_2667,negated_conjecture,
    element(sK2,sP2_iProver_def),
    inference(demodulation,[status(thm)],[c_52,c_2663,c_2664,c_2665]) ).

cnf(c_2668,negated_conjecture,
    ( in(sK3(X0),X0)
    | in(sK3(X0),sP1_iProver_def) ),
    inference(demodulation,[status(thm)],[c_51]) ).

cnf(c_2669,negated_conjecture,
    ( in(set_difference(sP3_iProver_def,sK3(X0)),sK2)
    | in(sK3(X0),X0) ),
    inference(demodulation,[status(thm)],[c_50,c_2666]) ).

cnf(c_2670,negated_conjecture,
    ( ~ in(set_difference(sP3_iProver_def,sK3(X0)),sK2)
    | ~ in(sK3(X0),X0)
    | ~ in(sK3(X0),sP1_iProver_def) ),
    inference(demodulation,[status(thm)],[c_49]) ).

cnf(c_3052,plain,
    ( ~ in(X0,sK11(sK1,X1))
    | ~ element(X1,sP2_iProver_def)
    | in(set_difference(sP3_iProver_def,X0),X1)
    | sP0(X1,sK1) ),
    inference(light_normalisation,[status(thm)],[c_851,c_2663,c_2664,c_2665,c_2666]) ).

cnf(c_3061,plain,
    ( ~ element(X0,sP2_iProver_def)
    | in(set_difference(sP3_iProver_def,sK3(sK11(sK1,X0))),X0)
    | in(set_difference(sP3_iProver_def,sK3(sK11(sK1,X0))),sK2)
    | sP0(X0,sK1) ),
    inference(superposition,[status(thm)],[c_2669,c_3052]) ).

cnf(c_3094,plain,
    ( ~ in(X0,sK11(sK1,X1))
    | ~ element(X1,sP2_iProver_def)
    | sK12(sK1,X1,X0) = X0
    | sP0(X1,sK1) ),
    inference(light_normalisation,[status(thm)],[c_833,c_2663,c_2664,c_2665]) ).

cnf(c_3104,plain,
    ( ~ element(X0,sP2_iProver_def)
    | sK12(sK1,X0,sK3(sK11(sK1,X0))) = sK3(sK11(sK1,X0))
    | in(sK3(sK11(sK1,X0)),sP1_iProver_def)
    | sP0(X0,sK1) ),
    inference(superposition,[status(thm)],[c_2668,c_3094]) ).

cnf(c_3135,plain,
    ( ~ element(sK2,sP2_iProver_def)
    | in(set_difference(sP3_iProver_def,sK3(sK11(sK1,sK2))),sK2)
    | sP0(sK2,sK1) ),
    inference(equality_factoring,[status(thm)],[c_3061]) ).

cnf(c_3137,plain,
    ( in(set_difference(sP3_iProver_def,sK3(sK11(sK1,sK2))),sK2)
    | sP0(sK2,sK1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3135,c_2667]) ).

cnf(c_3164,plain,
    ( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
    | ~ in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
    | sP0(sK2,sK1) ),
    inference(superposition,[status(thm)],[c_3137,c_2670]) ).

cnf(c_3176,plain,
    ( ~ in(X0,sK11(sK1,X1))
    | ~ element(X1,sP2_iProver_def)
    | in(sK12(sK1,X1,X0),sP1_iProver_def)
    | sP0(X1,sK1) ),
    inference(light_normalisation,[status(thm)],[c_815,c_2663,c_2664,c_2665]) ).

cnf(c_3193,plain,
    ( ~ in(set_difference(sP3_iProver_def,X0),X1)
    | ~ in(X0,sP1_iProver_def)
    | ~ element(X1,sP2_iProver_def)
    | in(X0,sK11(sK1,X1))
    | sP0(X1,sK1) ),
    inference(light_normalisation,[status(thm)],[c_869,c_2663,c_2664,c_2665,c_2666]) ).

cnf(c_3208,plain,
    ( ~ in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
    | ~ element(sK2,sP2_iProver_def)
    | in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
    | sP0(sK2,sK1) ),
    inference(superposition,[status(thm)],[c_3137,c_3193]) ).

cnf(c_3209,plain,
    ( ~ in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
    | in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
    | sP0(sK2,sK1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3208,c_2667]) ).

cnf(c_3323,plain,
    ( ~ in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
    | sP0(sK2,sK1) ),
    inference(global_subsumption_just,[status(thm)],[c_3209,c_3164,c_3209]) ).

cnf(c_3329,plain,
    ( in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
    | sP0(sK2,sK1) ),
    inference(superposition,[status(thm)],[c_2668,c_3323]) ).

cnf(c_3330,plain,
    ( ~ element(sK2,sP2_iProver_def)
    | sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2))
    | sP0(sK2,sK1) ),
    inference(superposition,[status(thm)],[c_3104,c_3323]) ).

cnf(c_3333,plain,
    ( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2))
    | sP0(sK2,sK1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3330,c_2667]) ).

cnf(c_3430,plain,
    ( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2))
    | sK10(sK2,sK1) = sK8(sK2,sK1) ),
    inference(superposition,[status(thm)],[c_3333,c_111]) ).

cnf(c_3468,plain,
    ( sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2))
    | sK9(sK2,sK1) = sK8(sK2,sK1) ),
    inference(superposition,[status(thm)],[c_3333,c_113]) ).

cnf(c_3619,plain,
    ( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
    | ~ element(sK2,sP2_iProver_def)
    | sK10(sK2,sK1) = sK8(sK2,sK1)
    | in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
    | sP0(sK2,sK1) ),
    inference(superposition,[status(thm)],[c_3430,c_3176]) ).

cnf(c_3620,plain,
    ( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
    | sK10(sK2,sK1) = sK8(sK2,sK1)
    | in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
    | sP0(sK2,sK1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3619,c_2667]) ).

cnf(c_3680,plain,
    ( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
    | ~ element(sK2,sP2_iProver_def)
    | sK9(sK2,sK1) = sK8(sK2,sK1)
    | in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
    | sP0(sK2,sK1) ),
    inference(superposition,[status(thm)],[c_3468,c_3176]) ).

cnf(c_3681,plain,
    ( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
    | sK9(sK2,sK1) = sK8(sK2,sK1)
    | in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
    | sP0(sK2,sK1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3680,c_2667]) ).

cnf(c_3707,plain,
    ( sK10(sK2,sK1) = sK8(sK2,sK1)
    | sP0(sK2,sK1) ),
    inference(global_subsumption_just,[status(thm)],[c_3620,c_3323,c_3329,c_3620]) ).

cnf(c_3711,plain,
    sK10(sK2,sK1) = sK8(sK2,sK1),
    inference(forward_subsumption_resolution,[status(thm)],[c_3707,c_111]) ).

cnf(c_3716,plain,
    ( sK9(sK2,sK1) = sK8(sK2,sK1)
    | sP0(sK2,sK1) ),
    inference(global_subsumption_just,[status(thm)],[c_3681,c_3323,c_3329,c_3681]) ).

cnf(c_3718,plain,
    ( sK9(sK2,sK1) = sK10(sK2,sK1)
    | sP0(sK2,sK1) ),
    inference(light_normalisation,[status(thm)],[c_3716,c_3711]) ).

cnf(c_3723,plain,
    ( sK9(sK2,sK1) = sK10(sK2,sK1)
    | sK9(sK2,sK1) = sK8(sK2,sK1) ),
    inference(superposition,[status(thm)],[c_3718,c_113]) ).

cnf(c_3725,plain,
    sK9(sK2,sK1) = sK10(sK2,sK1),
    inference(light_normalisation,[status(thm)],[c_3723,c_3711]) ).

cnf(c_3939,plain,
    ~ sP0(sK2,sK1),
    inference(superposition,[status(thm)],[c_3725,c_109]) ).

cnf(c_3950,plain,
    sK12(sK1,sK2,sK3(sK11(sK1,sK2))) = sK3(sK11(sK1,sK2)),
    inference(backward_subsumption_resolution,[status(thm)],[c_3333,c_3939]) ).

cnf(c_3951,plain,
    in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2)),
    inference(backward_subsumption_resolution,[status(thm)],[c_3329,c_3939]) ).

cnf(c_3952,plain,
    ~ in(sK3(sK11(sK1,sK2)),sP1_iProver_def),
    inference(backward_subsumption_resolution,[status(thm)],[c_3323,c_3939]) ).

cnf(c_4021,plain,
    ( ~ in(sK3(sK11(sK1,sK2)),sK11(sK1,sK2))
    | ~ element(sK2,sP2_iProver_def)
    | in(sK3(sK11(sK1,sK2)),sP1_iProver_def)
    | sP0(sK2,sK1) ),
    inference(superposition,[status(thm)],[c_3950,c_3176]) ).

cnf(c_4022,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_4021,c_3939,c_3952,c_2667,c_3951]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SEU310+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n020.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May  2 17:28:31 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.93/1.18  % SZS status Started for theBenchmark.p
% 3.93/1.18  % SZS status Theorem for theBenchmark.p
% 3.93/1.18  
% 3.93/1.18  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.93/1.18  
% 3.93/1.18  ------  iProver source info
% 3.93/1.18  
% 3.93/1.18  git: date: 2024-05-02 19:28:25 +0000
% 3.93/1.18  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.93/1.18  git: non_committed_changes: false
% 3.93/1.18  
% 3.93/1.18  ------ Parsing...
% 3.93/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.93/1.18  
% 3.93/1.18  ------ Preprocessing... sup_sim: 0  sf_s  rm: 50 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 8 0s  sf_e  pe_s  pe_e 
% 3.93/1.18  
% 3.93/1.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.93/1.18  
% 3.93/1.18  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.93/1.18  ------ Proving...
% 3.93/1.18  ------ Problem Properties 
% 3.93/1.18  
% 3.93/1.18  
% 3.93/1.18  clauses                                 26
% 3.93/1.18  conjectures                             4
% 3.93/1.18  EPR                                     3
% 3.93/1.18  Horn                                    19
% 3.93/1.18  unary                                   11
% 3.93/1.18  binary                                  10
% 3.93/1.18  lits                                    51
% 3.93/1.18  lits eq                                 8
% 3.93/1.18  fd_pure                                 0
% 3.93/1.18  fd_pseudo                               0
% 3.93/1.18  fd_cond                                 0
% 3.93/1.18  fd_pseudo_cond                          0
% 3.93/1.18  AC symbols                              0
% 3.93/1.18  
% 3.93/1.18  ------ Schedule dynamic 5 is on 
% 3.93/1.18  
% 3.93/1.18  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.93/1.18  
% 3.93/1.18  
% 3.93/1.18  ------ 
% 3.93/1.18  Current options:
% 3.93/1.18  ------ 
% 3.93/1.18  
% 3.93/1.18  
% 3.93/1.18  
% 3.93/1.18  
% 3.93/1.18  ------ Proving...
% 3.93/1.18  
% 3.93/1.18  
% 3.93/1.18  % SZS status Theorem for theBenchmark.p
% 3.93/1.18  
% 3.93/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.93/1.19  
% 3.93/1.19  
%------------------------------------------------------------------------------