TSTP Solution File: SEU168+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU168+3 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n019.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 : Mon Jun 24 15:16:57 EDT 2024

% Result   : Theorem 6.93s 1.63s
% Output   : CNFRefutation 6.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  110 (   4 unt;   0 def)
%            Number of atoms       :  484 (  18 equ)
%            Maximal formula atoms :   22 (   4 avg)
%            Number of connectives :  625 ( 251   ~; 236   |; 115   &)
%                                         (   4 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   1 con; 0-2 aty)
%            Number of variables   :  263 (   0 sgn 135   !;  47   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f7,conjecture,
    ! [X0] :
    ? [X1] :
      ( ! [X2] :
          ~ ( ~ in(X2,X1)
            & ~ are_equipotent(X2,X1)
            & subset(X2,X1) )
      & ! [X2] :
          ( in(X2,X1)
         => in(powerset(X2),X1) )
      & ! [X2,X3] :
          ( ( subset(X3,X2)
            & in(X2,X1) )
         => in(X3,X1) )
      & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t136_zfmisc_1) ).

fof(f8,negated_conjecture,
    ~ ! [X0] :
      ? [X1] :
        ( ! [X2] :
            ~ ( ~ in(X2,X1)
              & ~ are_equipotent(X2,X1)
              & subset(X2,X1) )
        & ! [X2] :
            ( in(X2,X1)
           => in(powerset(X2),X1) )
        & ! [X2,X3] :
            ( ( subset(X3,X2)
              & in(X2,X1) )
           => in(X3,X1) )
        & in(X0,X1) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f9,axiom,
    ! [X0] :
    ? [X1] :
      ( ! [X2] :
          ~ ( ~ in(X2,X1)
            & ~ are_equipotent(X2,X1)
            & subset(X2,X1) )
      & ! [X2] :
          ~ ( ! [X3] :
                ~ ( ! [X4] :
                      ( subset(X4,X2)
                     => in(X4,X3) )
                  & in(X3,X1) )
            & in(X2,X1) )
      & ! [X2,X3] :
          ( ( subset(X3,X2)
            & in(X2,X1) )
         => in(X3,X1) )
      & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_tarski) ).

fof(f11,plain,
    ~ ! [X0] :
      ? [X1] :
        ( ! [X2] :
            ~ ( ~ in(X2,X1)
              & ~ are_equipotent(X2,X1)
              & subset(X2,X1) )
        & ! [X3] :
            ( in(X3,X1)
           => in(powerset(X3),X1) )
        & ! [X4,X5] :
            ( ( subset(X5,X4)
              & in(X4,X1) )
           => in(X5,X1) )
        & in(X0,X1) ),
    inference(rectify,[],[f8]) ).

fof(f12,plain,
    ! [X0] :
    ? [X1] :
      ( ! [X2] :
          ~ ( ~ in(X2,X1)
            & ~ are_equipotent(X2,X1)
            & subset(X2,X1) )
      & ! [X3] :
          ~ ( ! [X4] :
                ~ ( ! [X5] :
                      ( subset(X5,X3)
                     => in(X5,X4) )
                  & in(X4,X1) )
            & in(X3,X1) )
      & ! [X6,X7] :
          ( ( subset(X7,X6)
            & in(X6,X1) )
         => in(X7,X1) )
      & in(X0,X1) ),
    inference(rectify,[],[f9]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f15,plain,
    ? [X0] :
    ! [X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & ~ are_equipotent(X2,X1)
          & subset(X2,X1) )
      | ? [X3] :
          ( ~ in(powerset(X3),X1)
          & in(X3,X1) )
      | ? [X4,X5] :
          ( ~ in(X5,X1)
          & subset(X5,X4)
          & in(X4,X1) )
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f16,plain,
    ? [X0] :
    ! [X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & ~ are_equipotent(X2,X1)
          & subset(X2,X1) )
      | ? [X3] :
          ( ~ in(powerset(X3),X1)
          & in(X3,X1) )
      | ? [X4,X5] :
          ( ~ in(X5,X1)
          & subset(X5,X4)
          & in(X4,X1) )
      | ~ in(X0,X1) ),
    inference(flattening,[],[f15]) ).

fof(f17,plain,
    ! [X0] :
    ? [X1] :
      ( ! [X2] :
          ( in(X2,X1)
          | are_equipotent(X2,X1)
          | ~ subset(X2,X1) )
      & ! [X3] :
          ( ? [X4] :
              ( ! [X5] :
                  ( in(X5,X4)
                  | ~ subset(X5,X3) )
              & in(X4,X1) )
          | ~ in(X3,X1) )
      & ! [X6,X7] :
          ( in(X7,X1)
          | ~ subset(X7,X6)
          | ~ in(X6,X1) )
      & in(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f18,plain,
    ! [X0] :
    ? [X1] :
      ( ! [X2] :
          ( in(X2,X1)
          | are_equipotent(X2,X1)
          | ~ subset(X2,X1) )
      & ! [X3] :
          ( ? [X4] :
              ( ! [X5] :
                  ( in(X5,X4)
                  | ~ subset(X5,X3) )
              & in(X4,X1) )
          | ~ in(X3,X1) )
      & ! [X6,X7] :
          ( in(X7,X1)
          | ~ subset(X7,X6)
          | ~ in(X6,X1) )
      & in(X0,X1) ),
    inference(flattening,[],[f17]) ).

fof(f19,plain,
    ! [X1] :
      ( ? [X4,X5] :
          ( ~ in(X5,X1)
          & subset(X5,X4)
          & in(X4,X1) )
      | ~ sP0(X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f20,plain,
    ? [X0] :
    ! [X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & ~ are_equipotent(X2,X1)
          & subset(X2,X1) )
      | ? [X3] :
          ( ~ in(powerset(X3),X1)
          & in(X3,X1) )
      | sP0(X1)
      | ~ in(X0,X1) ),
    inference(definition_folding,[],[f16,f19]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ subset(X2,X0) )
            & ( subset(X2,X0)
              | ~ in(X2,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(rectify,[],[f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( subset(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ subset(sK1(X0,X1),X0)
          | ~ in(sK1(X0,X1),X1) )
        & ( subset(sK1(X0,X1),X0)
          | in(sK1(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ( ( ~ subset(sK1(X0,X1),X0)
            | ~ in(sK1(X0,X1),X1) )
          & ( subset(sK1(X0,X1),X0)
            | in(sK1(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f22,f23]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f25]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK2(X0,X1),X1)
        & in(sK2(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK2(X0,X1),X1)
          & in(sK2(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f26,f27]) ).

fof(f33,plain,
    ! [X1] :
      ( ? [X4,X5] :
          ( ~ in(X5,X1)
          & subset(X5,X4)
          & in(X4,X1) )
      | ~ sP0(X1) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f34,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( ~ in(X2,X0)
          & subset(X2,X1)
          & in(X1,X0) )
      | ~ sP0(X0) ),
    inference(rectify,[],[f33]) ).

fof(f35,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( ~ in(X2,X0)
          & subset(X2,X1)
          & in(X1,X0) )
     => ( ~ in(sK6(X0),X0)
        & subset(sK6(X0),sK5(X0))
        & in(sK5(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ! [X0] :
      ( ( ~ in(sK6(X0),X0)
        & subset(sK6(X0),sK5(X0))
        & in(sK5(X0),X0) )
      | ~ sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f34,f35]) ).

fof(f37,plain,
    ( ? [X0] :
      ! [X1] :
        ( ? [X2] :
            ( ~ in(X2,X1)
            & ~ are_equipotent(X2,X1)
            & subset(X2,X1) )
        | ? [X3] :
            ( ~ in(powerset(X3),X1)
            & in(X3,X1) )
        | sP0(X1)
        | ~ in(X0,X1) )
   => ! [X1] :
        ( ? [X2] :
            ( ~ in(X2,X1)
            & ~ are_equipotent(X2,X1)
            & subset(X2,X1) )
        | ? [X3] :
            ( ~ in(powerset(X3),X1)
            & in(X3,X1) )
        | sP0(X1)
        | ~ in(sK7,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f38,plain,
    ! [X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & ~ are_equipotent(X2,X1)
          & subset(X2,X1) )
     => ( ~ in(sK8(X1),X1)
        & ~ are_equipotent(sK8(X1),X1)
        & subset(sK8(X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,plain,
    ! [X1] :
      ( ? [X3] :
          ( ~ in(powerset(X3),X1)
          & in(X3,X1) )
     => ( ~ in(powerset(sK9(X1)),X1)
        & in(sK9(X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ! [X1] :
      ( ( ~ in(sK8(X1),X1)
        & ~ are_equipotent(sK8(X1),X1)
        & subset(sK8(X1),X1) )
      | ( ~ in(powerset(sK9(X1)),X1)
        & in(sK9(X1),X1) )
      | sP0(X1)
      | ~ in(sK7,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f20,f39,f38,f37]) ).

fof(f41,plain,
    ! [X0] :
      ( ? [X1] :
          ( ! [X2] :
              ( in(X2,X1)
              | are_equipotent(X2,X1)
              | ~ subset(X2,X1) )
          & ! [X3] :
              ( ? [X4] :
                  ( ! [X5] :
                      ( in(X5,X4)
                      | ~ subset(X5,X3) )
                  & in(X4,X1) )
              | ~ in(X3,X1) )
          & ! [X6,X7] :
              ( in(X7,X1)
              | ~ subset(X7,X6)
              | ~ in(X6,X1) )
          & in(X0,X1) )
     => ( ! [X2] :
            ( in(X2,sK10(X0))
            | are_equipotent(X2,sK10(X0))
            | ~ subset(X2,sK10(X0)) )
        & ! [X3] :
            ( ? [X4] :
                ( ! [X5] :
                    ( in(X5,X4)
                    | ~ subset(X5,X3) )
                & in(X4,sK10(X0)) )
            | ~ in(X3,sK10(X0)) )
        & ! [X7,X6] :
            ( in(X7,sK10(X0))
            | ~ subset(X7,X6)
            | ~ in(X6,sK10(X0)) )
        & in(X0,sK10(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ! [X0,X3] :
      ( ? [X4] :
          ( ! [X5] :
              ( in(X5,X4)
              | ~ subset(X5,X3) )
          & in(X4,sK10(X0)) )
     => ( ! [X5] :
            ( in(X5,sK11(X0,X3))
            | ~ subset(X5,X3) )
        & in(sK11(X0,X3),sK10(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f43,plain,
    ! [X0] :
      ( ! [X2] :
          ( in(X2,sK10(X0))
          | are_equipotent(X2,sK10(X0))
          | ~ subset(X2,sK10(X0)) )
      & ! [X3] :
          ( ( ! [X5] :
                ( in(X5,sK11(X0,X3))
                | ~ subset(X5,X3) )
            & in(sK11(X0,X3),sK10(X0)) )
          | ~ in(X3,sK10(X0)) )
      & ! [X6,X7] :
          ( in(X7,sK10(X0))
          | ~ subset(X7,X6)
          | ~ in(X6,sK10(X0)) )
      & in(X0,sK10(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f18,f42,f41]) ).

fof(f45,plain,
    ! [X3,X0,X1] :
      ( subset(X3,X0)
      | ~ in(X3,X1)
      | powerset(X0) != X1 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK2(X0,X1),X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK2(X0,X1),X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f55,plain,
    ! [X0] :
      ( in(sK5(X0),X0)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f56,plain,
    ! [X0] :
      ( subset(sK6(X0),sK5(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f57,plain,
    ! [X0] :
      ( ~ in(sK6(X0),X0)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f58,plain,
    ! [X1] :
      ( subset(sK8(X1),X1)
      | in(sK9(X1),X1)
      | sP0(X1)
      | ~ in(sK7,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f59,plain,
    ! [X1] :
      ( subset(sK8(X1),X1)
      | ~ in(powerset(sK9(X1)),X1)
      | sP0(X1)
      | ~ in(sK7,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f60,plain,
    ! [X1] :
      ( ~ are_equipotent(sK8(X1),X1)
      | in(sK9(X1),X1)
      | sP0(X1)
      | ~ in(sK7,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f61,plain,
    ! [X1] :
      ( ~ are_equipotent(sK8(X1),X1)
      | ~ in(powerset(sK9(X1)),X1)
      | sP0(X1)
      | ~ in(sK7,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f62,plain,
    ! [X1] :
      ( ~ in(sK8(X1),X1)
      | in(sK9(X1),X1)
      | sP0(X1)
      | ~ in(sK7,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f63,plain,
    ! [X1] :
      ( ~ in(sK8(X1),X1)
      | ~ in(powerset(sK9(X1)),X1)
      | sP0(X1)
      | ~ in(sK7,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f64,plain,
    ! [X0] : in(X0,sK10(X0)),
    inference(cnf_transformation,[],[f43]) ).

fof(f65,plain,
    ! [X0,X6,X7] :
      ( in(X7,sK10(X0))
      | ~ subset(X7,X6)
      | ~ in(X6,sK10(X0)) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f66,plain,
    ! [X3,X0] :
      ( in(sK11(X0,X3),sK10(X0))
      | ~ in(X3,sK10(X0)) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f67,plain,
    ! [X3,X0,X5] :
      ( in(X5,sK11(X0,X3))
      | ~ subset(X5,X3)
      | ~ in(X3,sK10(X0)) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f68,plain,
    ! [X2,X0] :
      ( in(X2,sK10(X0))
      | are_equipotent(X2,sK10(X0))
      | ~ subset(X2,sK10(X0)) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f70,plain,
    ! [X3,X0] :
      ( subset(X3,X0)
      | ~ in(X3,powerset(X0)) ),
    inference(equality_resolution,[],[f45]) ).

cnf(c_53,plain,
    ( ~ in(X0,powerset(X1))
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f70]) ).

cnf(c_54,plain,
    ( ~ in(sK2(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_55,plain,
    ( in(sK2(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f50]) ).

cnf(c_60,plain,
    ( ~ in(sK6(X0),X0)
    | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_61,plain,
    ( ~ sP0(X0)
    | subset(sK6(X0),sK5(X0)) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_62,plain,
    ( ~ sP0(X0)
    | in(sK5(X0),X0) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_63,negated_conjecture,
    ( ~ in(powerset(sK9(X0)),X0)
    | ~ in(sK8(X0),X0)
    | ~ in(sK7,X0)
    | sP0(X0) ),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_64,negated_conjecture,
    ( ~ in(sK8(X0),X0)
    | ~ in(sK7,X0)
    | in(sK9(X0),X0)
    | sP0(X0) ),
    inference(cnf_transformation,[],[f62]) ).

cnf(c_65,negated_conjecture,
    ( ~ in(powerset(sK9(X0)),X0)
    | ~ are_equipotent(sK8(X0),X0)
    | ~ in(sK7,X0)
    | sP0(X0) ),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_66,negated_conjecture,
    ( ~ are_equipotent(sK8(X0),X0)
    | ~ in(sK7,X0)
    | in(sK9(X0),X0)
    | sP0(X0) ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_67,negated_conjecture,
    ( ~ in(powerset(sK9(X0)),X0)
    | ~ in(sK7,X0)
    | subset(sK8(X0),X0)
    | sP0(X0) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_68,negated_conjecture,
    ( ~ in(sK7,X0)
    | in(sK9(X0),X0)
    | subset(sK8(X0),X0)
    | sP0(X0) ),
    inference(cnf_transformation,[],[f58]) ).

cnf(c_69,plain,
    ( ~ subset(X0,sK10(X1))
    | in(X0,sK10(X1))
    | are_equipotent(X0,sK10(X1)) ),
    inference(cnf_transformation,[],[f68]) ).

cnf(c_70,plain,
    ( ~ in(X0,sK10(X1))
    | ~ subset(X2,X0)
    | in(X2,sK11(X1,X0)) ),
    inference(cnf_transformation,[],[f67]) ).

cnf(c_71,plain,
    ( ~ in(X0,sK10(X1))
    | in(sK11(X1,X0),sK10(X1)) ),
    inference(cnf_transformation,[],[f66]) ).

cnf(c_72,plain,
    ( ~ in(X0,sK10(X1))
    | ~ subset(X2,X0)
    | in(X2,sK10(X1)) ),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_73,plain,
    in(X0,sK10(X0)),
    inference(cnf_transformation,[],[f64]) ).

cnf(c_75,plain,
    in(sK7,sK10(sK7)),
    inference(instantiation,[status(thm)],[c_73]) ).

cnf(c_99,plain,
    ( ~ in(sK6(X0),X0)
    | ~ sP0(X0) ),
    inference(prop_impl_just,[status(thm)],[c_60]) ).

cnf(c_103,plain,
    ( ~ sP0(X0)
    | subset(sK6(X0),sK5(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_61]) ).

cnf(c_105,plain,
    ( ~ sP0(X0)
    | in(sK5(X0),X0) ),
    inference(prop_impl_just,[status(thm)],[c_62]) ).

cnf(c_298,plain,
    ( sK8(X0) != X1
    | sK10(X2) != X0
    | ~ subset(X1,sK10(X2))
    | ~ in(sK7,X0)
    | in(sK9(X0),X0)
    | in(X1,sK10(X2))
    | sP0(X0) ),
    inference(resolution_lifted,[status(thm)],[c_66,c_69]) ).

cnf(c_299,plain,
    ( ~ subset(sK8(sK10(X0)),sK10(X0))
    | ~ in(sK7,sK10(X0))
    | in(sK8(sK10(X0)),sK10(X0))
    | in(sK9(sK10(X0)),sK10(X0))
    | sP0(sK10(X0)) ),
    inference(unflattening,[status(thm)],[c_298]) ).

cnf(c_311,plain,
    ( ~ in(sK7,sK10(X0))
    | in(sK9(sK10(X0)),sK10(X0))
    | sP0(sK10(X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_299,c_64,c_68]) ).

cnf(c_316,plain,
    ( sK8(X0) != X1
    | sK10(X2) != X0
    | ~ in(powerset(sK9(X0)),X0)
    | ~ subset(X1,sK10(X2))
    | ~ in(sK7,X0)
    | in(X1,sK10(X2))
    | sP0(X0) ),
    inference(resolution_lifted,[status(thm)],[c_65,c_69]) ).

cnf(c_317,plain,
    ( ~ in(powerset(sK9(sK10(X0))),sK10(X0))
    | ~ subset(sK8(sK10(X0)),sK10(X0))
    | ~ in(sK7,sK10(X0))
    | in(sK8(sK10(X0)),sK10(X0))
    | sP0(sK10(X0)) ),
    inference(unflattening,[status(thm)],[c_316]) ).

cnf(c_329,plain,
    ( ~ in(powerset(sK9(sK10(X0))),sK10(X0))
    | ~ in(sK7,sK10(X0))
    | sP0(sK10(X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_317,c_63,c_67]) ).

cnf(c_508,plain,
    ( sK10(X0) != X1
    | ~ in(powerset(sK9(sK10(X0))),sK10(X0))
    | ~ in(sK7,sK10(X0))
    | in(sK5(X1),X1) ),
    inference(resolution_lifted,[status(thm)],[c_105,c_329]) ).

cnf(c_509,plain,
    ( ~ in(powerset(sK9(sK10(X0))),sK10(X0))
    | ~ in(sK7,sK10(X0))
    | in(sK5(sK10(X0)),sK10(X0)) ),
    inference(unflattening,[status(thm)],[c_508]) ).

cnf(c_520,plain,
    ( sK10(X0) != X1
    | ~ in(sK7,sK10(X0))
    | in(sK9(sK10(X0)),sK10(X0))
    | in(sK5(X1),X1) ),
    inference(resolution_lifted,[status(thm)],[c_105,c_311]) ).

cnf(c_521,plain,
    ( ~ in(sK7,sK10(X0))
    | in(sK5(sK10(X0)),sK10(X0))
    | in(sK9(sK10(X0)),sK10(X0)) ),
    inference(unflattening,[status(thm)],[c_520]) ).

cnf(c_532,plain,
    ( sK10(X0) != X1
    | ~ in(powerset(sK9(sK10(X0))),sK10(X0))
    | ~ in(sK7,sK10(X0))
    | subset(sK6(X1),sK5(X1)) ),
    inference(resolution_lifted,[status(thm)],[c_103,c_329]) ).

cnf(c_533,plain,
    ( ~ in(powerset(sK9(sK10(X0))),sK10(X0))
    | ~ in(sK7,sK10(X0))
    | subset(sK6(sK10(X0)),sK5(sK10(X0))) ),
    inference(unflattening,[status(thm)],[c_532]) ).

cnf(c_544,plain,
    ( sK10(X0) != X1
    | ~ in(sK7,sK10(X0))
    | in(sK9(sK10(X0)),sK10(X0))
    | subset(sK6(X1),sK5(X1)) ),
    inference(resolution_lifted,[status(thm)],[c_103,c_311]) ).

cnf(c_545,plain,
    ( ~ in(sK7,sK10(X0))
    | subset(sK6(sK10(X0)),sK5(sK10(X0)))
    | in(sK9(sK10(X0)),sK10(X0)) ),
    inference(unflattening,[status(thm)],[c_544]) ).

cnf(c_556,plain,
    ( sK10(X0) != X1
    | ~ in(powerset(sK9(sK10(X0))),sK10(X0))
    | ~ in(sK6(X1),X1)
    | ~ in(sK7,sK10(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_99,c_329]) ).

cnf(c_557,plain,
    ( ~ in(powerset(sK9(sK10(X0))),sK10(X0))
    | ~ in(sK6(sK10(X0)),sK10(X0))
    | ~ in(sK7,sK10(X0)) ),
    inference(unflattening,[status(thm)],[c_556]) ).

cnf(c_568,plain,
    ( sK10(X0) != X1
    | ~ in(sK6(X1),X1)
    | ~ in(sK7,sK10(X0))
    | in(sK9(sK10(X0)),sK10(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_99,c_311]) ).

cnf(c_569,plain,
    ( ~ in(sK6(sK10(X0)),sK10(X0))
    | ~ in(sK7,sK10(X0))
    | in(sK9(sK10(X0)),sK10(X0)) ),
    inference(unflattening,[status(thm)],[c_568]) ).

cnf(c_3082,plain,
    ( ~ subset(sK6(sK10(X0)),X1)
    | ~ in(X1,sK10(X0))
    | in(sK6(sK10(X0)),sK10(X0)) ),
    inference(instantiation,[status(thm)],[c_72]) ).

cnf(c_3110,plain,
    ( subset(sK2(powerset(X0),X1),X0)
    | subset(powerset(X0),X1) ),
    inference(superposition,[status(thm)],[c_55,c_53]) ).

cnf(c_3329,plain,
    ( ~ subset(X0,sK11(X1,X2))
    | ~ in(X2,sK10(X1))
    | in(X0,sK10(X1)) ),
    inference(superposition,[status(thm)],[c_71,c_72]) ).

cnf(c_3362,plain,
    ( ~ subset(sK6(sK10(X0)),sK5(sK10(X0)))
    | ~ in(sK5(sK10(X0)),sK10(X0))
    | in(sK6(sK10(X0)),sK10(X0)) ),
    inference(instantiation,[status(thm)],[c_3082]) ).

cnf(c_3366,plain,
    ( ~ subset(sK2(X0,sK11(X1,X2)),X2)
    | ~ in(X2,sK10(X1))
    | subset(X0,sK11(X1,X2)) ),
    inference(superposition,[status(thm)],[c_70,c_54]) ).

cnf(c_3431,plain,
    ( in(sK9(sK10(X0)),sK10(X0))
    | ~ in(sK7,sK10(X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_311,c_521,c_545,c_569,c_3362]) ).

cnf(c_3432,plain,
    ( ~ in(sK7,sK10(X0))
    | in(sK9(sK10(X0)),sK10(X0)) ),
    inference(renaming,[status(thm)],[c_3431]) ).

cnf(c_3433,plain,
    ( ~ in(sK7,sK10(sK7))
    | in(sK9(sK10(sK7)),sK10(sK7)) ),
    inference(instantiation,[status(thm)],[c_3432]) ).

cnf(c_3442,plain,
    ( ~ in(sK7,sK10(X0))
    | ~ in(powerset(sK9(sK10(X0))),sK10(X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_329,c_509,c_533,c_557,c_3362]) ).

cnf(c_3443,plain,
    ( ~ in(powerset(sK9(sK10(X0))),sK10(X0))
    | ~ in(sK7,sK10(X0)) ),
    inference(renaming,[status(thm)],[c_3442]) ).

cnf(c_3444,plain,
    ( ~ in(powerset(sK9(sK10(sK7))),sK10(sK7))
    | ~ in(sK7,sK10(sK7)) ),
    inference(instantiation,[status(thm)],[c_3443]) ).

cnf(c_4875,plain,
    ( ~ subset(sK2(powerset(X0),sK11(X1,X0)),X0)
    | ~ in(X0,sK10(X1))
    | subset(powerset(X0),sK11(X1,X0)) ),
    inference(instantiation,[status(thm)],[c_3366]) ).

cnf(c_4913,plain,
    ( ~ subset(powerset(sK9(sK10(X0))),sK11(X0,X1))
    | ~ in(X1,sK10(X0))
    | in(powerset(sK9(sK10(X0))),sK10(X0)) ),
    inference(instantiation,[status(thm)],[c_3329]) ).

cnf(c_5677,plain,
    ( ~ subset(sK2(powerset(sK9(sK10(X0))),sK11(X1,sK9(sK10(X0)))),sK9(sK10(X0)))
    | ~ in(sK9(sK10(X0)),sK10(X1))
    | subset(powerset(sK9(sK10(X0))),sK11(X1,sK9(sK10(X0)))) ),
    inference(instantiation,[status(thm)],[c_4875]) ).

cnf(c_5678,plain,
    ( ~ subset(sK2(powerset(sK9(sK10(sK7))),sK11(sK7,sK9(sK10(sK7)))),sK9(sK10(sK7)))
    | ~ in(sK9(sK10(sK7)),sK10(sK7))
    | subset(powerset(sK9(sK10(sK7))),sK11(sK7,sK9(sK10(sK7)))) ),
    inference(instantiation,[status(thm)],[c_5677]) ).

cnf(c_5989,plain,
    ( ~ subset(powerset(sK9(sK10(X0))),sK11(X0,sK9(sK10(X0))))
    | ~ in(sK9(sK10(X0)),sK10(X0))
    | in(powerset(sK9(sK10(X0))),sK10(X0)) ),
    inference(instantiation,[status(thm)],[c_4913]) ).

cnf(c_5990,plain,
    ( ~ subset(powerset(sK9(sK10(sK7))),sK11(sK7,sK9(sK10(sK7))))
    | ~ in(sK9(sK10(sK7)),sK10(sK7))
    | in(powerset(sK9(sK10(sK7))),sK10(sK7)) ),
    inference(instantiation,[status(thm)],[c_5989]) ).

cnf(c_11914,plain,
    ( subset(sK2(powerset(sK9(sK10(X0))),sK11(X1,sK9(sK10(X0)))),sK9(sK10(X0)))
    | subset(powerset(sK9(sK10(X0))),sK11(X1,sK9(sK10(X0)))) ),
    inference(instantiation,[status(thm)],[c_3110]) ).

cnf(c_11915,plain,
    ( subset(sK2(powerset(sK9(sK10(sK7))),sK11(sK7,sK9(sK10(sK7)))),sK9(sK10(sK7)))
    | subset(powerset(sK9(sK10(sK7))),sK11(sK7,sK9(sK10(sK7)))) ),
    inference(instantiation,[status(thm)],[c_11914]) ).

cnf(c_11916,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_11915,c_5990,c_5678,c_3444,c_3433,c_75]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SEU168+3 : TPTP v8.2.0. Released v3.2.0.
% 0.08/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.36  % Computer : n019.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Fri Jun 21 13:37:24 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.23/0.49  Running first-order theorem proving
% 0.23/0.49  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.93/1.63  % SZS status Started for theBenchmark.p
% 6.93/1.63  % SZS status Theorem for theBenchmark.p
% 6.93/1.63  
% 6.93/1.63  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 6.93/1.63  
% 6.93/1.63  ------  iProver source info
% 6.93/1.63  
% 6.93/1.63  git: date: 2024-06-12 09:56:46 +0000
% 6.93/1.63  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 6.93/1.63  git: non_committed_changes: false
% 6.93/1.63  
% 6.93/1.63  ------ Parsing...
% 6.93/1.63  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 6.93/1.63  
% 6.93/1.63  ------ 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: 3 0s  sf_e  pe_s  pe_e 
% 6.93/1.63  
% 6.93/1.63  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 6.93/1.63  
% 6.93/1.63  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 6.93/1.63  ------ Proving...
% 6.93/1.63  ------ Problem Properties 
% 6.93/1.63  
% 6.93/1.63  
% 6.93/1.63  clauses                                 23
% 6.93/1.63  conjectures                             4
% 6.93/1.63  EPR                                     4
% 6.93/1.63  Horn                                    17
% 6.93/1.63  unary                                   3
% 6.93/1.63  binary                                  9
% 6.93/1.63  lits                                    58
% 6.93/1.63  lits eq                                 3
% 6.93/1.63  fd_pure                                 0
% 6.93/1.63  fd_pseudo                               0
% 6.93/1.63  fd_cond                                 0
% 6.93/1.63  fd_pseudo_cond                          2
% 6.93/1.63  AC symbols                              0
% 6.93/1.63  
% 6.93/1.63  ------ Input Options Time Limit: Unbounded
% 6.93/1.63  
% 6.93/1.63  
% 6.93/1.63  ------ 
% 6.93/1.63  Current options:
% 6.93/1.63  ------ 
% 6.93/1.63  
% 6.93/1.63  
% 6.93/1.63  
% 6.93/1.63  
% 6.93/1.63  ------ Proving...
% 6.93/1.63  
% 6.93/1.63  
% 6.93/1.63  % SZS status Theorem for theBenchmark.p
% 6.93/1.63  
% 6.93/1.63  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.93/1.63  
% 6.93/1.63  
%------------------------------------------------------------------------------