TSTP Solution File: SEU322+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU322+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 03:05:28 EDT 2024

% Result   : Theorem 17.58s 3.21s
% Output   : CNFRefutation 17.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  151 (  16 unt;   0 def)
%            Number of atoms       :  431 (  30 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  516 ( 236   ~; 221   |;  28   &)
%                                         (   8 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-2 aty)
%            Number of variables   :  251 (   2 sgn 131   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f17,axiom,
    ! [X0] :
      ( one_sorted_str(X0)
     => ( empty_carrier(X0)
      <=> empty(the_carrier(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_struct_0) ).

fof(f18,axiom,
    ! [X0] :
      ( top_str(X0)
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f20,axiom,
    ! [X0,X1] :
      ( ( element(X1,powerset(the_carrier(X0)))
        & top_str(X0) )
     => element(interior(X0,X1),powerset(the_carrier(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => element(subset_complement(X0,X1),powerset(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).

fof(f24,axiom,
    ! [X0,X1] :
      ( ( element(X1,powerset(the_carrier(X0)))
        & top_str(X0) )
     => element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).

fof(f25,axiom,
    ! [X0] :
      ( top_str(X0)
     => one_sorted_str(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).

fof(f35,axiom,
    ! [X0] :
      ( ( one_sorted_str(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( in(X2,subset_complement(the_carrier(X0),X1))
              <=> ~ in(X2,X1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l40_tops_1) ).

fof(f42,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

fof(f43,conjecture,
    ! [X0] :
      ( top_str(X0)
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => subset(interior(X0,X1),X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_tops_1) ).

fof(f44,negated_conjecture,
    ~ ! [X0] :
        ( top_str(X0)
       => ! [X1] :
            ( element(X1,powerset(the_carrier(X0)))
           => subset(interior(X0,X1),X1) ) ),
    inference(negated_conjecture,[],[f43]) ).

fof(f45,axiom,
    ! [X0] :
      ( top_str(X0)
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => subset(X1,topstr_closure(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_pre_topc) ).

fof(f46,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

fof(f47,axiom,
    ! [X0,X1,X2] :
      ( element(X2,powerset(X0))
     => ~ ( in(X1,X2)
          & in(X1,subset_complement(X0,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).

fof(f48,axiom,
    ! [X0,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f79,plain,
    ! [X0] :
      ( ( empty_carrier(X0)
      <=> empty(the_carrier(X0)) )
      | ~ one_sorted_str(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f80,plain,
    ! [X0] :
      ( ! [X1] :
          ( interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1)))
          | ~ element(X1,powerset(the_carrier(X0))) )
      | ~ top_str(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( element(interior(X0,X1),powerset(the_carrier(X0)))
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( element(interior(X0,X1),powerset(the_carrier(X0)))
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0) ),
    inference(flattening,[],[f82]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( element(subset_complement(X0,X1),powerset(X0))
      | ~ element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0) ),
    inference(flattening,[],[f85]) ).

fof(f87,plain,
    ! [X0] :
      ( one_sorted_str(X0)
      | ~ top_str(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f91,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( in(X2,subset_complement(the_carrier(X0),X1))
              <=> ~ in(X2,X1) )
              | ~ element(X2,the_carrier(X0)) )
          | ~ element(X1,powerset(the_carrier(X0))) )
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f92,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( in(X2,subset_complement(the_carrier(X0),X1))
              <=> ~ in(X2,X1) )
              | ~ element(X2,the_carrier(X0)) )
          | ~ element(X1,powerset(the_carrier(X0))) )
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f91]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ~ subset(interior(X0,X1),X1)
          & element(X1,powerset(the_carrier(X0))) )
      & top_str(X0) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f99,plain,
    ! [X0] :
      ( ! [X1] :
          ( subset(X1,topstr_closure(X0,X1))
          | ~ element(X1,powerset(the_carrier(X0))) )
      | ~ top_str(X0) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f100,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f101,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f100]) ).

fof(f102,plain,
    ! [X0,X1,X2] :
      ( ~ in(X1,X2)
      | ~ in(X1,subset_complement(X0,X2))
      | ~ element(X2,powerset(X0)) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( ~ in(X1,X2)
      | ~ in(X1,subset_complement(X0,X2))
      | ~ element(X2,powerset(X0)) ),
    inference(flattening,[],[f102]) ).

fof(f104,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f108,plain,
    ! [X0] :
      ( ( ( empty_carrier(X0)
          | ~ empty(the_carrier(X0)) )
        & ( empty(the_carrier(X0))
          | ~ empty_carrier(X0) ) )
      | ~ one_sorted_str(X0) ),
    inference(nnf_transformation,[],[f79]) ).

fof(f109,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,[],[f81]) ).

fof(f110,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,[],[f109]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK0(X0,X1),X1)
        & in(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK0(X0,X1),X1)
          & in(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f110,f111]) ).

fof(f119,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( in(X2,subset_complement(the_carrier(X0),X1))
                  | in(X2,X1) )
                & ( ~ in(X2,X1)
                  | ~ in(X2,subset_complement(the_carrier(X0),X1)) ) )
              | ~ element(X2,the_carrier(X0)) )
          | ~ element(X1,powerset(the_carrier(X0))) )
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(nnf_transformation,[],[f92]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f42]) ).

fof(f127,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ~ subset(interior(X0,X1),X1)
            & element(X1,powerset(the_carrier(X0))) )
        & top_str(X0) )
   => ( ? [X1] :
          ( ~ subset(interior(sK7,X1),X1)
          & element(X1,powerset(the_carrier(sK7))) )
      & top_str(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f128,plain,
    ( ? [X1] :
        ( ~ subset(interior(sK7,X1),X1)
        & element(X1,powerset(the_carrier(sK7))) )
   => ( ~ subset(interior(sK7,sK8),sK8)
      & element(sK8,powerset(the_carrier(sK7))) ) ),
    introduced(choice_axiom,[]) ).

fof(f129,plain,
    ( ~ subset(interior(sK7,sK8),sK8)
    & element(sK8,powerset(the_carrier(sK7)))
    & top_str(sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f98,f128,f127]) ).

fof(f130,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f155,plain,
    ! [X0] :
      ( empty(the_carrier(X0))
      | ~ empty_carrier(X0)
      | ~ one_sorted_str(X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1)))
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f158,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( element(interior(X0,X1),powerset(the_carrier(X0)))
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( element(subset_complement(X0,X1),powerset(X0))
      | ~ element(X1,powerset(X0)) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f164,plain,
    ! [X0] :
      ( one_sorted_str(X0)
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f177,plain,
    ! [X2,X0,X1] :
      ( in(X2,subset_complement(the_carrier(X0),X1))
      | in(X2,X1)
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ one_sorted_str(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f119]) ).

fof(f191,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f192,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f193,plain,
    top_str(sK7),
    inference(cnf_transformation,[],[f129]) ).

fof(f194,plain,
    element(sK8,powerset(the_carrier(sK7))),
    inference(cnf_transformation,[],[f129]) ).

fof(f195,plain,
    ~ subset(interior(sK7,sK8),sK8),
    inference(cnf_transformation,[],[f129]) ).

fof(f196,plain,
    ! [X0,X1] :
      ( subset(X1,topstr_closure(X0,X1))
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f197,plain,
    ! [X2,X0,X1] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f198,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,X2)
      | ~ in(X1,subset_complement(X0,X2))
      | ~ element(X2,powerset(X0)) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f199,plain,
    ! [X2,X0,X1] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f104]) ).

cnf(c_49,plain,
    ( ~ in(X0,X1)
    | ~ in(X1,X0) ),
    inference(cnf_transformation,[],[f130]) ).

cnf(c_75,plain,
    ( ~ empty_carrier(X0)
    | ~ one_sorted_str(X0)
    | empty(the_carrier(X0)) ),
    inference(cnf_transformation,[],[f155]) ).

cnf(c_76,plain,
    ( ~ element(X0,powerset(the_carrier(X1)))
    | ~ top_str(X1)
    | subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X0))) = interior(X1,X0) ),
    inference(cnf_transformation,[],[f157]) ).

cnf(c_77,plain,
    ( ~ in(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f160]) ).

cnf(c_78,plain,
    ( in(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_79,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | in(X0,X2) ),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_80,plain,
    ( ~ element(X0,powerset(the_carrier(X1)))
    | ~ top_str(X1)
    | element(interior(X1,X0),powerset(the_carrier(X1))) ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_81,plain,
    ( ~ element(X0,powerset(X1))
    | element(subset_complement(X1,X0),powerset(X1)) ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_82,plain,
    ( ~ element(X0,powerset(the_carrier(X1)))
    | ~ top_str(X1)
    | element(topstr_closure(X1,X0),powerset(the_carrier(X1))) ),
    inference(cnf_transformation,[],[f163]) ).

cnf(c_83,plain,
    ( ~ top_str(X0)
    | one_sorted_str(X0) ),
    inference(cnf_transformation,[],[f164]) ).

cnf(c_95,plain,
    ( ~ element(X0,powerset(the_carrier(X1)))
    | ~ element(X2,the_carrier(X1))
    | ~ one_sorted_str(X1)
    | in(X2,subset_complement(the_carrier(X1),X0))
    | in(X2,X0)
    | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f177]) ).

cnf(c_110,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f192]) ).

cnf(c_111,plain,
    ( ~ element(X0,powerset(X1))
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f191]) ).

cnf(c_112,negated_conjecture,
    ~ subset(interior(sK7,sK8),sK8),
    inference(cnf_transformation,[],[f195]) ).

cnf(c_113,negated_conjecture,
    element(sK8,powerset(the_carrier(sK7))),
    inference(cnf_transformation,[],[f194]) ).

cnf(c_114,negated_conjecture,
    top_str(sK7),
    inference(cnf_transformation,[],[f193]) ).

cnf(c_115,plain,
    ( ~ element(X0,powerset(the_carrier(X1)))
    | ~ top_str(X1)
    | subset(X0,topstr_closure(X1,X0)) ),
    inference(cnf_transformation,[],[f196]) ).

cnf(c_116,plain,
    ( ~ element(X0,powerset(X1))
    | ~ in(X2,X0)
    | element(X2,X1) ),
    inference(cnf_transformation,[],[f197]) ).

cnf(c_117,plain,
    ( ~ in(X0,subset_complement(X1,X2))
    | ~ element(X2,powerset(X1))
    | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_118,plain,
    ( ~ element(X0,powerset(X1))
    | ~ in(X2,X0)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_143,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_110]) ).

cnf(c_189,plain,
    ( one_sorted_str(X0)
    | ~ top_str(X0) ),
    inference(prop_impl_just,[status(thm)],[c_83]) ).

cnf(c_190,plain,
    ( ~ top_str(X0)
    | one_sorted_str(X0) ),
    inference(renaming,[status(thm)],[c_189]) ).

cnf(c_191,plain,
    ( ~ in(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_77]) ).

cnf(c_193,plain,
    ( ~ subset(X0,X1)
    | element(subset_complement(X1,X0),powerset(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_110,c_81]) ).

cnf(c_203,plain,
    ( subset(X0,X1)
    | in(sK0(X0,X1),X0) ),
    inference(prop_impl_just,[status(thm)],[c_78]) ).

cnf(c_204,plain,
    ( in(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_203]) ).

cnf(c_317,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | element(X0,X2) ),
    inference(bin_hyper_res,[status(thm)],[c_116,c_143]) ).

cnf(c_318,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | ~ empty(X2) ),
    inference(bin_hyper_res,[status(thm)],[c_118,c_143]) ).

cnf(c_685,plain,
    ( X0 != sK7
    | ~ element(X1,powerset(the_carrier(X0)))
    | subset(X1,topstr_closure(X0,X1)) ),
    inference(resolution_lifted,[status(thm)],[c_115,c_114]) ).

cnf(c_686,plain,
    ( ~ element(X0,powerset(the_carrier(sK7)))
    | subset(X0,topstr_closure(sK7,X0)) ),
    inference(unflattening,[status(thm)],[c_685]) ).

cnf(c_694,plain,
    ( X0 != sK7
    | ~ element(X1,powerset(the_carrier(X0)))
    | element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
    inference(resolution_lifted,[status(thm)],[c_82,c_114]) ).

cnf(c_695,plain,
    ( ~ element(X0,powerset(the_carrier(sK7)))
    | element(topstr_closure(sK7,X0),powerset(the_carrier(sK7))) ),
    inference(unflattening,[status(thm)],[c_694]) ).

cnf(c_703,plain,
    ( X0 != sK7
    | ~ element(X1,powerset(the_carrier(X0)))
    | element(interior(X0,X1),powerset(the_carrier(X0))) ),
    inference(resolution_lifted,[status(thm)],[c_80,c_114]) ).

cnf(c_704,plain,
    ( ~ element(X0,powerset(the_carrier(sK7)))
    | element(interior(sK7,X0),powerset(the_carrier(sK7))) ),
    inference(unflattening,[status(thm)],[c_703]) ).

cnf(c_712,plain,
    ( X0 != sK7
    | ~ element(X1,powerset(the_carrier(X0)))
    | subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) = interior(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_76,c_114]) ).

cnf(c_713,plain,
    ( ~ element(X0,powerset(the_carrier(sK7)))
    | subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),X0))) = interior(sK7,X0) ),
    inference(unflattening,[status(thm)],[c_712]) ).

cnf(c_726,plain,
    ( X0 != sK7
    | one_sorted_str(X0) ),
    inference(resolution_lifted,[status(thm)],[c_190,c_114]) ).

cnf(c_727,plain,
    one_sorted_str(sK7),
    inference(unflattening,[status(thm)],[c_726]) ).

cnf(c_906,plain,
    ( X0 != sK7
    | ~ element(X1,powerset(the_carrier(X0)))
    | ~ element(X2,the_carrier(X0))
    | in(X2,subset_complement(the_carrier(X0),X1))
    | in(X2,X1)
    | empty_carrier(X0) ),
    inference(resolution_lifted,[status(thm)],[c_95,c_727]) ).

cnf(c_907,plain,
    ( ~ element(X0,powerset(the_carrier(sK7)))
    | ~ element(X1,the_carrier(sK7))
    | in(X1,subset_complement(the_carrier(sK7),X0))
    | in(X1,X0)
    | empty_carrier(sK7) ),
    inference(unflattening,[status(thm)],[c_906]) ).

cnf(c_1027,plain,
    ( X0 != sK7
    | ~ empty_carrier(X0)
    | empty(the_carrier(X0)) ),
    inference(resolution_lifted,[status(thm)],[c_75,c_727]) ).

cnf(c_1028,plain,
    ( ~ empty_carrier(sK7)
    | empty(the_carrier(sK7)) ),
    inference(unflattening,[status(thm)],[c_1027]) ).

cnf(c_1274,plain,
    ( interior(sK7,sK8) != X0
    | X1 != sK8
    | in(sK0(X0,X1),X0) ),
    inference(resolution_lifted,[status(thm)],[c_204,c_112]) ).

cnf(c_1275,plain,
    in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8)),
    inference(unflattening,[status(thm)],[c_1274]) ).

cnf(c_1279,plain,
    ( interior(sK7,sK8) != X0
    | X1 != sK8
    | ~ in(sK0(X0,X1),X1) ),
    inference(resolution_lifted,[status(thm)],[c_191,c_112]) ).

cnf(c_1280,plain,
    ~ in(sK0(interior(sK7,sK8),sK8),sK8),
    inference(unflattening,[status(thm)],[c_1279]) ).

cnf(c_2202,plain,
    ( ~ subset(X0,X1)
    | element(subset_complement(X1,X0),powerset(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_193]) ).

cnf(c_2236,plain,
    ( ~ element(X0,powerset(the_carrier(sK7)))
    | subset(X0,topstr_closure(sK7,X0)) ),
    inference(prop_impl_just,[status(thm)],[c_686]) ).

cnf(c_2238,plain,
    ( ~ element(X0,powerset(the_carrier(sK7)))
    | element(topstr_closure(sK7,X0),powerset(the_carrier(sK7))) ),
    inference(prop_impl_just,[status(thm)],[c_695]) ).

cnf(c_2240,plain,
    ( ~ element(X0,powerset(the_carrier(sK7)))
    | element(interior(sK7,X0),powerset(the_carrier(sK7))) ),
    inference(prop_impl_just,[status(thm)],[c_704]) ).

cnf(c_2242,plain,
    ( ~ element(X0,powerset(the_carrier(sK7)))
    | subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),X0))) = interior(sK7,X0) ),
    inference(prop_impl_just,[status(thm)],[c_713]) ).

cnf(c_3642,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_3645,plain,
    ( X0 != X1
    | X2 != X3
    | ~ in(X1,X3)
    | in(X0,X2) ),
    theory(equality) ).

cnf(c_4685,plain,
    ( ~ subset(X0,the_carrier(sK7))
    | ~ in(X1,X0)
    | element(X1,the_carrier(sK7)) ),
    inference(instantiation,[status(thm)],[c_317]) ).

cnf(c_4730,plain,
    ( ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
    | ~ subset(interior(sK7,sK8),the_carrier(sK7))
    | element(sK0(interior(sK7,sK8),sK8),the_carrier(sK7)) ),
    inference(instantiation,[status(thm)],[c_4685]) ).

cnf(c_4731,plain,
    ( ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
    | ~ subset(interior(sK7,sK8),X0)
    | ~ empty(X0) ),
    inference(instantiation,[status(thm)],[c_318]) ).

cnf(c_4764,plain,
    ( ~ element(interior(sK7,sK8),powerset(the_carrier(sK7)))
    | subset(interior(sK7,sK8),the_carrier(sK7)) ),
    inference(instantiation,[status(thm)],[c_111]) ).

cnf(c_4793,plain,
    ( X0 != sK0(interior(sK7,sK8),sK8)
    | X1 != interior(sK7,sK8)
    | ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
    | in(X0,X1) ),
    inference(instantiation,[status(thm)],[c_3645]) ).

cnf(c_4960,plain,
    ( ~ element(sK8,powerset(the_carrier(sK7)))
    | element(interior(sK7,sK8),powerset(the_carrier(sK7))) ),
    inference(instantiation,[status(thm)],[c_2240]) ).

cnf(c_5060,plain,
    ( ~ element(sK0(interior(sK7,sK8),sK8),the_carrier(sK7))
    | ~ element(X0,powerset(the_carrier(sK7)))
    | in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),X0))
    | in(sK0(interior(sK7,sK8),sK8),X0)
    | empty_carrier(sK7) ),
    inference(instantiation,[status(thm)],[c_907]) ).

cnf(c_5099,plain,
    ( ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
    | ~ subset(interior(sK7,sK8),the_carrier(sK7))
    | ~ empty(the_carrier(sK7)) ),
    inference(instantiation,[status(thm)],[c_4731]) ).

cnf(c_5123,plain,
    ( ~ in(X0,subset_complement(the_carrier(sK7),X1))
    | ~ element(X1,powerset(the_carrier(sK7)))
    | ~ in(X0,X1) ),
    inference(instantiation,[status(thm)],[c_117]) ).

cnf(c_5170,plain,
    ( subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) != interior(sK7,sK8)
    | X0 != sK0(interior(sK7,sK8),sK8)
    | ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
    | in(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))) ),
    inference(instantiation,[status(thm)],[c_4793]) ).

cnf(c_5172,plain,
    ( in(X1,X0)
    | in(X1,subset_complement(the_carrier(sK7),X0))
    | ~ element(X1,the_carrier(sK7))
    | ~ element(X0,powerset(the_carrier(sK7))) ),
    inference(global_subsumption_just,[status(thm)],[c_907,c_113,c_907,c_1028,c_1275,c_4764,c_4960,c_5099]) ).

cnf(c_5173,plain,
    ( ~ element(X0,powerset(the_carrier(sK7)))
    | ~ element(X1,the_carrier(sK7))
    | in(X1,subset_complement(the_carrier(sK7),X0))
    | in(X1,X0) ),
    inference(renaming,[status(thm)],[c_5172]) ).

cnf(c_5266,plain,
    subset(sK8,the_carrier(sK7)),
    inference(superposition,[status(thm)],[c_113,c_111]) ).

cnf(c_5336,plain,
    ( ~ element(sK0(X0,subset_complement(the_carrier(sK7),X1)),the_carrier(sK7))
    | ~ element(X1,powerset(the_carrier(sK7)))
    | in(sK0(X0,subset_complement(the_carrier(sK7),X1)),X1)
    | subset(X0,subset_complement(the_carrier(sK7),X1)) ),
    inference(superposition,[status(thm)],[c_5173,c_77]) ).

cnf(c_5539,plain,
    ( ~ subset(X0,the_carrier(sK7))
    | element(subset_complement(the_carrier(sK7),X0),powerset(the_carrier(sK7))) ),
    inference(instantiation,[status(thm)],[c_2202]) ).

cnf(c_6532,plain,
    ( ~ element(sK8,powerset(the_carrier(sK7)))
    | subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) = interior(sK7,sK8) ),
    inference(instantiation,[status(thm)],[c_2242]) ).

cnf(c_8671,plain,
    ( ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),X0))
    | ~ subset(subset_complement(the_carrier(sK7),X0),X1)
    | in(sK0(interior(sK7,sK8),sK8),X1) ),
    inference(instantiation,[status(thm)],[c_79]) ).

cnf(c_8692,plain,
    ( ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),X0))
    | ~ in(sK0(interior(sK7,sK8),sK8),X0)
    | ~ element(X0,powerset(the_carrier(sK7))) ),
    inference(instantiation,[status(thm)],[c_5123]) ).

cnf(c_9735,plain,
    ( subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) != interior(sK7,sK8)
    | sK0(interior(sK7,sK8),sK8) != sK0(interior(sK7,sK8),sK8)
    | ~ in(sK0(interior(sK7,sK8),sK8),interior(sK7,sK8))
    | in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))) ),
    inference(instantiation,[status(thm)],[c_5170]) ).

cnf(c_9931,plain,
    ( ~ element(subset_complement(the_carrier(sK7),sK8),powerset(the_carrier(sK7)))
    | subset(subset_complement(the_carrier(sK7),sK8),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) ),
    inference(instantiation,[status(thm)],[c_2236]) ).

cnf(c_10009,plain,
    ( ~ subset(sK8,the_carrier(sK7))
    | element(subset_complement(the_carrier(sK7),sK8),powerset(the_carrier(sK7))) ),
    inference(instantiation,[status(thm)],[c_5539]) ).

cnf(c_15468,plain,
    sK0(interior(sK7,sK8),sK8) = sK0(interior(sK7,sK8),sK8),
    inference(instantiation,[status(thm)],[c_3642]) ).

cnf(c_18555,plain,
    ( ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),sK8))
    | ~ subset(subset_complement(the_carrier(sK7),sK8),X0)
    | in(sK0(interior(sK7,sK8),sK8),X0) ),
    inference(instantiation,[status(thm)],[c_8671]) ).

cnf(c_26970,plain,
    ( ~ element(sK0(interior(sK7,sK8),sK8),the_carrier(sK7))
    | ~ element(sK8,powerset(the_carrier(sK7)))
    | in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),sK8))
    | in(sK0(interior(sK7,sK8),sK8),sK8)
    | empty_carrier(sK7) ),
    inference(instantiation,[status(thm)],[c_5060]) ).

cnf(c_43122,plain,
    subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) = interior(sK7,sK8),
    inference(superposition,[status(thm)],[c_113,c_2242]) ).

cnf(c_43144,plain,
    ( ~ element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7)))
    | ~ element(sK0(X0,interior(sK7,sK8)),the_carrier(sK7))
    | in(sK0(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))
    | subset(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))) ),
    inference(superposition,[status(thm)],[c_43122,c_5336]) ).

cnf(c_43245,plain,
    ( ~ in(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),sK0(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))))
    | ~ element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7)))
    | ~ element(sK0(X0,interior(sK7,sK8)),the_carrier(sK7))
    | subset(X0,subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))) ),
    inference(superposition,[status(thm)],[c_43144,c_49]) ).

cnf(c_50490,plain,
    ( ~ subset(subset_complement(the_carrier(sK7),sK8),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))
    | ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),sK8))
    | in(sK0(interior(sK7,sK8),sK8),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))) ),
    inference(instantiation,[status(thm)],[c_18555]) ).

cnf(c_57530,plain,
    ( ~ in(sK0(interior(sK7,sK8),sK8),subset_complement(the_carrier(sK7),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8))))
    | ~ in(sK0(interior(sK7,sK8),sK8),topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)))
    | ~ element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7))) ),
    inference(instantiation,[status(thm)],[c_8692]) ).

cnf(c_58335,plain,
    ~ element(topstr_closure(sK7,subset_complement(the_carrier(sK7),sK8)),powerset(the_carrier(sK7))),
    inference(global_subsumption_just,[status(thm)],[c_43245,c_113,c_1028,c_1275,c_1280,c_4730,c_4764,c_4960,c_5099,c_5266,c_6532,c_9735,c_9931,c_10009,c_15468,c_26970,c_50490,c_57530]) ).

cnf(c_58338,plain,
    ~ element(subset_complement(the_carrier(sK7),sK8),powerset(the_carrier(sK7))),
    inference(superposition,[status(thm)],[c_2238,c_58335]) ).

cnf(c_58339,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_58338,c_10009,c_5266]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SEU322+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n018.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 18:01:16 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  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
% 17.58/3.21  % SZS status Started for theBenchmark.p
% 17.58/3.21  % SZS status Theorem for theBenchmark.p
% 17.58/3.21  
% 17.58/3.21  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.58/3.21  
% 17.58/3.21  ------  iProver source info
% 17.58/3.21  
% 17.58/3.21  git: date: 2024-05-02 19:28:25 +0000
% 17.58/3.21  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.58/3.21  git: non_committed_changes: false
% 17.58/3.21  
% 17.58/3.21  ------ Parsing...
% 17.58/3.21  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 17.58/3.21  
% 17.58/3.21  ------ Preprocessing... sup_sim: 0  sf_s  rm: 40 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 
% 17.58/3.21  
% 17.58/3.21  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 17.58/3.21  
% 17.58/3.21  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 17.58/3.21  ------ Proving...
% 17.58/3.21  ------ Problem Properties 
% 17.58/3.21  
% 17.58/3.21  
% 17.58/3.21  clauses                                 50
% 17.58/3.21  conjectures                             2
% 17.58/3.21  EPR                                     13
% 17.58/3.21  Horn                                    41
% 17.58/3.21  unary                                   10
% 17.58/3.21  binary                                  30
% 17.58/3.21  lits                                    107
% 17.58/3.21  lits eq                                 5
% 17.58/3.21  fd_pure                                 0
% 17.58/3.21  fd_pseudo                               0
% 17.58/3.21  fd_cond                                 1
% 17.58/3.21  fd_pseudo_cond                          1
% 17.58/3.21  AC symbols                              0
% 17.58/3.21  
% 17.58/3.21  ------ Input Options Time Limit: Unbounded
% 17.58/3.21  
% 17.58/3.21  
% 17.58/3.21  ------ 
% 17.58/3.21  Current options:
% 17.58/3.21  ------ 
% 17.58/3.21  
% 17.58/3.21  
% 17.58/3.21  
% 17.58/3.21  
% 17.58/3.21  ------ Proving...
% 17.58/3.21  
% 17.58/3.21  
% 17.58/3.21  % SZS status Theorem for theBenchmark.p
% 17.58/3.21  
% 17.58/3.21  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.58/3.22  
% 17.58/3.22  
%------------------------------------------------------------------------------