TSTP Solution File: SEU169+2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU169+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 17:04:21 EDT 2023

% Result   : Theorem 3.62s 1.12s
% Output   : CNFRefutation 3.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   53 (  18 unt;   0 def)
%            Number of atoms       :  211 (  29 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  246 (  88   ~;  89   |;  50   &)
%                                         (   8 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :  105 (   2 sgn;  75   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ( empty(X0)
       => ( element(X1,X0)
        <=> empty(X1) ) )
      & ( ~ empty(X0)
       => ( element(X1,X0)
        <=> in(X1,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).

fof(f12,axiom,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f33,axiom,
    ! [X0] : ~ empty(powerset(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

fof(f47,conjecture,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_subset_1) ).

fof(f48,negated_conjecture,
    ~ ! [X0,X1] :
        ( element(X1,powerset(X0))
       => ! [X2] :
            ( in(X2,X1)
           => in(X2,X0) ) ),
    inference(negated_conjecture,[],[f47]) ).

fof(f62,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_union2(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ( ( element(X1,X0)
        <=> empty(X1) )
        | ~ empty(X0) )
      & ( ( element(X1,X0)
        <=> in(X1,X0) )
        | empty(X0) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f129,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X0)
          & in(X2,X1) )
      & element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( set_union2(X0,X1) = X1
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f62]) ).

fof(f180,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,[],[f9]) ).

fof(f181,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,[],[f180]) ).

fof(f182,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( subset(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ subset(sK2(X0,X1),X0)
          | ~ in(sK2(X0,X1),X1) )
        & ( subset(sK2(X0,X1),X0)
          | in(sK2(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ( ( ~ subset(sK2(X0,X1),X0)
            | ~ in(sK2(X0,X1),X1) )
          & ( subset(sK2(X0,X1),X0)
            | in(sK2(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,[sK2])],[f181,f182]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ( ( ( element(X1,X0)
            | ~ empty(X1) )
          & ( empty(X1)
            | ~ element(X1,X0) ) )
        | ~ empty(X0) )
      & ( ( ( element(X1,X0)
            | ~ in(X1,X0) )
          & ( in(X1,X0)
            | ~ element(X1,X0) ) )
        | empty(X0) ) ),
    inference(nnf_transformation,[],[f120]) ).

fof(f190,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f191,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(flattening,[],[f190]) ).

fof(f192,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(rectify,[],[f191]) ).

fof(f193,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X1)
              & ~ in(X3,X0) )
            | ~ in(X3,X2) )
          & ( in(X3,X1)
            | in(X3,X0)
            | in(X3,X2) ) )
     => ( ( ( ~ in(sK4(X0,X1,X2),X1)
            & ~ in(sK4(X0,X1,X2),X0) )
          | ~ in(sK4(X0,X1,X2),X2) )
        & ( in(sK4(X0,X1,X2),X1)
          | in(sK4(X0,X1,X2),X0)
          | in(sK4(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f194,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ( ( ( ~ in(sK4(X0,X1,X2),X1)
              & ~ in(sK4(X0,X1,X2),X0) )
            | ~ in(sK4(X0,X1,X2),X2) )
          & ( in(sK4(X0,X1,X2),X1)
            | in(sK4(X0,X1,X2),X0)
            | in(sK4(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f192,f193]) ).

fof(f226,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ~ in(X2,X0)
            & in(X2,X1) )
        & element(X1,powerset(X0)) )
   => ( ? [X2] :
          ( ~ in(X2,sK17)
          & in(X2,sK18) )
      & element(sK18,powerset(sK17)) ) ),
    introduced(choice_axiom,[]) ).

fof(f227,plain,
    ( ? [X2] :
        ( ~ in(X2,sK17)
        & in(X2,sK18) )
   => ( ~ in(sK19,sK17)
      & in(sK19,sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f228,plain,
    ( ~ in(sK19,sK17)
    & in(sK19,sK18)
    & element(sK18,powerset(sK17)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f129,f227,f226]) ).

fof(f266,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f4]) ).

fof(f277,plain,
    ! [X3,X0,X1] :
      ( subset(X3,X0)
      | ~ in(X3,X1)
      | powerset(X0) != X1 ),
    inference(cnf_transformation,[],[f183]) ).

fof(f281,plain,
    ! [X0,X1] :
      ( in(X1,X0)
      | ~ element(X1,X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f184]) ).

fof(f293,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f194]) ).

fof(f331,plain,
    ! [X0] : ~ empty(powerset(X0)),
    inference(cnf_transformation,[],[f33]) ).

fof(f347,plain,
    element(sK18,powerset(sK17)),
    inference(cnf_transformation,[],[f228]) ).

fof(f348,plain,
    in(sK19,sK18),
    inference(cnf_transformation,[],[f228]) ).

fof(f349,plain,
    ~ in(sK19,sK17),
    inference(cnf_transformation,[],[f228]) ).

fof(f371,plain,
    ! [X0,X1] :
      ( set_union2(X0,X1) = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f139]) ).

fof(f498,plain,
    ! [X3,X0] :
      ( subset(X3,X0)
      | ~ in(X3,powerset(X0)) ),
    inference(equality_resolution,[],[f277]) ).

fof(f504,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_union2(X0,X1))
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f293]) ).

cnf(c_52,plain,
    set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f266]) ).

cnf(c_66,plain,
    ( ~ in(X0,powerset(X1))
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f498]) ).

cnf(c_70,plain,
    ( ~ element(X0,X1)
    | in(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f281]) ).

cnf(c_80,plain,
    ( ~ in(X0,X1)
    | in(X0,set_union2(X2,X1)) ),
    inference(cnf_transformation,[],[f504]) ).

cnf(c_116,plain,
    ~ empty(powerset(X0)),
    inference(cnf_transformation,[],[f331]) ).

cnf(c_132,negated_conjecture,
    ~ in(sK19,sK17),
    inference(cnf_transformation,[],[f349]) ).

cnf(c_133,negated_conjecture,
    in(sK19,sK18),
    inference(cnf_transformation,[],[f348]) ).

cnf(c_134,negated_conjecture,
    element(sK18,powerset(sK17)),
    inference(cnf_transformation,[],[f347]) ).

cnf(c_156,plain,
    ( ~ subset(X0,X1)
    | set_union2(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f371]) ).

cnf(c_1998,plain,
    ( powerset(sK17) != X1
    | X0 != sK18
    | in(X0,X1)
    | empty(X1) ),
    inference(resolution_lifted,[status(thm)],[c_70,c_134]) ).

cnf(c_1999,plain,
    ( in(sK18,powerset(sK17))
    | empty(powerset(sK17)) ),
    inference(unflattening,[status(thm)],[c_1998]) ).

cnf(c_2004,plain,
    in(sK18,powerset(sK17)),
    inference(forward_subsumption_resolution,[status(thm)],[c_1999,c_116]) ).

cnf(c_6126,plain,
    subset(sK18,sK17),
    inference(superposition,[status(thm)],[c_2004,c_66]) ).

cnf(c_6866,plain,
    set_union2(sK18,sK17) = sK17,
    inference(superposition,[status(thm)],[c_6126,c_156]) ).

cnf(c_6901,plain,
    set_union2(sK17,sK18) = sK17,
    inference(demodulation,[status(thm)],[c_6866,c_52]) ).

cnf(c_6915,plain,
    ( ~ in(X0,sK18)
    | in(X0,sK17) ),
    inference(superposition,[status(thm)],[c_6901,c_80]) ).

cnf(c_6953,plain,
    in(sK19,sK17),
    inference(superposition,[status(thm)],[c_133,c_6915]) ).

cnf(c_6957,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_6953,c_132]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SEU169+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.32  % Computer : n017.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Wed Aug 23 13:56:53 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.17/0.43  Running first-order theorem proving
% 0.17/0.43  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.62/1.12  % SZS status Started for theBenchmark.p
% 3.62/1.12  % SZS status Theorem for theBenchmark.p
% 3.62/1.12  
% 3.62/1.12  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.62/1.12  
% 3.62/1.12  ------  iProver source info
% 3.62/1.12  
% 3.62/1.12  git: date: 2023-05-31 18:12:56 +0000
% 3.62/1.12  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.62/1.12  git: non_committed_changes: false
% 3.62/1.12  git: last_make_outside_of_git: false
% 3.62/1.12  
% 3.62/1.12  ------ Parsing...
% 3.62/1.12  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.62/1.12  
% 3.62/1.12  ------ Preprocessing... sup_sim: 5  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 3.62/1.12  
% 3.62/1.12  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.62/1.12  
% 3.62/1.12  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.62/1.12  ------ Proving...
% 3.62/1.12  ------ Problem Properties 
% 3.62/1.12  
% 3.62/1.12  
% 3.62/1.12  clauses                                 142
% 3.62/1.12  conjectures                             2
% 3.62/1.12  EPR                                     23
% 3.62/1.12  Horn                                    111
% 3.62/1.12  unary                                   31
% 3.62/1.12  binary                                  63
% 3.62/1.12  lits                                    308
% 3.62/1.12  lits eq                                 81
% 3.62/1.12  fd_pure                                 0
% 3.62/1.12  fd_pseudo                               0
% 3.62/1.12  fd_cond                                 3
% 3.62/1.12  fd_pseudo_cond                          35
% 3.62/1.12  AC symbols                              0
% 3.62/1.12  
% 3.62/1.12  ------ Schedule dynamic 5 is on 
% 3.62/1.12  
% 3.62/1.12  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.62/1.12  
% 3.62/1.12  
% 3.62/1.12  ------ 
% 3.62/1.12  Current options:
% 3.62/1.12  ------ 
% 3.62/1.12  
% 3.62/1.12  
% 3.62/1.12  
% 3.62/1.12  
% 3.62/1.12  ------ Proving...
% 3.62/1.12  
% 3.62/1.12  
% 3.62/1.12  % SZS status Theorem for theBenchmark.p
% 3.62/1.12  
% 3.62/1.12  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.62/1.12  
% 3.62/1.12  
%------------------------------------------------------------------------------