TSTP Solution File: SEU230+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU230+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n005.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 17:04:59 EDT 2023

% Result   : Theorem 2.00s 1.17s
% Output   : CNFRefutation 2.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   30 (  13 unt;   0 def)
%            Number of atoms       :  140 (  39 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  179 (  69   ~;  68   |;  35   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-3 aty)
%            Number of variables   :   67 (   1 sgn;  54   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f8,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(f28,conjecture,
    ! [X0] : in(X0,succ(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).

fof(f29,negated_conjecture,
    ~ ! [X0] : in(X0,succ(X0)),
    inference(negated_conjecture,[],[f28]) ).

fof(f52,plain,
    ? [X0] : ~ in(X0,succ(X0)),
    inference(ennf_transformation,[],[f29]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f59]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK0(X0,X1) != X0
          | ~ in(sK0(X0,X1),X1) )
        & ( sK0(X0,X1) = X0
          | in(sK0(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK0(X0,X1) != X0
            | ~ in(sK0(X0,X1),X1) )
          & ( sK0(X0,X1) = X0
            | in(sK0(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f60,f61]) ).

fof(f63,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,[],[f8]) ).

fof(f64,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,[],[f63]) ).

fof(f65,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,[],[f64]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X1)
              & ~ in(X3,X0) )
            | ~ in(X3,X2) )
          & ( in(X3,X1)
            | in(X3,X0)
            | in(X3,X2) ) )
     => ( ( ( ~ in(sK1(X0,X1,X2),X1)
            & ~ in(sK1(X0,X1,X2),X0) )
          | ~ in(sK1(X0,X1,X2),X2) )
        & ( in(sK1(X0,X1,X2),X1)
          | in(sK1(X0,X1,X2),X0)
          | in(sK1(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ( ( ( ~ in(sK1(X0,X1,X2),X1)
              & ~ in(sK1(X0,X1,X2),X0) )
            | ~ in(sK1(X0,X1,X2),X2) )
          & ( in(sK1(X0,X1,X2),X1)
            | in(sK1(X0,X1,X2),X0)
            | in(sK1(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,[sK1])],[f65,f66]) ).

fof(f90,plain,
    ( ? [X0] : ~ in(X0,succ(X0))
   => ~ in(sK13,succ(sK13)) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ~ in(sK13,succ(sK13)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f52,f90]) ).

fof(f98,plain,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    inference(cnf_transformation,[],[f6]) ).

fof(f100,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f62]) ).

fof(f105,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f67]) ).

fof(f138,plain,
    ~ in(sK13,succ(sK13)),
    inference(cnf_transformation,[],[f91]) ).

fof(f146,plain,
    ~ in(sK13,set_union2(sK13,singleton(sK13))),
    inference(definition_unfolding,[],[f138,f98]) ).

fof(f147,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f100]) ).

fof(f148,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f147]) ).

fof(f150,plain,
    ! [X0,X1,X4] :
      ( in(X4,set_union2(X0,X1))
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f105]) ).

cnf(c_55,plain,
    in(X0,singleton(X0)),
    inference(cnf_transformation,[],[f148]) ).

cnf(c_60,plain,
    ( ~ in(X0,X1)
    | in(X0,set_union2(X2,X1)) ),
    inference(cnf_transformation,[],[f150]) ).

cnf(c_92,negated_conjecture,
    ~ in(sK13,set_union2(sK13,singleton(sK13))),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_941,plain,
    ~ in(sK13,singleton(sK13)),
    inference(superposition,[status(thm)],[c_60,c_92]) ).

cnf(c_943,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_941,c_55]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU230+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command  : run_iprover %s %d THM
% 0.17/0.35  % Computer : n005.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Wed Aug 23 15:16:24 EDT 2023
% 0.17/0.36  % CPUTime  : 
% 0.22/0.48  Running first-order theorem proving
% 0.22/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.00/1.17  % SZS status Started for theBenchmark.p
% 2.00/1.17  % SZS status Theorem for theBenchmark.p
% 2.00/1.17  
% 2.00/1.17  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.00/1.17  
% 2.00/1.17  ------  iProver source info
% 2.00/1.17  
% 2.00/1.17  git: date: 2023-05-31 18:12:56 +0000
% 2.00/1.17  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.00/1.17  git: non_committed_changes: false
% 2.00/1.17  git: last_make_outside_of_git: false
% 2.00/1.17  
% 2.00/1.17  ------ Parsing...
% 2.00/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.00/1.17  
% 2.00/1.17  ------ Preprocessing... sup_sim: 0  sf_s  rm: 20 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e 
% 2.00/1.17  
% 2.00/1.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.00/1.17  
% 2.00/1.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.00/1.17  ------ Proving...
% 2.00/1.17  ------ Problem Properties 
% 2.00/1.17  
% 2.00/1.17  
% 2.00/1.17  clauses                                 28
% 2.00/1.17  conjectures                             1
% 2.00/1.17  EPR                                     10
% 2.00/1.17  Horn                                    24
% 2.00/1.17  unary                                   12
% 2.00/1.17  binary                                  9
% 2.00/1.17  lits                                    52
% 2.00/1.17  lits eq                                 13
% 2.00/1.17  fd_pure                                 0
% 2.00/1.17  fd_pseudo                               0
% 2.00/1.17  fd_cond                                 1
% 2.00/1.17  fd_pseudo_cond                          6
% 2.00/1.17  AC symbols                              0
% 2.00/1.17  
% 2.00/1.17  ------ Schedule dynamic 5 is on 
% 2.00/1.17  
% 2.00/1.17  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.00/1.17  
% 2.00/1.17  
% 2.00/1.17  ------ 
% 2.00/1.17  Current options:
% 2.00/1.17  ------ 
% 2.00/1.17  
% 2.00/1.17  
% 2.00/1.17  
% 2.00/1.17  
% 2.00/1.17  ------ Proving...
% 2.00/1.17  
% 2.00/1.17  
% 2.00/1.17  % SZS status Theorem for theBenchmark.p
% 2.00/1.17  
% 2.00/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.00/1.17  
% 2.00/1.17  
%------------------------------------------------------------------------------