TSTP Solution File: SEU117+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU117+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n021.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 17:03:47 EDT 2023

% Result   : Theorem 2.08s 1.13s
% Output   : CNFRefutation 2.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   45 (  14 unt;   0 def)
%            Number of atoms       :  161 (  13 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  186 (  70   ~;  71   |;  34   &)
%                                         (   5 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   71 (   2 sgn;  47   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(f11,axiom,
    ! [X0] : preboolean(finite_subsets(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).

fof(f13,axiom,
    ! [X0] :
      ( preboolean(finite_subsets(X0))
      & diff_closed(finite_subsets(X0))
      & cup_closed(finite_subsets(X0))
      & ~ empty(finite_subsets(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finsub_1) ).

fof(f28,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

fof(f31,conjecture,
    ! [X0,X1] :
      ( element(X1,finite_subsets(X0))
     => element(X1,powerset(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finsub_1) ).

fof(f32,negated_conjecture,
    ~ ! [X0,X1] :
        ( element(X1,finite_subsets(X0))
       => element(X1,powerset(X0)) ),
    inference(negated_conjecture,[],[f31]) ).

fof(f33,axiom,
    ! [X0,X1] :
      ( preboolean(X1)
     => ( finite_subsets(X0) = X1
      <=> ! [X2] :
            ( in(X2,X1)
          <=> ( finite(X2)
              & subset(X2,X0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).

fof(f46,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f46]) ).

fof(f62,plain,
    ? [X0,X1] :
      ( ~ element(X1,powerset(X0))
      & element(X1,finite_subsets(X0)) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ( finite_subsets(X0) = X1
      <=> ! [X2] :
            ( in(X2,X1)
          <=> ( finite(X2)
              & subset(X2,X0) ) ) )
      | ~ preboolean(X1) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f28]) ).

fof(f85,plain,
    ( ? [X0,X1] :
        ( ~ element(X1,powerset(X0))
        & element(X1,finite_subsets(X0)) )
   => ( ~ element(sK11,powerset(sK10))
      & element(sK11,finite_subsets(sK10)) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ( ~ element(sK11,powerset(sK10))
    & element(sK11,finite_subsets(sK10)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f62,f85]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ( ( finite_subsets(X0) = X1
          | ? [X2] :
              ( ( ~ finite(X2)
                | ~ subset(X2,X0)
                | ~ in(X2,X1) )
              & ( ( finite(X2)
                  & subset(X2,X0) )
                | in(X2,X1) ) ) )
        & ( ! [X2] :
              ( ( in(X2,X1)
                | ~ finite(X2)
                | ~ subset(X2,X0) )
              & ( ( finite(X2)
                  & subset(X2,X0) )
                | ~ in(X2,X1) ) )
          | finite_subsets(X0) != X1 ) )
      | ~ preboolean(X1) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ( ( finite_subsets(X0) = X1
          | ? [X2] :
              ( ( ~ finite(X2)
                | ~ subset(X2,X0)
                | ~ in(X2,X1) )
              & ( ( finite(X2)
                  & subset(X2,X0) )
                | in(X2,X1) ) ) )
        & ( ! [X2] :
              ( ( in(X2,X1)
                | ~ finite(X2)
                | ~ subset(X2,X0) )
              & ( ( finite(X2)
                  & subset(X2,X0) )
                | ~ in(X2,X1) ) )
          | finite_subsets(X0) != X1 ) )
      | ~ preboolean(X1) ),
    inference(flattening,[],[f87]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ( ( finite_subsets(X0) = X1
          | ? [X2] :
              ( ( ~ finite(X2)
                | ~ subset(X2,X0)
                | ~ in(X2,X1) )
              & ( ( finite(X2)
                  & subset(X2,X0) )
                | in(X2,X1) ) ) )
        & ( ! [X3] :
              ( ( in(X3,X1)
                | ~ finite(X3)
                | ~ subset(X3,X0) )
              & ( ( finite(X3)
                  & subset(X3,X0) )
                | ~ in(X3,X1) ) )
          | finite_subsets(X0) != X1 ) )
      | ~ preboolean(X1) ),
    inference(rectify,[],[f88]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ finite(X2)
            | ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( ( finite(X2)
              & subset(X2,X0) )
            | in(X2,X1) ) )
     => ( ( ~ finite(sK12(X0,X1))
          | ~ subset(sK12(X0,X1),X0)
          | ~ in(sK12(X0,X1),X1) )
        & ( ( finite(sK12(X0,X1))
            & subset(sK12(X0,X1),X0) )
          | in(sK12(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ( ( finite_subsets(X0) = X1
          | ( ( ~ finite(sK12(X0,X1))
              | ~ subset(sK12(X0,X1),X0)
              | ~ in(sK12(X0,X1),X1) )
            & ( ( finite(sK12(X0,X1))
                & subset(sK12(X0,X1),X0) )
              | in(sK12(X0,X1),X1) ) ) )
        & ( ! [X3] :
              ( ( in(X3,X1)
                | ~ finite(X3)
                | ~ subset(X3,X0) )
              & ( ( finite(X3)
                  & subset(X3,X0) )
                | ~ in(X3,X1) ) )
          | finite_subsets(X0) != X1 ) )
      | ~ preboolean(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f89,f90]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f102,plain,
    ! [X0] : preboolean(finite_subsets(X0)),
    inference(cnf_transformation,[],[f11]) ).

fof(f107,plain,
    ! [X0] : ~ empty(finite_subsets(X0)),
    inference(cnf_transformation,[],[f13]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f142,plain,
    element(sK11,finite_subsets(sK10)),
    inference(cnf_transformation,[],[f86]) ).

fof(f143,plain,
    ~ element(sK11,powerset(sK10)),
    inference(cnf_transformation,[],[f86]) ).

fof(f144,plain,
    ! [X3,X0,X1] :
      ( subset(X3,X0)
      | ~ in(X3,X1)
      | finite_subsets(X0) != X1
      | ~ preboolean(X1) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f152,plain,
    ! [X3,X0] :
      ( subset(X3,X0)
      | ~ in(X3,finite_subsets(X0))
      | ~ preboolean(finite_subsets(X0)) ),
    inference(equality_resolution,[],[f144]) ).

cnf(c_52,plain,
    ( ~ element(X0,X1)
    | in(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_59,plain,
    preboolean(finite_subsets(X0)),
    inference(cnf_transformation,[],[f102]) ).

cnf(c_67,plain,
    ~ empty(finite_subsets(X0)),
    inference(cnf_transformation,[],[f107]) ).

cnf(c_95,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f139]) ).

cnf(c_99,negated_conjecture,
    ~ element(sK11,powerset(sK10)),
    inference(cnf_transformation,[],[f143]) ).

cnf(c_100,negated_conjecture,
    element(sK11,finite_subsets(sK10)),
    inference(cnf_transformation,[],[f142]) ).

cnf(c_106,plain,
    ( ~ in(X0,finite_subsets(X1))
    | ~ preboolean(finite_subsets(X1))
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f152]) ).

cnf(c_304,plain,
    ( ~ in(X0,finite_subsets(X1))
    | subset(X0,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_106,c_59]) ).

cnf(c_921,plain,
    ( finite_subsets(sK10) != X1
    | X0 != sK11
    | in(X0,X1)
    | empty(X1) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_100]) ).

cnf(c_922,plain,
    ( in(sK11,finite_subsets(sK10))
    | empty(finite_subsets(sK10)) ),
    inference(unflattening,[status(thm)],[c_921]) ).

cnf(c_927,plain,
    in(sK11,finite_subsets(sK10)),
    inference(forward_subsumption_resolution,[status(thm)],[c_922,c_67]) ).

cnf(c_1600,plain,
    ( subset(X0,X1)
    | ~ in(X0,finite_subsets(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_304]) ).

cnf(c_1601,plain,
    ( ~ in(X0,finite_subsets(X1))
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_1600]) ).

cnf(c_3617,plain,
    ( in(sK11,finite_subsets(sK10))
    | empty(finite_subsets(sK10)) ),
    inference(superposition,[status(thm)],[c_100,c_52]) ).

cnf(c_3623,plain,
    in(sK11,finite_subsets(sK10)),
    inference(global_subsumption_just,[status(thm)],[c_3617,c_927]) ).

cnf(c_3785,plain,
    ~ subset(sK11,sK10),
    inference(superposition,[status(thm)],[c_95,c_99]) ).

cnf(c_3918,plain,
    subset(sK11,sK10),
    inference(superposition,[status(thm)],[c_3623,c_1601]) ).

cnf(c_3919,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_3918,c_3785]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU117+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 14:40:09 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.08/1.13  % SZS status Started for theBenchmark.p
% 2.08/1.13  % SZS status Theorem for theBenchmark.p
% 2.08/1.13  
% 2.08/1.13  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.08/1.13  
% 2.08/1.13  ------  iProver source info
% 2.08/1.13  
% 2.08/1.13  git: date: 2023-05-31 18:12:56 +0000
% 2.08/1.13  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.08/1.13  git: non_committed_changes: false
% 2.08/1.13  git: last_make_outside_of_git: false
% 2.08/1.13  
% 2.08/1.13  ------ Parsing...
% 2.08/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.08/1.13  
% 2.08/1.13  ------ 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 
% 2.08/1.13  
% 2.08/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.08/1.13  
% 2.08/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.08/1.13  ------ Proving...
% 2.08/1.13  ------ Problem Properties 
% 2.08/1.13  
% 2.08/1.13  
% 2.08/1.13  clauses                                 47
% 2.08/1.13  conjectures                             2
% 2.08/1.13  EPR                                     18
% 2.08/1.13  Horn                                    39
% 2.08/1.13  unary                                   20
% 2.08/1.13  binary                                  18
% 2.08/1.13  lits                                    87
% 2.08/1.13  lits eq                                 5
% 2.08/1.13  fd_pure                                 0
% 2.08/1.13  fd_pseudo                               0
% 2.08/1.13  fd_cond                                 1
% 2.08/1.13  fd_pseudo_cond                          4
% 2.08/1.13  AC symbols                              0
% 2.08/1.13  
% 2.08/1.13  ------ Schedule dynamic 5 is on 
% 2.08/1.13  
% 2.08/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.08/1.13  
% 2.08/1.13  
% 2.08/1.13  ------ 
% 2.08/1.13  Current options:
% 2.08/1.13  ------ 
% 2.08/1.13  
% 2.08/1.13  
% 2.08/1.13  
% 2.08/1.13  
% 2.08/1.13  ------ Proving...
% 2.08/1.13  
% 2.08/1.13  
% 2.08/1.13  % SZS status Theorem for theBenchmark.p
% 2.08/1.13  
% 2.08/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.08/1.13  
% 2.08/1.13  
%------------------------------------------------------------------------------