TSTP Solution File: SET366+4 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET366+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n025.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 15:07:42 EDT 2023

% Result   : Theorem 2.46s 1.17s
% Output   : CNFRefutation 2.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   27 (  13 unt;   0 def)
%            Number of atoms       :   59 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   60 (  28   ~;  16   |;   9   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   43 (   2 sgn;  32   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).

fof(f3,axiom,
    ! [X2,X0] :
      ( member(X2,power_set(X0))
    <=> subset(X2,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_set) ).

fof(f6,axiom,
    ! [X2] : ~ member(X2,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).

fof(f12,conjecture,
    ! [X0] : member(empty_set,power_set(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI47) ).

fof(f13,negated_conjecture,
    ~ ! [X0] : member(empty_set,power_set(X0)),
    inference(negated_conjecture,[],[f12]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
    <=> subset(X0,X1) ),
    inference(rectify,[],[f3]) ).

fof(f17,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f25,plain,
    ? [X0] : ~ member(empty_set,power_set(X0)),
    inference(ennf_transformation,[],[f13]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f26]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f27,f28]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( member(X0,power_set(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ member(X0,power_set(X1)) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f48,plain,
    ( ? [X0] : ~ member(empty_set,power_set(X0))
   => ~ member(empty_set,power_set(sK3)) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ~ member(empty_set,power_set(sK3)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f25,f48]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f61,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f17]) ).

fof(f76,plain,
    ~ member(empty_set,power_set(sK3)),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_50,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_52,plain,
    ( ~ subset(X0,X1)
    | member(X0,power_set(X1)) ),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_60,plain,
    ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_75,negated_conjecture,
    ~ member(empty_set,power_set(sK3)),
    inference(cnf_transformation,[],[f76]) ).

cnf(c_962,plain,
    subset(empty_set,X0),
    inference(superposition,[status(thm)],[c_50,c_60]) ).

cnf(c_968,plain,
    ~ subset(empty_set,sK3),
    inference(superposition,[status(thm)],[c_52,c_75]) ).

cnf(c_969,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_968,c_962]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET366+4 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat Aug 26 15:08:53 EDT 2023
% 0.12/0.34  % 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
% 2.46/1.17  % SZS status Started for theBenchmark.p
% 2.46/1.17  % SZS status Theorem for theBenchmark.p
% 2.46/1.17  
% 2.46/1.17  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.46/1.17  
% 2.46/1.17  ------  iProver source info
% 2.46/1.17  
% 2.46/1.17  git: date: 2023-05-31 18:12:56 +0000
% 2.46/1.17  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.46/1.17  git: non_committed_changes: false
% 2.46/1.17  git: last_make_outside_of_git: false
% 2.46/1.17  
% 2.46/1.17  ------ Parsing...
% 2.46/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.46/1.17  
% 2.46/1.17  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 2.46/1.17  
% 2.46/1.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.46/1.17  
% 2.46/1.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.46/1.17  ------ Proving...
% 2.46/1.17  ------ Problem Properties 
% 2.46/1.17  
% 2.46/1.17  
% 2.46/1.17  clauses                                 27
% 2.46/1.17  conjectures                             1
% 2.46/1.17  EPR                                     2
% 2.46/1.17  Horn                                    22
% 2.46/1.17  unary                                   5
% 2.46/1.17  binary                                  15
% 2.46/1.17  lits                                    56
% 2.46/1.17  lits eq                                 3
% 2.46/1.17  fd_pure                                 0
% 2.46/1.17  fd_pseudo                               0
% 2.46/1.17  fd_cond                                 0
% 2.46/1.17  fd_pseudo_cond                          2
% 2.46/1.17  AC symbols                              0
% 2.46/1.17  
% 2.46/1.17  ------ Schedule dynamic 5 is on 
% 2.46/1.17  
% 2.46/1.17  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.46/1.17  
% 2.46/1.17  
% 2.46/1.17  ------ 
% 2.46/1.17  Current options:
% 2.46/1.17  ------ 
% 2.46/1.17  
% 2.46/1.17  
% 2.46/1.17  
% 2.46/1.17  
% 2.46/1.17  ------ Proving...
% 2.46/1.17  
% 2.46/1.17  
% 2.46/1.17  % SZS status Theorem for theBenchmark.p
% 2.46/1.17  
% 2.46/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.46/1.17  
% 2.46/1.17  
%------------------------------------------------------------------------------