TSTP Solution File: SET014+4 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET014+4 : TPTP v8.1.2. Released v2.2.0.
% 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 15:05:28 EDT 2023

% Result   : Theorem 10.67s 2.20s
% Output   : CNFRefutation 10.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   55 (   3 unt;   0 def)
%            Number of atoms       :  171 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  182 (  66   ~;  79   |;  26   &)
%                                         (   7 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  105 (   4 sgn;  54   !;  15   ?)

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

fof(f5,axiom,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).

fof(f12,conjecture,
    ! [X0,X2,X4] :
      ( ( subset(X4,X0)
        & subset(X2,X0) )
    <=> subset(union(X2,X4),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI45) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X2,X4] :
        ( ( subset(X4,X0)
          & subset(X2,X0) )
      <=> subset(union(X2,X4),X0) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
    <=> ( member(X0,X2)
        | member(X0,X1) ) ),
    inference(rectify,[],[f5]) ).

fof(f23,plain,
    ~ ! [X0,X1,X2] :
        ( ( subset(X2,X0)
          & subset(X1,X0) )
      <=> subset(union(X1,X2),X0) ),
    inference(rectify,[],[f13]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f26,plain,
    ? [X0,X1,X2] :
      ( ( subset(X2,X0)
        & subset(X1,X0) )
    <~> subset(union(X1,X2),X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f27,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,[],[f24]) ).

fof(f28,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,[],[f27]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,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])],[f28,f29]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X2)
          & ~ member(X0,X1) ) )
      & ( member(X0,X2)
        | member(X0,X1)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(flattening,[],[f34]) ).

fof(f49,plain,
    ? [X0,X1,X2] :
      ( ( ~ subset(union(X1,X2),X0)
        | ~ subset(X2,X0)
        | ~ subset(X1,X0) )
      & ( subset(union(X1,X2),X0)
        | ( subset(X2,X0)
          & subset(X1,X0) ) ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f50,plain,
    ? [X0,X1,X2] :
      ( ( ~ subset(union(X1,X2),X0)
        | ~ subset(X2,X0)
        | ~ subset(X1,X0) )
      & ( subset(union(X1,X2),X0)
        | ( subset(X2,X0)
          & subset(X1,X0) ) ) ),
    inference(flattening,[],[f49]) ).

fof(f51,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ subset(union(X1,X2),X0)
          | ~ subset(X2,X0)
          | ~ subset(X1,X0) )
        & ( subset(union(X1,X2),X0)
          | ( subset(X2,X0)
            & subset(X1,X0) ) ) )
   => ( ( ~ subset(union(sK4,sK5),sK3)
        | ~ subset(sK5,sK3)
        | ~ subset(sK4,sK3) )
      & ( subset(union(sK4,sK5),sK3)
        | ( subset(sK5,sK3)
          & subset(sK4,sK3) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ( ( ~ subset(union(sK4,sK5),sK3)
      | ~ subset(sK5,sK3)
      | ~ subset(sK4,sK3) )
    & ( subset(union(sK4,sK5),sK3)
      | ( subset(sK5,sK3)
        & subset(sK4,sK3) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f50,f51]) ).

fof(f53,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f61,plain,
    ! [X2,X0,X1] :
      ( member(X0,X2)
      | member(X0,X1)
      | ~ member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f62,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f63,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f79,plain,
    ( subset(union(sK4,sK5),sK3)
    | subset(sK4,sK3) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f80,plain,
    ( subset(union(sK4,sK5),sK3)
    | subset(sK5,sK3) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f81,plain,
    ( ~ subset(union(sK4,sK5),sK3)
    | ~ subset(sK5,sK3)
    | ~ subset(sK4,sK3) ),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_49,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_50,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_51,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_57,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_58,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f62]) ).

cnf(c_59,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_75,negated_conjecture,
    ( ~ subset(union(sK4,sK5),sK3)
    | ~ subset(sK4,sK3)
    | ~ subset(sK5,sK3) ),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_76,negated_conjecture,
    ( subset(union(sK4,sK5),sK3)
    | subset(sK5,sK3) ),
    inference(cnf_transformation,[],[f80]) ).

cnf(c_77,negated_conjecture,
    ( subset(union(sK4,sK5),sK3)
    | subset(sK4,sK3) ),
    inference(cnf_transformation,[],[f79]) ).

cnf(c_1229,plain,
    ( ~ member(sK0(sK4,sK3),sK3)
    | subset(sK4,sK3) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_2289,plain,
    ( ~ subset(union(X0,X1),X2)
    | ~ member(X3,X1)
    | member(X3,X2) ),
    inference(superposition,[status(thm)],[c_57,c_51]) ).

cnf(c_2290,plain,
    ( ~ subset(union(X0,X1),X2)
    | ~ member(X3,X0)
    | member(X3,X2) ),
    inference(superposition,[status(thm)],[c_58,c_51]) ).

cnf(c_2561,plain,
    ( member(sK0(union(X0,X1),X2),X0)
    | member(sK0(union(X0,X1),X2),X1)
    | subset(union(X0,X1),X2) ),
    inference(superposition,[status(thm)],[c_50,c_59]) ).

cnf(c_7018,plain,
    ( ~ member(sK0(union(sK4,sK5),sK3),sK3)
    | subset(union(sK4,sK5),sK3) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_35506,plain,
    ( ~ member(X0,sK5)
    | member(X0,sK3)
    | subset(sK5,sK3) ),
    inference(superposition,[status(thm)],[c_76,c_2289]) ).

cnf(c_36779,plain,
    ( ~ member(X0,sK5)
    | member(X0,sK3) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_35506,c_51]) ).

cnf(c_36782,plain,
    ( member(sK0(sK5,X0),sK3)
    | subset(sK5,X0) ),
    inference(superposition,[status(thm)],[c_50,c_36779]) ).

cnf(c_36816,plain,
    ( ~ member(X0,sK4)
    | member(X0,sK3)
    | subset(sK4,sK3) ),
    inference(superposition,[status(thm)],[c_77,c_2290]) ).

cnf(c_38117,plain,
    ( ~ member(X0,sK4)
    | member(X0,sK3) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_36816,c_51]) ).

cnf(c_38120,plain,
    ( member(sK0(sK4,X0),sK3)
    | subset(sK4,X0) ),
    inference(superposition,[status(thm)],[c_50,c_38117]) ).

cnf(c_38142,plain,
    ( member(sK0(sK4,sK3),sK3)
    | subset(sK4,sK3) ),
    inference(instantiation,[status(thm)],[c_38120]) ).

cnf(c_38246,plain,
    subset(sK5,sK3),
    inference(superposition,[status(thm)],[c_36782,c_49]) ).

cnf(c_38257,plain,
    ( ~ subset(union(sK4,sK5),sK3)
    | ~ subset(sK4,sK3) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_75,c_38246]) ).

cnf(c_38295,plain,
    ~ subset(union(sK4,sK5),sK3),
    inference(global_subsumption_just,[status(thm)],[c_38257,c_75,c_1229,c_38142,c_38246]) ).

cnf(c_43965,plain,
    ( member(sK0(union(X0,sK5),X1),X0)
    | member(sK0(union(X0,sK5),X1),sK3)
    | subset(union(X0,sK5),X1) ),
    inference(superposition,[status(thm)],[c_2561,c_36779]) ).

cnf(c_47424,plain,
    ( member(sK0(union(sK4,sK5),X0),sK3)
    | subset(union(sK4,sK5),X0) ),
    inference(superposition,[status(thm)],[c_43965,c_38117]) ).

cnf(c_47505,plain,
    ( member(sK0(union(sK4,sK5),sK3),sK3)
    | subset(union(sK4,sK5),sK3) ),
    inference(instantiation,[status(thm)],[c_47424]) ).

cnf(c_47506,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_47505,c_38295,c_7018]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET014+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Aug 26 15:58:11 EDT 2023
% 0.13/0.35  % 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 --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.67/2.20  % SZS status Started for theBenchmark.p
% 10.67/2.20  % SZS status Theorem for theBenchmark.p
% 10.67/2.20  
% 10.67/2.20  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 10.67/2.20  
% 10.67/2.20  ------  iProver source info
% 10.67/2.20  
% 10.67/2.20  git: date: 2023-05-31 18:12:56 +0000
% 10.67/2.20  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 10.67/2.20  git: non_committed_changes: false
% 10.67/2.20  git: last_make_outside_of_git: false
% 10.67/2.20  
% 10.67/2.20  ------ Parsing...
% 10.67/2.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 10.67/2.20  
% 10.67/2.20  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 10.67/2.20  
% 10.67/2.20  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 10.67/2.20  
% 10.67/2.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 10.67/2.20  ------ Proving...
% 10.67/2.20  ------ Problem Properties 
% 10.67/2.20  
% 10.67/2.20  
% 10.67/2.20  clauses                                 29
% 10.67/2.20  conjectures                             3
% 10.67/2.20  EPR                                     2
% 10.67/2.20  Horn                                    22
% 10.67/2.20  unary                                   4
% 10.67/2.20  binary                                  17
% 10.67/2.20  lits                                    62
% 10.67/2.20  lits eq                                 3
% 10.67/2.20  fd_pure                                 0
% 10.67/2.20  fd_pseudo                               0
% 10.67/2.20  fd_cond                                 0
% 10.67/2.20  fd_pseudo_cond                          2
% 10.67/2.20  AC symbols                              0
% 10.67/2.20  
% 10.67/2.20  ------ Schedule dynamic 5 is on 
% 10.67/2.20  
% 10.67/2.20  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.67/2.20  
% 10.67/2.20  
% 10.67/2.20  ------ 
% 10.67/2.20  Current options:
% 10.67/2.20  ------ 
% 10.67/2.20  
% 10.67/2.20  
% 10.67/2.20  
% 10.67/2.20  
% 10.67/2.20  ------ Proving...
% 10.67/2.20  
% 10.67/2.20  
% 10.67/2.20  % SZS status Theorem for theBenchmark.p
% 10.67/2.20  
% 10.67/2.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.67/2.20  
% 10.67/2.20  
%------------------------------------------------------------------------------