TSTP Solution File: SET027+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET027+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.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 : Fri May  3 02:59:26 EDT 2024

% Result   : Theorem 1.71s 1.13s
% Output   : CNFRefutation 1.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   32 (   9 unt;   0 def)
%            Number of atoms       :   87 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   92 (  37   ~;  28   |;  20   &)
%                                         (   2 <=>;   5  =>;   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;   3 con; 0-2 aty)
%            Number of variables   :   53 (   0 sgn  30   !;  12   ?)

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

fof(f3,conjecture,
    ! [X0,X1,X2] :
      ( ( subset(X1,X2)
        & subset(X0,X1) )
     => subset(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).

fof(f4,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( subset(X1,X2)
          & subset(X0,X1) )
       => subset(X0,X2) ),
    inference(negated_conjecture,[],[f3]) ).

fof(f5,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f6,plain,
    ? [X0,X1,X2] :
      ( ~ subset(X0,X2)
      & subset(X1,X2)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f7,plain,
    ? [X0,X1,X2] :
      ( ~ subset(X0,X2)
      & subset(X1,X2)
      & subset(X0,X1) ),
    inference(flattening,[],[f6]) ).

fof(f8,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,[],[f5]) ).

fof(f9,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,[],[f8]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,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])],[f9,f10]) ).

fof(f12,plain,
    ( ? [X0,X1,X2] :
        ( ~ subset(X0,X2)
        & subset(X1,X2)
        & subset(X0,X1) )
   => ( ~ subset(sK1,sK3)
      & subset(sK2,sK3)
      & subset(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ( ~ subset(sK1,sK3)
    & subset(sK2,sK3)
    & subset(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f7,f12]) ).

fof(f14,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f18,plain,
    subset(sK1,sK2),
    inference(cnf_transformation,[],[f13]) ).

fof(f19,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f13]) ).

fof(f20,plain,
    ~ subset(sK1,sK3),
    inference(cnf_transformation,[],[f13]) ).

cnf(c_49,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f16]) ).

cnf(c_50,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f15]) ).

cnf(c_51,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f14]) ).

cnf(c_53,negated_conjecture,
    ~ subset(sK1,sK3),
    inference(cnf_transformation,[],[f20]) ).

cnf(c_54,negated_conjecture,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f19]) ).

cnf(c_55,negated_conjecture,
    subset(sK1,sK2),
    inference(cnf_transformation,[],[f18]) ).

cnf(c_100,plain,
    member(sK0(sK1,sK3),sK1),
    inference(resolution,[status(thm)],[c_50,c_53]) ).

cnf(c_104,plain,
    ~ member(sK0(sK1,sK3),sK3),
    inference(resolution,[status(thm)],[c_49,c_53]) ).

cnf(c_141,plain,
    ( ~ member(sK0(sK1,sK3),sK1)
    | ~ subset(sK1,X0)
    | member(sK0(sK1,sK3),X0) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_142,plain,
    ( ~ member(sK0(sK1,sK3),X0)
    | ~ subset(X0,X1)
    | member(sK0(sK1,sK3),X1) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_145,plain,
    ( ~ member(sK0(sK1,sK3),X0)
    | ~ subset(X0,sK3)
    | member(sK0(sK1,sK3),sK3) ),
    inference(instantiation,[status(thm)],[c_142]) ).

cnf(c_149,plain,
    ( ~ member(sK0(sK1,sK3),sK2)
    | ~ subset(sK2,sK3)
    | member(sK0(sK1,sK3),sK3) ),
    inference(instantiation,[status(thm)],[c_145]) ).

cnf(c_150,plain,
    ( ~ member(sK0(sK1,sK3),sK1)
    | ~ subset(sK1,sK2)
    | member(sK0(sK1,sK3),sK2) ),
    inference(instantiation,[status(thm)],[c_141]) ).

cnf(c_151,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_150,c_149,c_104,c_100,c_54,c_55]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET027+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n008.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 20:23:42 EDT 2024
% 0.11/0.32  % 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 --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.71/1.13  % SZS status Started for theBenchmark.p
% 1.71/1.13  % SZS status Theorem for theBenchmark.p
% 1.71/1.13  
% 1.71/1.13  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.71/1.13  
% 1.71/1.13  ------  iProver source info
% 1.71/1.13  
% 1.71/1.13  git: date: 2024-05-02 19:28:25 +0000
% 1.71/1.13  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.71/1.13  git: non_committed_changes: false
% 1.71/1.13  
% 1.71/1.13  ------ Parsing...
% 1.71/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.71/1.13  
% 1.71/1.13  ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 1.71/1.13  
% 1.71/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.71/1.13  ------ Proving...
% 1.71/1.13  ------ Problem Properties 
% 1.71/1.13  
% 1.71/1.13  
% 1.71/1.13  clauses                                 7
% 1.71/1.13  conjectures                             3
% 1.71/1.13  EPR                                     5
% 1.71/1.13  Horn                                    6
% 1.71/1.13  unary                                   4
% 1.71/1.13  binary                                  2
% 1.71/1.13  lits                                    11
% 1.71/1.13  lits eq                                 0
% 1.71/1.13  fd_pure                                 0
% 1.71/1.13  fd_pseudo                               0
% 1.71/1.13  fd_cond                                 0
% 1.71/1.13  fd_pseudo_cond                          0
% 1.71/1.13  AC symbols                              0
% 1.71/1.13  
% 1.71/1.13  ------ Schedule dynamic 5 is on 
% 1.71/1.13  
% 1.71/1.13  ------ no equalities: superposition off 
% 1.71/1.13  
% 1.71/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.71/1.13  
% 1.71/1.13  
% 1.71/1.13  ------ 
% 1.71/1.13  Current options:
% 1.71/1.13  ------ 
% 1.71/1.13  
% 1.71/1.13  
% 1.71/1.13  
% 1.71/1.13  
% 1.71/1.13  ------ Proving...
% 1.71/1.13  
% 1.71/1.13  
% 1.71/1.13  % SZS status Theorem for theBenchmark.p
% 1.71/1.13  
% 1.71/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.71/1.13  
% 1.71/1.13  
%------------------------------------------------------------------------------