TSTP Solution File: SET200+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n023.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 15:07:08 EDT 2023

% Result   : Theorem 0.44s 1.14s
% Output   : CNFRefutation 0.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   44 (  12 unt;   0 def)
%            Number of atoms       :  116 (   2 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  123 (  51   ~;  40   |;  24   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   85 (   2 sgn;  50   !;  15   ?)

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

fof(f2,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(f6,conjecture,
    ! [X0,X1,X2,X3] :
      ( ( subset(X2,X3)
        & subset(X0,X1) )
     => subset(union(X0,X2),union(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th34) ).

fof(f7,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( ( subset(X2,X3)
          & subset(X0,X1) )
       => subset(union(X0,X2),union(X1,X3)) ),
    inference(negated_conjecture,[],[f6]) ).

fof(f8,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f9,plain,
    ? [X0,X1,X2,X3] :
      ( ~ subset(union(X0,X2),union(X1,X3))
      & subset(X2,X3)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f10,plain,
    ? [X0,X1,X2,X3] :
      ( ~ subset(union(X0,X2),union(X1,X3))
      & subset(X2,X3)
      & subset(X0,X1) ),
    inference(flattening,[],[f9]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f12,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f11]) ).

fof(f13,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,[],[f8]) ).

fof(f14,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,[],[f13]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,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])],[f14,f15]) ).

fof(f21,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ subset(union(X0,X2),union(X1,X3))
        & subset(X2,X3)
        & subset(X0,X1) )
   => ( ~ subset(union(sK2,sK4),union(sK3,sK5))
      & subset(sK4,sK5)
      & subset(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ( ~ subset(union(sK2,sK4),union(sK3,sK5))
    & subset(sK4,sK5)
    & subset(sK2,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f10,f21]) ).

fof(f23,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | member(X2,X0)
      | ~ member(X2,union(X0,X1)) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f24,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f25,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f26,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f35,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f22]) ).

fof(f36,plain,
    subset(sK4,sK5),
    inference(cnf_transformation,[],[f22]) ).

fof(f37,plain,
    ~ subset(union(sK2,sK4),union(sK3,sK5)),
    inference(cnf_transformation,[],[f22]) ).

cnf(c_49,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X2,X1)) ),
    inference(cnf_transformation,[],[f25]) ).

cnf(c_50,plain,
    ( ~ member(X0,X1)
    | member(X0,union(X1,X2)) ),
    inference(cnf_transformation,[],[f24]) ).

cnf(c_51,plain,
    ( ~ member(X0,union(X1,X2))
    | member(X0,X1)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f23]) ).

cnf(c_52,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_53,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_54,plain,
    ( ~ member(X0,X1)
    | ~ subset(X1,X2)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f26]) ).

cnf(c_59,negated_conjecture,
    ~ subset(union(sK2,sK4),union(sK3,sK5)),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_60,negated_conjecture,
    subset(sK4,sK5),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_61,negated_conjecture,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_166,plain,
    ( union(sK2,sK4) != X0
    | union(sK3,sK5) != X1
    | member(sK0(X0,X1),X0) ),
    inference(resolution_lifted,[status(thm)],[c_53,c_59]) ).

cnf(c_167,plain,
    member(sK0(union(sK2,sK4),union(sK3,sK5)),union(sK2,sK4)),
    inference(unflattening,[status(thm)],[c_166]) ).

cnf(c_394,plain,
    ~ member(sK0(union(sK2,sK4),union(sK3,sK5)),union(sK3,sK5)),
    inference(resolution,[status(thm)],[c_52,c_59]) ).

cnf(c_396,plain,
    ~ member(sK0(union(sK2,sK4),union(sK3,sK5)),sK3),
    inference(resolution,[status(thm)],[c_394,c_50]) ).

cnf(c_397,plain,
    ~ member(sK0(union(sK2,sK4),union(sK3,sK5)),sK5),
    inference(resolution,[status(thm)],[c_394,c_49]) ).

cnf(c_439,plain,
    ( ~ member(sK0(union(sK2,sK4),union(sK3,sK5)),union(sK2,sK4))
    | member(sK0(union(sK2,sK4),union(sK3,sK5)),sK2)
    | member(sK0(union(sK2,sK4),union(sK3,sK5)),sK4) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_692,plain,
    ( ~ member(sK0(union(sK2,sK4),union(sK3,sK5)),X0)
    | ~ subset(X0,sK3) ),
    inference(resolution,[status(thm)],[c_54,c_396]) ).

cnf(c_693,plain,
    ( ~ member(sK0(union(sK2,sK4),union(sK3,sK5)),sK2)
    | ~ subset(sK2,sK3) ),
    inference(instantiation,[status(thm)],[c_692]) ).

cnf(c_694,plain,
    ( ~ member(sK0(union(sK2,sK4),union(sK3,sK5)),X0)
    | ~ subset(X0,sK5) ),
    inference(resolution,[status(thm)],[c_54,c_397]) ).

cnf(c_1215,plain,
    ~ member(sK0(union(sK2,sK4),union(sK3,sK5)),sK4),
    inference(resolution,[status(thm)],[c_694,c_60]) ).

cnf(c_1216,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_1215,c_693,c_439,c_167,c_61]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Aug 26 14:34:41 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.46  Running first-order theorem proving
% 0.18/0.46  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.44/1.14  % SZS status Started for theBenchmark.p
% 0.44/1.14  % SZS status Theorem for theBenchmark.p
% 0.44/1.14  
% 0.44/1.14  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.44/1.14  
% 0.44/1.14  ------  iProver source info
% 0.44/1.14  
% 0.44/1.14  git: date: 2023-05-31 18:12:56 +0000
% 0.44/1.14  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.44/1.14  git: non_committed_changes: false
% 0.44/1.14  git: last_make_outside_of_git: false
% 0.44/1.14  
% 0.44/1.14  ------ Parsing...
% 0.44/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.44/1.14  
% 0.44/1.14  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 0.44/1.14  
% 0.44/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.44/1.14  
% 0.44/1.14  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.44/1.14  ------ Proving...
% 0.44/1.14  ------ Problem Properties 
% 0.44/1.14  
% 0.44/1.14  
% 0.44/1.14  clauses                                 13
% 0.44/1.14  conjectures                             3
% 0.44/1.14  EPR                                     4
% 0.44/1.14  Horn                                    10
% 0.44/1.14  unary                                   5
% 0.44/1.14  binary                                  4
% 0.44/1.14  lits                                    25
% 0.44/1.14  lits eq                                 3
% 0.44/1.14  fd_pure                                 0
% 0.44/1.14  fd_pseudo                               0
% 0.44/1.14  fd_cond                                 0
% 0.44/1.14  fd_pseudo_cond                          2
% 0.44/1.14  AC symbols                              0
% 0.44/1.14  
% 0.44/1.14  ------ Input Options Time Limit: Unbounded
% 0.44/1.14  
% 0.44/1.14  
% 0.44/1.14  ------ 
% 0.44/1.14  Current options:
% 0.44/1.14  ------ 
% 0.44/1.14  
% 0.44/1.14  
% 0.44/1.14  
% 0.44/1.14  
% 0.44/1.14  ------ Proving...
% 0.44/1.14  
% 0.44/1.14  
% 0.44/1.14  % SZS status Theorem for theBenchmark.p
% 0.44/1.14  
% 0.44/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.44/1.14  
% 0.44/1.14  
%------------------------------------------------------------------------------