TSTP Solution File: SET586+3 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET586+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n027.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 15:08:25 EDT 2023

% Result   : Theorem 2.76s 1.16s
% Output   : CNFRefutation 2.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   45 (  11 unt;   0 def)
%            Number of atoms       :  116 (   7 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  127 (  56   ~;  46   |;  17   &)
%                                         (   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    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   85 (   2 sgn;  52   !;   9   ?)

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

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

fof(f3,axiom,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(f6,conjecture,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
     => subset(intersection(X0,X2),intersection(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_of_subset) ).

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

fof(f10,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(flattening,[],[f10]) ).

fof(f12,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(f13,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,[],[f12]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,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])],[f13,f14]) ).

fof(f20,plain,
    ( ? [X0,X1,X2] :
        ( ~ subset(intersection(X0,X2),intersection(X1,X2))
        & subset(X0,X1) )
   => ( ~ subset(intersection(sK2,sK4),intersection(sK3,sK4))
      & subset(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ( ~ subset(intersection(sK2,sK4),intersection(sK3,sK4))
    & subset(sK2,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f9,f20]) ).

fof(f22,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f23,plain,
    ! [X2,X0,X1] :
      ( member(X2,X1)
      | ~ member(X2,intersection(X0,X1)) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f24,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f25,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f28,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f34,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f21]) ).

fof(f35,plain,
    ~ subset(intersection(sK2,sK4),intersection(sK3,sK4)),
    inference(cnf_transformation,[],[f21]) ).

cnf(c_49,plain,
    ( ~ member(X0,X1)
    | ~ member(X0,X2)
    | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[],[f24]) ).

cnf(c_50,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f23]) ).

cnf(c_51,plain,
    ( ~ member(X0,intersection(X1,X2))
    | member(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

cnf(c_52,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_53,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

cnf(c_54,plain,
    ( ~ member(X0,X1)
    | ~ subset(X1,X2)
    | member(X0,X2) ),
    inference(cnf_transformation,[],[f25]) ).

cnf(c_55,plain,
    intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_59,negated_conjecture,
    ~ subset(intersection(sK2,sK4),intersection(sK3,sK4)),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_60,negated_conjecture,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f34]) ).

cnf(c_115,plain,
    ~ subset(intersection(sK2,sK4),intersection(sK4,sK3)),
    inference(demodulation,[status(thm)],[c_59,c_55]) ).

cnf(c_193,plain,
    ( intersection(sK2,sK4) != X0
    | intersection(sK4,sK3) != X1
    | member(sK0(X0,X1),X0) ),
    inference(resolution_lifted,[status(thm)],[c_53,c_115]) ).

cnf(c_194,plain,
    member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),intersection(sK2,sK4)),
    inference(unflattening,[status(thm)],[c_193]) ).

cnf(c_198,plain,
    ( intersection(sK2,sK4) != X0
    | intersection(sK4,sK3) != X1
    | ~ member(sK0(X0,X1),X1) ),
    inference(resolution_lifted,[status(thm)],[c_52,c_115]) ).

cnf(c_199,plain,
    ~ member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),intersection(sK4,sK3)),
    inference(unflattening,[status(thm)],[c_198]) ).

cnf(c_564,plain,
    ( ~ member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),intersection(sK2,sK4))
    | member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),sK2) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_565,plain,
    ( ~ member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),intersection(sK2,sK4))
    | member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),sK4) ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_740,plain,
    ( ~ member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),sK2)
    | ~ subset(sK2,X0)
    | member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),X0) ),
    inference(instantiation,[status(thm)],[c_54]) ).

cnf(c_828,plain,
    ( ~ member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),X0)
    | ~ member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),sK4)
    | member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),intersection(sK4,X0)) ),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_2054,plain,
    ( ~ member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),sK4)
    | ~ member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),sK3)
    | member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),intersection(sK4,sK3)) ),
    inference(instantiation,[status(thm)],[c_828]) ).

cnf(c_3329,plain,
    ( ~ member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),sK2)
    | ~ subset(sK2,sK3)
    | member(sK0(intersection(sK2,sK4),intersection(sK4,sK3)),sK3) ),
    inference(instantiation,[status(thm)],[c_740]) ).

cnf(c_3331,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_3329,c_2054,c_564,c_565,c_199,c_194,c_60]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET586+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n027.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 16:19:50 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.48  Running first-order theorem proving
% 0.21/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.76/1.16  % SZS status Started for theBenchmark.p
% 2.76/1.16  % SZS status Theorem for theBenchmark.p
% 2.76/1.16  
% 2.76/1.16  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.76/1.16  
% 2.76/1.16  ------  iProver source info
% 2.76/1.16  
% 2.76/1.16  git: date: 2023-05-31 18:12:56 +0000
% 2.76/1.16  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.76/1.16  git: non_committed_changes: false
% 2.76/1.16  git: last_make_outside_of_git: false
% 2.76/1.16  
% 2.76/1.16  ------ Parsing...
% 2.76/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.76/1.16  
% 2.76/1.16  ------ Preprocessing... sup_sim: 1  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 2.76/1.16  
% 2.76/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.76/1.16  
% 2.76/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.76/1.16  ------ Proving...
% 2.76/1.16  ------ Problem Properties 
% 2.76/1.16  
% 2.76/1.16  
% 2.76/1.16  clauses                                 12
% 2.76/1.16  conjectures                             1
% 2.76/1.16  EPR                                     3
% 2.76/1.16  Horn                                    10
% 2.76/1.16  unary                                   4
% 2.76/1.16  binary                                  4
% 2.76/1.16  lits                                    24
% 2.76/1.16  lits eq                                 3
% 2.76/1.16  fd_pure                                 0
% 2.76/1.16  fd_pseudo                               0
% 2.76/1.16  fd_cond                                 0
% 2.76/1.16  fd_pseudo_cond                          2
% 2.76/1.16  AC symbols                              0
% 2.76/1.16  
% 2.76/1.16  ------ Schedule dynamic 5 is on 
% 2.76/1.16  
% 2.76/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.76/1.16  
% 2.76/1.16  
% 2.76/1.16  ------ 
% 2.76/1.16  Current options:
% 2.76/1.16  ------ 
% 2.76/1.16  
% 2.76/1.16  
% 2.76/1.16  
% 2.76/1.16  
% 2.76/1.16  ------ Proving...
% 2.76/1.16  
% 2.76/1.16  
% 2.76/1.16  % SZS status Theorem for theBenchmark.p
% 2.76/1.16  
% 2.76/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.76/1.16  
% 2.76/1.16  
%------------------------------------------------------------------------------