TSTP Solution File: SET984+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n026.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 03:02:10 EDT 2024

% Result   : Theorem 7.29s 1.63s
% Output   : CNFRefutation 7.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   65 (  24 unt;   0 def)
%            Number of atoms       :  161 ( 122 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  138 (  42   ~;  71   |;  19   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  102 (   9 sgn  62   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( empty_set = cartesian_product2(X0,X1)
    <=> ( empty_set = X1
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).

fof(f8,axiom,
    ! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t123_zfmisc_1) ).

fof(f9,axiom,
    ! [X0,X1,X2,X3] :
      ( cartesian_product2(X0,X1) = cartesian_product2(X2,X3)
     => ( ( X1 = X3
          & X0 = X2 )
        | empty_set = X1
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).

fof(f10,conjecture,
    ! [X0,X1,X2,X3] :
      ( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
     => ( ( subset(X1,X3)
          & subset(X0,X2) )
        | empty_set = cartesian_product2(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).

fof(f11,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
       => ( ( subset(X1,X3)
            & subset(X0,X2) )
          | empty_set = cartesian_product2(X0,X1) ) ),
    inference(negated_conjecture,[],[f10]) ).

fof(f12,axiom,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).

fof(f13,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_intersection2(X0,X1) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).

fof(f16,plain,
    ! [X0,X1,X2,X3] :
      ( ( X1 = X3
        & X0 = X2 )
      | empty_set = X1
      | empty_set = X0
      | cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f17,plain,
    ! [X0,X1,X2,X3] :
      ( ( X1 = X3
        & X0 = X2 )
      | empty_set = X1
      | empty_set = X0
      | cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
    inference(flattening,[],[f16]) ).

fof(f18,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ subset(X1,X3)
        | ~ subset(X0,X2) )
      & empty_set != cartesian_product2(X0,X1)
      & subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f19,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ subset(X1,X3)
        | ~ subset(X0,X2) )
      & empty_set != cartesian_product2(X0,X1)
      & subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
    inference(flattening,[],[f18]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) = X0
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( empty_set = cartesian_product2(X0,X1)
        | ( empty_set != X1
          & empty_set != X0 ) )
      & ( empty_set = X1
        | empty_set = X0
        | empty_set != cartesian_product2(X0,X1) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( empty_set = cartesian_product2(X0,X1)
        | ( empty_set != X1
          & empty_set != X0 ) )
      & ( empty_set = X1
        | empty_set = X0
        | empty_set != cartesian_product2(X0,X1) ) ),
    inference(flattening,[],[f25]) ).

fof(f27,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( ~ subset(X1,X3)
          | ~ subset(X0,X2) )
        & empty_set != cartesian_product2(X0,X1)
        & subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
   => ( ( ~ subset(sK3,sK5)
        | ~ subset(sK2,sK4) )
      & empty_set != cartesian_product2(sK2,sK3)
      & subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ( ( ~ subset(sK3,sK5)
      | ~ subset(sK2,sK4) )
    & empty_set != cartesian_product2(sK2,sK3)
    & subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f19,f27]) ).

fof(f29,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( empty_set = cartesian_product2(X0,X1)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( empty_set = cartesian_product2(X0,X1)
      | empty_set != X1 ),
    inference(cnf_transformation,[],[f26]) ).

fof(f38,plain,
    ! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
    inference(cnf_transformation,[],[f8]) ).

fof(f39,plain,
    ! [X2,X3,X0,X1] :
      ( X0 = X2
      | empty_set = X1
      | empty_set = X0
      | cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f40,plain,
    ! [X2,X3,X0,X1] :
      ( X1 = X3
      | empty_set = X1
      | empty_set = X0
      | cartesian_product2(X0,X1) != cartesian_product2(X2,X3) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f41,plain,
    subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)),
    inference(cnf_transformation,[],[f28]) ).

fof(f42,plain,
    empty_set != cartesian_product2(sK2,sK3),
    inference(cnf_transformation,[],[f28]) ).

fof(f43,plain,
    ( ~ subset(sK3,sK5)
    | ~ subset(sK2,sK4) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f44,plain,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    inference(cnf_transformation,[],[f12]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) = X0
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f46,plain,
    ! [X0] : empty_set = cartesian_product2(X0,empty_set),
    inference(equality_resolution,[],[f37]) ).

fof(f47,plain,
    ! [X1] : empty_set = cartesian_product2(empty_set,X1),
    inference(equality_resolution,[],[f36]) ).

cnf(c_49,plain,
    set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_55,plain,
    cartesian_product2(X0,empty_set) = empty_set,
    inference(cnf_transformation,[],[f46]) ).

cnf(c_56,plain,
    cartesian_product2(empty_set,X0) = empty_set,
    inference(cnf_transformation,[],[f47]) ).

cnf(c_58,plain,
    set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = cartesian_product2(set_intersection2(X0,X2),set_intersection2(X1,X3)),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_59,plain,
    ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
    | X0 = empty_set
    | X1 = X3
    | X1 = empty_set ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_60,plain,
    ( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
    | X0 = X2
    | X0 = empty_set
    | X1 = empty_set ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_61,negated_conjecture,
    ( ~ subset(sK3,sK5)
    | ~ subset(sK2,sK4) ),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_62,negated_conjecture,
    cartesian_product2(sK2,sK3) != empty_set,
    inference(cnf_transformation,[],[f42]) ).

cnf(c_63,negated_conjecture,
    subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_64,plain,
    subset(set_intersection2(X0,X1),X0),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_65,plain,
    ( ~ subset(X0,X1)
    | set_intersection2(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_405,plain,
    set_intersection2(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) = cartesian_product2(sK2,sK3),
    inference(superposition,[status(thm)],[c_63,c_65]) ).

cnf(c_582,plain,
    cartesian_product2(set_intersection2(sK2,sK4),set_intersection2(sK3,sK5)) = cartesian_product2(sK2,sK3),
    inference(superposition,[status(thm)],[c_58,c_405]) ).

cnf(c_1320,plain,
    subset(set_intersection2(X0,X1),X1),
    inference(superposition,[status(thm)],[c_49,c_64]) ).

cnf(c_3159,plain,
    ( cartesian_product2(X0,X1) != cartesian_product2(sK2,sK3)
    | set_intersection2(sK3,sK5) = X1
    | set_intersection2(sK3,sK5) = empty_set
    | set_intersection2(sK2,sK4) = empty_set ),
    inference(superposition,[status(thm)],[c_582,c_59]) ).

cnf(c_3285,plain,
    ( set_intersection2(sK3,sK5) = empty_set
    | set_intersection2(sK3,sK5) = sK3
    | set_intersection2(sK2,sK4) = empty_set ),
    inference(equality_resolution,[status(thm)],[c_3159]) ).

cnf(c_3839,plain,
    ( cartesian_product2(empty_set,set_intersection2(sK3,sK5)) = cartesian_product2(sK2,sK3)
    | set_intersection2(sK3,sK5) = empty_set
    | set_intersection2(sK3,sK5) = sK3 ),
    inference(superposition,[status(thm)],[c_3285,c_582]) ).

cnf(c_3982,plain,
    ( set_intersection2(sK3,sK5) = empty_set
    | set_intersection2(sK3,sK5) = sK3
    | cartesian_product2(sK2,sK3) = empty_set ),
    inference(superposition,[status(thm)],[c_3839,c_56]) ).

cnf(c_6341,plain,
    ( cartesian_product2(X0,X1) != cartesian_product2(sK2,sK3)
    | set_intersection2(sK3,sK5) = X1
    | set_intersection2(sK3,sK5) = empty_set
    | set_intersection2(sK2,sK4) = empty_set ),
    inference(superposition,[status(thm)],[c_582,c_59]) ).

cnf(c_6364,plain,
    ( cartesian_product2(X0,X1) != cartesian_product2(sK2,sK3)
    | set_intersection2(sK3,sK5) = empty_set
    | set_intersection2(sK2,sK4) = X0
    | set_intersection2(sK2,sK4) = empty_set ),
    inference(superposition,[status(thm)],[c_582,c_60]) ).

cnf(c_6414,plain,
    ( set_intersection2(sK3,sK5) = empty_set
    | set_intersection2(sK3,sK5) = sK3
    | set_intersection2(sK2,sK4) = empty_set ),
    inference(equality_resolution,[status(thm)],[c_6341]) ).

cnf(c_6426,plain,
    ( set_intersection2(sK3,sK5) = empty_set
    | set_intersection2(sK2,sK4) = empty_set
    | set_intersection2(sK2,sK4) = sK2 ),
    inference(equality_resolution,[status(thm)],[c_6364]) ).

cnf(c_6891,plain,
    ( set_intersection2(sK3,sK5) = sK3
    | set_intersection2(sK3,sK5) = empty_set ),
    inference(global_subsumption_just,[status(thm)],[c_6414,c_62,c_3982]) ).

cnf(c_6892,plain,
    ( set_intersection2(sK3,sK5) = empty_set
    | set_intersection2(sK3,sK5) = sK3 ),
    inference(renaming,[status(thm)],[c_6891]) ).

cnf(c_6895,plain,
    ( set_intersection2(sK3,sK5) = empty_set
    | subset(sK3,sK5) ),
    inference(superposition,[status(thm)],[c_6892,c_1320]) ).

cnf(c_6944,plain,
    ( set_intersection2(sK3,sK5) = empty_set
    | set_intersection2(sK2,sK4) = empty_set
    | subset(sK2,sK4) ),
    inference(superposition,[status(thm)],[c_6426,c_1320]) ).

cnf(c_6963,plain,
    ( cartesian_product2(sK2,set_intersection2(sK3,sK5)) = cartesian_product2(sK2,sK3)
    | set_intersection2(sK3,sK5) = empty_set
    | set_intersection2(sK2,sK4) = empty_set ),
    inference(superposition,[status(thm)],[c_6426,c_582]) ).

cnf(c_6974,plain,
    ( set_intersection2(sK3,sK5) = empty_set
    | set_intersection2(sK2,sK4) = empty_set ),
    inference(global_subsumption_just,[status(thm)],[c_6963,c_61,c_6895,c_6944]) ).

cnf(c_6978,plain,
    ( set_intersection2(sK3,sK5) = empty_set
    | subset(empty_set,sK4) ),
    inference(superposition,[status(thm)],[c_6974,c_1320]) ).

cnf(c_6998,plain,
    ( cartesian_product2(empty_set,set_intersection2(sK3,sK5)) = cartesian_product2(sK2,sK3)
    | set_intersection2(sK3,sK5) = empty_set ),
    inference(superposition,[status(thm)],[c_6974,c_582]) ).

cnf(c_7259,plain,
    ( set_intersection2(sK3,sK5) = empty_set
    | cartesian_product2(sK2,sK3) = empty_set ),
    inference(superposition,[status(thm)],[c_6998,c_56]) ).

cnf(c_7357,plain,
    set_intersection2(sK3,sK5) = empty_set,
    inference(global_subsumption_just,[status(thm)],[c_6978,c_62,c_7259]) ).

cnf(c_7382,plain,
    cartesian_product2(set_intersection2(sK2,sK4),empty_set) = cartesian_product2(sK2,sK3),
    inference(superposition,[status(thm)],[c_7357,c_582]) ).

cnf(c_7481,plain,
    cartesian_product2(sK2,sK3) = empty_set,
    inference(superposition,[status(thm)],[c_7382,c_55]) ).

cnf(c_7506,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_7481,c_62]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n026.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 20:43:06 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.16/0.43  Running first-order theorem proving
% 0.16/0.43  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.29/1.63  % SZS status Started for theBenchmark.p
% 7.29/1.63  % SZS status Theorem for theBenchmark.p
% 7.29/1.63  
% 7.29/1.63  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.29/1.63  
% 7.29/1.63  ------  iProver source info
% 7.29/1.63  
% 7.29/1.63  git: date: 2024-05-02 19:28:25 +0000
% 7.29/1.63  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.29/1.63  git: non_committed_changes: false
% 7.29/1.63  
% 7.29/1.63  ------ Parsing...
% 7.29/1.63  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.29/1.63  
% 7.29/1.63  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 7.29/1.63  
% 7.29/1.63  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.29/1.63  
% 7.29/1.63  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.29/1.63  ------ Proving...
% 7.29/1.63  ------ Problem Properties 
% 7.29/1.63  
% 7.29/1.63  
% 7.29/1.63  clauses                                 17
% 7.29/1.63  conjectures                             3
% 7.29/1.63  EPR                                     5
% 7.29/1.63  Horn                                    14
% 7.29/1.63  unary                                   12
% 7.29/1.63  binary                                  2
% 7.29/1.63  lits                                    27
% 7.29/1.63  lits eq                                 18
% 7.29/1.63  fd_pure                                 0
% 7.29/1.63  fd_pseudo                               0
% 7.29/1.63  fd_cond                                 1
% 7.29/1.63  fd_pseudo_cond                          2
% 7.29/1.63  AC symbols                              0
% 7.29/1.63  
% 7.29/1.63  ------ Input Options Time Limit: Unbounded
% 7.29/1.63  
% 7.29/1.63  
% 7.29/1.63  ------ 
% 7.29/1.63  Current options:
% 7.29/1.63  ------ 
% 7.29/1.63  
% 7.29/1.63  
% 7.29/1.63  
% 7.29/1.63  
% 7.29/1.63  ------ Proving...
% 7.29/1.63  
% 7.29/1.63  
% 7.29/1.63  % SZS status Theorem for theBenchmark.p
% 7.29/1.63  
% 7.29/1.63  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.29/1.63  
% 7.29/1.63  
%------------------------------------------------------------------------------