TSTP Solution File: SET971+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET971+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n016.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 15:10:52 EDT 2023

% Result   : Theorem 1.87s 1.15s
% Output   : CNFRefutation 1.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   30 (  18 unt;   0 def)
%            Number of atoms       :   53 (  30 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   40 (  17   ~;   7   |;  12   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   52 (   0 sgn;  26   !;  12   ?)

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

fof(f6,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/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).

fof(f7,conjecture,
    ! [X0,X1,X2,X3] :
      ( ( subset(X2,X3)
        & subset(X0,X1) )
     => cartesian_product2(X0,X2) = set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_zfmisc_1) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( ( subset(X2,X3)
          & subset(X0,X1) )
       => cartesian_product2(X0,X2) = set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2)) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_intersection2(X0,X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

fof(f12,plain,
    ? [X0,X1,X2,X3] :
      ( cartesian_product2(X0,X2) != set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2))
      & subset(X2,X3)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f13,plain,
    ? [X0,X1,X2,X3] :
      ( cartesian_product2(X0,X2) != set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2))
      & subset(X2,X3)
      & subset(X0,X1) ),
    inference(flattening,[],[f12]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) = X0
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f19,plain,
    ( ? [X0,X1,X2,X3] :
        ( cartesian_product2(X0,X2) != set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2))
        & subset(X2,X3)
        & subset(X0,X1) )
   => ( cartesian_product2(sK2,sK4) != set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4))
      & subset(sK4,sK5)
      & subset(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ( cartesian_product2(sK2,sK4) != set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4))
    & subset(sK4,sK5)
    & subset(sK2,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f13,f19]) ).

fof(f21,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f26,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,[],[f6]) ).

fof(f27,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f20]) ).

fof(f28,plain,
    subset(sK4,sK5),
    inference(cnf_transformation,[],[f20]) ).

fof(f29,plain,
    cartesian_product2(sK2,sK4) != set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4)),
    inference(cnf_transformation,[],[f20]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) = X0
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f14]) ).

cnf(c_49,plain,
    set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f21]) ).

cnf(c_54,plain,
    set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = cartesian_product2(set_intersection2(X0,X2),set_intersection2(X1,X3)),
    inference(cnf_transformation,[],[f26]) ).

cnf(c_55,negated_conjecture,
    set_intersection2(cartesian_product2(sK2,sK5),cartesian_product2(sK3,sK4)) != cartesian_product2(sK2,sK4),
    inference(cnf_transformation,[],[f29]) ).

cnf(c_56,negated_conjecture,
    subset(sK4,sK5),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_57,negated_conjecture,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f27]) ).

cnf(c_58,plain,
    ( ~ subset(X0,X1)
    | set_intersection2(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_101,plain,
    ( X0 != sK4
    | X1 != sK5
    | set_intersection2(X0,X1) = X0 ),
    inference(resolution_lifted,[status(thm)],[c_56,c_58]) ).

cnf(c_102,plain,
    set_intersection2(sK4,sK5) = sK4,
    inference(unflattening,[status(thm)],[c_101]) ).

cnf(c_106,plain,
    ( X0 != sK2
    | X1 != sK3
    | set_intersection2(X0,X1) = X0 ),
    inference(resolution_lifted,[status(thm)],[c_57,c_58]) ).

cnf(c_107,plain,
    set_intersection2(sK2,sK3) = sK2,
    inference(unflattening,[status(thm)],[c_106]) ).

cnf(c_175,plain,
    set_intersection2(cartesian_product2(sK2,X0),cartesian_product2(sK3,X1)) = cartesian_product2(sK2,set_intersection2(X0,X1)),
    inference(superposition,[status(thm)],[c_107,c_54]) ).

cnf(c_181,plain,
    cartesian_product2(sK2,set_intersection2(sK5,sK4)) != cartesian_product2(sK2,sK4),
    inference(demodulation,[status(thm)],[c_55,c_175]) ).

cnf(c_182,plain,
    cartesian_product2(sK2,sK4) != cartesian_product2(sK2,sK4),
    inference(demodulation,[status(thm)],[c_181,c_49,c_102]) ).

cnf(c_183,plain,
    $false,
    inference(equality_resolution_simp,[status(thm)],[c_182]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET971+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.16/0.34  % Computer : n016.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Sat Aug 26 11:58:42 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.18/0.47  Running first-order theorem proving
% 0.18/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.87/1.15  % SZS status Started for theBenchmark.p
% 1.87/1.15  % SZS status Theorem for theBenchmark.p
% 1.87/1.15  
% 1.87/1.15  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.87/1.15  
% 1.87/1.15  ------  iProver source info
% 1.87/1.15  
% 1.87/1.15  git: date: 2023-05-31 18:12:56 +0000
% 1.87/1.15  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.87/1.15  git: non_committed_changes: false
% 1.87/1.15  git: last_make_outside_of_git: false
% 1.87/1.15  
% 1.87/1.15  ------ Parsing...
% 1.87/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.87/1.15  
% 1.87/1.15  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e 
% 1.87/1.15  
% 1.87/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.87/1.15  
% 1.87/1.15  ------ Preprocessing... sf_s  rm: 0 0s  sf_e 
% 1.87/1.15  ------ Proving...
% 1.87/1.15  ------ Problem Properties 
% 1.87/1.15  
% 1.87/1.15  
% 1.87/1.15  clauses                                 7
% 1.87/1.15  conjectures                             1
% 1.87/1.15  EPR                                     1
% 1.87/1.15  Horn                                    7
% 1.87/1.15  unary                                   7
% 1.87/1.15  binary                                  0
% 1.87/1.15  lits                                    7
% 1.87/1.15  lits eq                                 7
% 1.87/1.15  fd_pure                                 0
% 1.87/1.15  fd_pseudo                               0
% 1.87/1.15  fd_cond                                 0
% 1.87/1.15  fd_pseudo_cond                          0
% 1.87/1.15  AC symbols                              0
% 1.87/1.15  
% 1.87/1.15  ------ Schedule UEQ
% 1.87/1.15  
% 1.87/1.15  ------ Option_UEQ Time Limit: 10.
% 1.87/1.15  
% 1.87/1.15  
% 1.87/1.15  ------ 
% 1.87/1.15  Current options:
% 1.87/1.15  ------ 
% 1.87/1.15  
% 1.87/1.15  
% 1.87/1.15  
% 1.87/1.15  
% 1.87/1.15  ------ Proving...
% 1.87/1.15  
% 1.87/1.15  
% 1.87/1.15  % SZS status Theorem for theBenchmark.p
% 1.87/1.15  
% 1.87/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.87/1.15  
% 1.87/1.15  
%------------------------------------------------------------------------------