TSTP Solution File: SET974+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n005.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 03:02:09 EDT 2024

% Result   : Theorem 2.84s 1.16s
% Output   : CNFRefutation 2.84s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( disjoint(X0,X1)
     => disjoint(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

fof(f10,axiom,
    ! [X0,X1,X2,X3,X4] :
      ~ ( ! [X5,X6] :
            ~ ( in(X6,set_intersection2(X2,X4))
              & in(X5,set_intersection2(X1,X3))
              & ordered_pair(X5,X6) = X0 )
        & in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t104_zfmisc_1) ).

fof(f11,conjecture,
    ! [X0,X1,X2,X3] :
      ( ( disjoint(X2,X3)
        | disjoint(X0,X1) )
     => disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( ( disjoint(X2,X3)
          | disjoint(X0,X1) )
       => disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f13,axiom,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] : in(X2,set_intersection2(X0,X1)) )
      & ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
          & ~ disjoint(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ~ ( disjoint(X0,X1)
          & ? [X2] : in(X2,set_intersection2(X0,X1)) )
      & ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
          & ~ disjoint(X0,X1) ) ),
    inference(rectify,[],[f13]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( disjoint(X1,X0)
      | ~ disjoint(X0,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f18,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ? [X5,X6] :
          ( in(X6,set_intersection2(X2,X4))
          & in(X5,set_intersection2(X1,X3))
          & ordered_pair(X5,X6) = X0 )
      | ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f19,plain,
    ? [X0,X1,X2,X3] :
      ( ~ disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
      & ( disjoint(X2,X3)
        | disjoint(X0,X1) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
      & ( ? [X3] : in(X3,set_intersection2(X0,X1))
        | disjoint(X0,X1) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f25,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ? [X5,X6] :
          ( in(X6,set_intersection2(X2,X4))
          & in(X5,set_intersection2(X1,X3))
          & ordered_pair(X5,X6) = X0 )
     => ( in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
        & in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
        & ordered_pair(sK2(X0,X1,X2,X3,X4),sK3(X0,X1,X2,X3,X4)) = X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
        & in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
        & ordered_pair(sK2(X0,X1,X2,X3,X4),sK3(X0,X1,X2,X3,X4)) = X0 )
      | ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f18,f25]) ).

fof(f27,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
        & ( disjoint(X2,X3)
          | disjoint(X0,X1) ) )
   => ( ~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7))
      & ( disjoint(sK6,sK7)
        | disjoint(sK4,sK5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ( ~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7))
    & ( disjoint(sK6,sK7)
      | disjoint(sK4,sK5) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f19,f27]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ? [X3] : in(X3,set_intersection2(X0,X1))
     => in(sK8(X0,X1),set_intersection2(X0,X1)) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X0,X1)
        | ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
      & ( in(sK8(X0,X1),set_intersection2(X0,X1))
        | disjoint(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f20,f29]) ).

fof(f33,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( disjoint(X1,X0)
      | ~ disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f41,plain,
    ! [X2,X3,X0,X1,X4] :
      ( in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3))
      | ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f42,plain,
    ! [X2,X3,X0,X1,X4] :
      ( in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4))
      | ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f43,plain,
    ( disjoint(sK6,sK7)
    | disjoint(sK4,sK5) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f44,plain,
    ~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7)),
    inference(cnf_transformation,[],[f28]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( in(sK8(X0,X1),set_intersection2(X0,X1))
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( ~ disjoint(X0,X1)
      | ~ in(X2,set_intersection2(X0,X1)) ),
    inference(cnf_transformation,[],[f30]) ).

cnf(c_51,plain,
    set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f33]) ).

cnf(c_56,plain,
    ( ~ disjoint(X0,X1)
    | disjoint(X1,X0) ),
    inference(cnf_transformation,[],[f39]) ).

cnf(c_57,plain,
    ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
    | in(sK3(X0,X1,X2,X3,X4),set_intersection2(X2,X4)) ),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_58,plain,
    ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
    | in(sK2(X0,X1,X2,X3,X4),set_intersection2(X1,X3)) ),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_60,negated_conjecture,
    ~ disjoint(cartesian_product2(sK4,sK6),cartesian_product2(sK5,sK7)),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_61,negated_conjecture,
    ( disjoint(sK4,sK5)
    | disjoint(sK6,sK7) ),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_62,plain,
    ( ~ in(X0,set_intersection2(X1,X2))
    | ~ disjoint(X1,X2) ),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_63,plain,
    ( in(sK8(X0,X1),set_intersection2(X0,X1))
    | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_175,plain,
    cartesian_product2(sK4,sK6) = sP0_iProver_def,
    definition ).

cnf(c_176,plain,
    cartesian_product2(sK5,sK7) = sP1_iProver_def,
    definition ).

cnf(c_177,negated_conjecture,
    ( disjoint(sK4,sK5)
    | disjoint(sK6,sK7) ),
    inference(demodulation,[status(thm)],[c_61]) ).

cnf(c_178,negated_conjecture,
    ~ disjoint(sP0_iProver_def,sP1_iProver_def),
    inference(demodulation,[status(thm)],[c_60,c_176,c_175]) ).

cnf(c_405,plain,
    ( disjoint(sK4,sK5)
    | disjoint(sK7,sK6) ),
    inference(superposition,[status(thm)],[c_177,c_56]) ).

cnf(c_425,plain,
    ( ~ in(X0,set_intersection2(X1,X2))
    | ~ disjoint(X2,X1) ),
    inference(superposition,[status(thm)],[c_51,c_62]) ).

cnf(c_562,plain,
    ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
    | ~ disjoint(X4,X2) ),
    inference(superposition,[status(thm)],[c_57,c_425]) ).

cnf(c_589,plain,
    ( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
    | ~ disjoint(X3,X1) ),
    inference(superposition,[status(thm)],[c_58,c_425]) ).

cnf(c_682,plain,
    ( ~ disjoint(X0,X1)
    | disjoint(cartesian_product2(X2,X1),cartesian_product2(X3,X0)) ),
    inference(superposition,[status(thm)],[c_63,c_562]) ).

cnf(c_780,plain,
    ( ~ disjoint(X0,sK6)
    | disjoint(sP0_iProver_def,cartesian_product2(X1,X0)) ),
    inference(superposition,[status(thm)],[c_175,c_682]) ).

cnf(c_814,plain,
    ( ~ disjoint(sK7,sK6)
    | disjoint(sP0_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_176,c_780]) ).

cnf(c_816,plain,
    ~ disjoint(sK7,sK6),
    inference(forward_subsumption_resolution,[status(thm)],[c_814,c_178]) ).

cnf(c_819,plain,
    disjoint(sK4,sK5),
    inference(backward_subsumption_resolution,[status(thm)],[c_405,c_816]) ).

cnf(c_828,plain,
    disjoint(sK5,sK4),
    inference(superposition,[status(thm)],[c_819,c_56]) ).

cnf(c_1131,plain,
    ( ~ disjoint(X0,X1)
    | disjoint(cartesian_product2(X1,X2),cartesian_product2(X0,X3)) ),
    inference(superposition,[status(thm)],[c_63,c_589]) ).

cnf(c_1251,plain,
    ( ~ disjoint(X0,sK4)
    | disjoint(sP0_iProver_def,cartesian_product2(X0,X1)) ),
    inference(superposition,[status(thm)],[c_175,c_1131]) ).

cnf(c_1284,plain,
    ( ~ disjoint(sK5,sK4)
    | disjoint(sP0_iProver_def,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_176,c_1251]) ).

cnf(c_1286,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1284,c_178,c_828]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.33  % Computer : n005.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu May  2 20:25:56 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.17/0.46  Running first-order theorem proving
% 0.17/0.46  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
% 2.84/1.16  % SZS status Started for theBenchmark.p
% 2.84/1.16  % SZS status Theorem for theBenchmark.p
% 2.84/1.16  
% 2.84/1.16  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.84/1.16  
% 2.84/1.16  ------  iProver source info
% 2.84/1.16  
% 2.84/1.16  git: date: 2024-05-02 19:28:25 +0000
% 2.84/1.16  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.84/1.16  git: non_committed_changes: false
% 2.84/1.16  
% 2.84/1.16  ------ Parsing...
% 2.84/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.84/1.16  
% 2.84/1.16  ------ Preprocessing... sup_sim: 2  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 2.84/1.16  
% 2.84/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.84/1.16  
% 2.84/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.84/1.16  ------ Proving...
% 2.84/1.16  ------ Problem Properties 
% 2.84/1.16  
% 2.84/1.16  
% 2.84/1.16  clauses                                 17
% 2.84/1.16  conjectures                             2
% 2.84/1.16  EPR                                     6
% 2.84/1.16  Horn                                    15
% 2.84/1.16  unary                                   9
% 2.84/1.16  binary                                  8
% 2.84/1.16  lits                                    25
% 2.84/1.16  lits eq                                 6
% 2.84/1.16  fd_pure                                 0
% 2.84/1.16  fd_pseudo                               0
% 2.84/1.16  fd_cond                                 0
% 2.84/1.16  fd_pseudo_cond                          0
% 2.84/1.16  AC symbols                              0
% 2.84/1.16  
% 2.84/1.16  ------ Schedule dynamic 5 is on 
% 2.84/1.16  
% 2.84/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.84/1.16  
% 2.84/1.16  
% 2.84/1.16  ------ 
% 2.84/1.16  Current options:
% 2.84/1.16  ------ 
% 2.84/1.16  
% 2.84/1.16  
% 2.84/1.16  
% 2.84/1.16  
% 2.84/1.16  ------ Proving...
% 2.84/1.16  
% 2.84/1.16  
% 2.84/1.16  % SZS status Theorem for theBenchmark.p
% 2.84/1.16  
% 2.84/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.84/1.16  
% 2.84/1.16  
%------------------------------------------------------------------------------