TSTP Solution File: SET755+4 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 : Thu Aug 31 15:09:29 EDT 2023

% Result   : Theorem 80.26s 11.77s
% Output   : CNFRefutation 80.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   49 (   7 unt;   0 def)
%            Number of atoms       :  159 (   4 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  171 (  61   ~;  52   |;  47   &)
%                                         (   4 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-3 aty)
%            Number of variables   :  122 (   0 sgn;  70   !;  23   ?)

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

fof(f24,axiom,
    ! [X5,X1,X2] :
      ( member(X2,inverse_image2(X5,X1))
    <=> ? [X4] :
          ( apply(X5,X2,X4)
          & member(X4,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_image2) ).

fof(f29,conjecture,
    ! [X5,X0,X1,X2,X4] :
      ( ( subset(X2,X4)
        & subset(X4,X1)
        & subset(X2,X1)
        & maps(X5,X0,X1) )
     => subset(inverse_image2(X5,X2),inverse_image2(X5,X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa05) ).

fof(f30,negated_conjecture,
    ~ ! [X5,X0,X1,X2,X4] :
        ( ( subset(X2,X4)
          & subset(X4,X1)
          & subset(X2,X1)
          & maps(X5,X0,X1) )
       => subset(inverse_image2(X5,X2),inverse_image2(X5,X4)) ),
    inference(negated_conjecture,[],[f29]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( member(X2,inverse_image2(X0,X1))
    <=> ? [X3] :
          ( apply(X0,X2,X3)
          & member(X3,X1) ) ),
    inference(rectify,[],[f24]) ).

fof(f57,plain,
    ~ ! [X0,X1,X2,X3,X4] :
        ( ( subset(X3,X4)
          & subset(X4,X2)
          & subset(X3,X2)
          & maps(X0,X1,X2) )
       => subset(inverse_image2(X0,X3),inverse_image2(X0,X4)) ),
    inference(rectify,[],[f30]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f67,plain,
    ? [X0,X1,X2,X3,X4] :
      ( ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4))
      & subset(X3,X4)
      & subset(X4,X2)
      & subset(X3,X2)
      & maps(X0,X1,X2) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f68,plain,
    ? [X0,X1,X2,X3,X4] :
      ( ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4))
      & subset(X3,X4)
      & subset(X4,X2)
      & subset(X3,X2)
      & maps(X0,X1,X2) ),
    inference(flattening,[],[f67]) ).

fof(f69,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,[],[f59]) ).

fof(f70,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,[],[f69]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f72,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])],[f70,f71]) ).

fof(f107,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,inverse_image2(X0,X1))
        | ! [X3] :
            ( ~ apply(X0,X2,X3)
            | ~ member(X3,X1) ) )
      & ( ? [X3] :
            ( apply(X0,X2,X3)
            & member(X3,X1) )
        | ~ member(X2,inverse_image2(X0,X1)) ) ),
    inference(nnf_transformation,[],[f52]) ).

fof(f108,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,inverse_image2(X0,X1))
        | ! [X3] :
            ( ~ apply(X0,X2,X3)
            | ~ member(X3,X1) ) )
      & ( ? [X4] :
            ( apply(X0,X2,X4)
            & member(X4,X1) )
        | ~ member(X2,inverse_image2(X0,X1)) ) ),
    inference(rectify,[],[f107]) ).

fof(f109,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( apply(X0,X2,X4)
          & member(X4,X1) )
     => ( apply(X0,X2,sK7(X0,X1,X2))
        & member(sK7(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f110,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,inverse_image2(X0,X1))
        | ! [X3] :
            ( ~ apply(X0,X2,X3)
            | ~ member(X3,X1) ) )
      & ( ( apply(X0,X2,sK7(X0,X1,X2))
          & member(sK7(X0,X1,X2),X1) )
        | ~ member(X2,inverse_image2(X0,X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f108,f109]) ).

fof(f116,plain,
    ( ? [X0,X1,X2,X3,X4] :
        ( ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4))
        & subset(X3,X4)
        & subset(X4,X2)
        & subset(X3,X2)
        & maps(X0,X1,X2) )
   => ( ~ subset(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))
      & subset(sK12,sK13)
      & subset(sK13,sK11)
      & subset(sK12,sK11)
      & maps(sK9,sK10,sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f117,plain,
    ( ~ subset(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))
    & subset(sK12,sK13)
    & subset(sK13,sK11)
    & subset(sK12,sK11)
    & maps(sK9,sK10,sK11) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13])],[f68,f116]) ).

fof(f118,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f160,plain,
    ! [X2,X0,X1] :
      ( member(sK7(X0,X1,X2),X1)
      | ~ member(X2,inverse_image2(X0,X1)) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f161,plain,
    ! [X2,X0,X1] :
      ( apply(X0,X2,sK7(X0,X1,X2))
      | ~ member(X2,inverse_image2(X0,X1)) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f162,plain,
    ! [X2,X3,X0,X1] :
      ( member(X2,inverse_image2(X0,X1))
      | ~ apply(X0,X2,X3)
      | ~ member(X3,X1) ),
    inference(cnf_transformation,[],[f110]) ).

fof(f170,plain,
    subset(sK12,sK13),
    inference(cnf_transformation,[],[f117]) ).

fof(f171,plain,
    ~ subset(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),
    inference(cnf_transformation,[],[f117]) ).

cnf(c_49,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f120]) ).

cnf(c_50,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_51,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_91,plain,
    ( ~ apply(X0,X1,X2)
    | ~ member(X2,X3)
    | member(X1,inverse_image2(X0,X3)) ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_92,plain,
    ( ~ member(X0,inverse_image2(X1,X2))
    | apply(X1,X0,sK7(X1,X2,X0)) ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_93,plain,
    ( ~ member(X0,inverse_image2(X1,X2))
    | member(sK7(X1,X2,X0),X2) ),
    inference(cnf_transformation,[],[f160]) ).

cnf(c_98,negated_conjecture,
    ~ subset(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),
    inference(cnf_transformation,[],[f171]) ).

cnf(c_99,negated_conjecture,
    subset(sK12,sK13),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_150,plain,
    ( ~ member(sK0(X0,X1),X1)
    | subset(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_49]) ).

cnf(c_154,plain,
    ( subset(X0,X1)
    | member(sK0(X0,X1),X0) ),
    inference(prop_impl_just,[status(thm)],[c_50]) ).

cnf(c_155,plain,
    ( member(sK0(X0,X1),X0)
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_154]) ).

cnf(c_960,plain,
    ( inverse_image2(sK9,sK12) != X0
    | inverse_image2(sK9,sK13) != X1
    | member(sK0(X0,X1),X0) ),
    inference(resolution_lifted,[status(thm)],[c_155,c_98]) ).

cnf(c_961,plain,
    member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,sK12)),
    inference(unflattening,[status(thm)],[c_960]) ).

cnf(c_965,plain,
    ( inverse_image2(sK9,sK12) != X0
    | inverse_image2(sK9,sK13) != X1
    | ~ member(sK0(X0,X1),X1) ),
    inference(resolution_lifted,[status(thm)],[c_150,c_98]) ).

cnf(c_966,plain,
    ~ member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,sK13)),
    inference(unflattening,[status(thm)],[c_965]) ).

cnf(c_4693,plain,
    ( ~ member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,sK12))
    | apply(sK9,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)))) ),
    inference(instantiation,[status(thm)],[c_92]) ).

cnf(c_4694,plain,
    ( ~ member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,sK12))
    | member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK12) ),
    inference(instantiation,[status(thm)],[c_93]) ).

cnf(c_319431,plain,
    ( ~ apply(sK9,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))))
    | ~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),X0)
    | member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,X0)) ),
    inference(instantiation,[status(thm)],[c_91]) ).

cnf(c_319485,plain,
    ( ~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK12)
    | ~ subset(sK12,X0)
    | member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),X0) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_330145,plain,
    ( ~ apply(sK9,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))))
    | ~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK13)
    | member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,sK13)) ),
    inference(instantiation,[status(thm)],[c_319431]) ).

cnf(c_336504,plain,
    ( ~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK12)
    | ~ subset(sK12,sK13)
    | member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK13) ),
    inference(instantiation,[status(thm)],[c_319485]) ).

cnf(c_336505,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_336504,c_330145,c_4693,c_4694,c_966,c_961,c_99]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.13/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 09:54:23 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 80.26/11.77  % SZS status Started for theBenchmark.p
% 80.26/11.77  % SZS status Theorem for theBenchmark.p
% 80.26/11.77  
% 80.26/11.77  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 80.26/11.77  
% 80.26/11.77  ------  iProver source info
% 80.26/11.77  
% 80.26/11.77  git: date: 2023-05-31 18:12:56 +0000
% 80.26/11.77  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 80.26/11.77  git: non_committed_changes: false
% 80.26/11.77  git: last_make_outside_of_git: false
% 80.26/11.77  
% 80.26/11.77  ------ Parsing...
% 80.26/11.77  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 80.26/11.77  
% 80.26/11.77  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 80.26/11.77  
% 80.26/11.77  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 80.26/11.77  
% 80.26/11.77  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 80.26/11.77  ------ Proving...
% 80.26/11.77  ------ Problem Properties 
% 80.26/11.77  
% 80.26/11.77  
% 80.26/11.77  clauses                                 53
% 80.26/11.77  conjectures                             4
% 80.26/11.77  EPR                                     6
% 80.26/11.77  Horn                                    48
% 80.26/11.77  unary                                   8
% 80.26/11.77  binary                                  27
% 80.26/11.77  lits                                    129
% 80.26/11.77  lits eq                                 4
% 80.26/11.77  fd_pure                                 0
% 80.26/11.77  fd_pseudo                               0
% 80.26/11.77  fd_cond                                 0
% 80.26/11.77  fd_pseudo_cond                          3
% 80.26/11.77  AC symbols                              0
% 80.26/11.77  
% 80.26/11.77  ------ Schedule dynamic 5 is on 
% 80.26/11.77  
% 80.26/11.77  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 80.26/11.77  
% 80.26/11.77  
% 80.26/11.77  ------ 
% 80.26/11.77  Current options:
% 80.26/11.77  ------ 
% 80.26/11.77  
% 80.26/11.77  
% 80.26/11.77  
% 80.26/11.77  
% 80.26/11.77  ------ Proving...
% 80.26/11.77  Proof_search_loop: time out after: 7968 full_loop iterations
% 80.26/11.77  
% 80.26/11.77  ------ Input Options"--res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 80.26/11.77  
% 80.26/11.77  
% 80.26/11.77  ------ 
% 80.26/11.77  Current options:
% 80.26/11.77  ------ 
% 80.26/11.77  
% 80.26/11.77  
% 80.26/11.77  
% 80.26/11.77  
% 80.26/11.77  ------ Proving...
% 80.26/11.77  
% 80.26/11.77  
% 80.26/11.77  % SZS status Theorem for theBenchmark.p
% 80.26/11.77  
% 80.26/11.77  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 80.26/11.78  
% 80.26/11.78  
%------------------------------------------------------------------------------