TSTP Solution File: SET797+4 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET797+4 : 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 03:01:33 EDT 2024

% Result   : Theorem 7.86s 1.63s
% Output   : CNFRefutation 7.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   49 (   9 unt;   0 def)
%            Number of atoms       :  180 (   6 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  199 (  68   ~;  52   |;  57   &)
%                                         (   5 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :  133 (   0 sgn  72   !;  29   ?)

% 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(f14,axiom,
    ! [X5,X3,X7] :
      ( upper_bound(X7,X5,X3)
    <=> ! [X2] :
          ( member(X2,X3)
         => apply(X5,X2,X7) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_bound) ).

fof(f22,conjecture,
    ! [X5,X3] :
      ( order(X5,X3)
     => ! [X2,X4] :
          ( ( subset(X2,X4)
            & subset(X4,X3)
            & subset(X2,X3) )
         => ! [X7] :
              ( upper_bound(X7,X5,X4)
             => upper_bound(X7,X5,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV9) ).

fof(f23,negated_conjecture,
    ~ ! [X5,X3] :
        ( order(X5,X3)
       => ! [X2,X4] :
            ( ( subset(X2,X4)
              & subset(X4,X3)
              & subset(X2,X3) )
           => ! [X7] :
                ( upper_bound(X7,X5,X4)
               => upper_bound(X7,X5,X2) ) ) ),
    inference(negated_conjecture,[],[f22]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( upper_bound(X2,X0,X1)
    <=> ! [X3] :
          ( member(X3,X1)
         => apply(X0,X3,X2) ) ),
    inference(rectify,[],[f14]) ).

fof(f43,plain,
    ~ ! [X0,X1] :
        ( order(X0,X1)
       => ! [X2,X3] :
            ( ( subset(X2,X3)
              & subset(X3,X1)
              & subset(X2,X1) )
           => ! [X4] :
                ( upper_bound(X4,X0,X3)
               => upper_bound(X4,X0,X2) ) ) ),
    inference(rectify,[],[f23]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( upper_bound(X2,X0,X1)
    <=> ! [X3] :
          ( apply(X0,X3,X2)
          | ~ member(X3,X1) ) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f50,plain,
    ? [X0,X1] :
      ( ? [X2,X3] :
          ( ? [X4] :
              ( ~ upper_bound(X4,X0,X2)
              & upper_bound(X4,X0,X3) )
          & subset(X2,X3)
          & subset(X3,X1)
          & subset(X2,X1) )
      & order(X0,X1) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f51,plain,
    ? [X0,X1] :
      ( ? [X2,X3] :
          ( ? [X4] :
              ( ~ upper_bound(X4,X0,X2)
              & upper_bound(X4,X0,X3) )
          & subset(X2,X3)
          & subset(X3,X1)
          & subset(X2,X1) )
      & order(X0,X1) ),
    inference(flattening,[],[f50]) ).

fof(f52,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,[],[f45]) ).

fof(f53,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,[],[f52]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,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])],[f53,f54]) ).

fof(f74,plain,
    ! [X0,X1,X2] :
      ( ( upper_bound(X2,X0,X1)
        | ? [X3] :
            ( ~ apply(X0,X3,X2)
            & member(X3,X1) ) )
      & ( ! [X3] :
            ( apply(X0,X3,X2)
            | ~ member(X3,X1) )
        | ~ upper_bound(X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( ( upper_bound(X2,X0,X1)
        | ? [X3] :
            ( ~ apply(X0,X3,X2)
            & member(X3,X1) ) )
      & ( ! [X4] :
            ( apply(X0,X4,X2)
            | ~ member(X4,X1) )
        | ~ upper_bound(X2,X0,X1) ) ),
    inference(rectify,[],[f74]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ apply(X0,X3,X2)
          & member(X3,X1) )
     => ( ~ apply(X0,sK3(X0,X1,X2),X2)
        & member(sK3(X0,X1,X2),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( ( upper_bound(X2,X0,X1)
        | ( ~ apply(X0,sK3(X0,X1,X2),X2)
          & member(sK3(X0,X1,X2),X1) ) )
      & ( ! [X4] :
            ( apply(X0,X4,X2)
            | ~ member(X4,X1) )
        | ~ upper_bound(X2,X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f75,f76]) ).

fof(f78,plain,
    ( ? [X0,X1] :
        ( ? [X2,X3] :
            ( ? [X4] :
                ( ~ upper_bound(X4,X0,X2)
                & upper_bound(X4,X0,X3) )
            & subset(X2,X3)
            & subset(X3,X1)
            & subset(X2,X1) )
        & order(X0,X1) )
   => ( ? [X3,X2] :
          ( ? [X4] :
              ( ~ upper_bound(X4,sK4,X2)
              & upper_bound(X4,sK4,X3) )
          & subset(X2,X3)
          & subset(X3,sK5)
          & subset(X2,sK5) )
      & order(sK4,sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f79,plain,
    ( ? [X3,X2] :
        ( ? [X4] :
            ( ~ upper_bound(X4,sK4,X2)
            & upper_bound(X4,sK4,X3) )
        & subset(X2,X3)
        & subset(X3,sK5)
        & subset(X2,sK5) )
   => ( ? [X4] :
          ( ~ upper_bound(X4,sK4,sK6)
          & upper_bound(X4,sK4,sK7) )
      & subset(sK6,sK7)
      & subset(sK7,sK5)
      & subset(sK6,sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f80,plain,
    ( ? [X4] :
        ( ~ upper_bound(X4,sK4,sK6)
        & upper_bound(X4,sK4,sK7) )
   => ( ~ upper_bound(sK8,sK4,sK6)
      & upper_bound(sK8,sK4,sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ( ~ upper_bound(sK8,sK4,sK6)
    & upper_bound(sK8,sK4,sK7)
    & subset(sK6,sK7)
    & subset(sK7,sK5)
    & subset(sK6,sK5)
    & order(sK4,sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f51,f80,f79,f78]) ).

fof(f82,plain,
    ! [X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(X3,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f111,plain,
    ! [X2,X0,X1,X4] :
      ( apply(X0,X4,X2)
      | ~ member(X4,X1)
      | ~ upper_bound(X2,X0,X1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f112,plain,
    ! [X2,X0,X1] :
      ( upper_bound(X2,X0,X1)
      | member(sK3(X0,X1,X2),X1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f113,plain,
    ! [X2,X0,X1] :
      ( upper_bound(X2,X0,X1)
      | ~ apply(X0,sK3(X0,X1,X2),X2) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f117,plain,
    subset(sK6,sK7),
    inference(cnf_transformation,[],[f81]) ).

fof(f118,plain,
    upper_bound(sK8,sK4,sK7),
    inference(cnf_transformation,[],[f81]) ).

fof(f119,plain,
    ~ upper_bound(sK8,sK4,sK6),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_51,plain,
    ( ~ subset(X0,X1)
    | ~ member(X2,X0)
    | member(X2,X1) ),
    inference(cnf_transformation,[],[f82]) ).

cnf(c_78,plain,
    ( ~ apply(X0,sK3(X0,X1,X2),X2)
    | upper_bound(X2,X0,X1) ),
    inference(cnf_transformation,[],[f113]) ).

cnf(c_79,plain,
    ( member(sK3(X0,X1,X2),X1)
    | upper_bound(X2,X0,X1) ),
    inference(cnf_transformation,[],[f112]) ).

cnf(c_80,plain,
    ( ~ upper_bound(X0,X1,X2)
    | ~ member(X3,X2)
    | apply(X1,X3,X0) ),
    inference(cnf_transformation,[],[f111]) ).

cnf(c_81,negated_conjecture,
    ~ upper_bound(sK8,sK4,sK6),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_82,negated_conjecture,
    upper_bound(sK8,sK4,sK7),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_83,negated_conjecture,
    subset(sK6,sK7),
    inference(cnf_transformation,[],[f117]) ).

cnf(c_156,plain,
    ( ~ apply(X0,sK3(X0,X1,X2),X2)
    | upper_bound(X2,X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_78]) ).

cnf(c_166,plain,
    ( member(sK3(X0,X1,X2),X1)
    | upper_bound(X2,X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_79]) ).

cnf(c_441,plain,
    ( X0 != sK4
    | X1 != sK6
    | X2 != sK8
    | member(sK3(X0,X1,X2),X1) ),
    inference(resolution_lifted,[status(thm)],[c_166,c_81]) ).

cnf(c_442,plain,
    member(sK3(sK4,sK6,sK8),sK6),
    inference(unflattening,[status(thm)],[c_441]) ).

cnf(c_446,plain,
    ( X0 != sK4
    | X1 != sK6
    | X2 != sK8
    | ~ apply(X0,sK3(X0,X1,X2),X2) ),
    inference(resolution_lifted,[status(thm)],[c_156,c_81]) ).

cnf(c_447,plain,
    ~ apply(sK4,sK3(sK4,sK6,sK8),sK8),
    inference(unflattening,[status(thm)],[c_446]) ).

cnf(c_1894,plain,
    ( ~ member(sK3(X0,X1,X2),X1)
    | ~ subset(X1,X3)
    | member(sK3(X0,X1,X2),X3) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_1923,plain,
    ( ~ upper_bound(sK8,sK4,sK7)
    | ~ member(X0,sK7)
    | apply(sK4,X0,sK8) ),
    inference(instantiation,[status(thm)],[c_80]) ).

cnf(c_3645,plain,
    ( ~ member(sK3(sK4,sK6,sK8),sK6)
    | ~ subset(sK6,X0)
    | member(sK3(sK4,sK6,sK8),X0) ),
    inference(instantiation,[status(thm)],[c_1894]) ).

cnf(c_7154,plain,
    ( ~ member(sK3(sK4,X0,sK8),sK7)
    | ~ upper_bound(sK8,sK4,sK7)
    | apply(sK4,sK3(sK4,X0,sK8),sK8) ),
    inference(instantiation,[status(thm)],[c_1923]) ).

cnf(c_8969,plain,
    ( ~ member(sK3(sK4,sK6,sK8),sK6)
    | ~ subset(sK6,sK7)
    | member(sK3(sK4,sK6,sK8),sK7) ),
    inference(instantiation,[status(thm)],[c_3645]) ).

cnf(c_12140,plain,
    ( ~ member(sK3(sK4,sK6,sK8),sK7)
    | ~ upper_bound(sK8,sK4,sK7)
    | apply(sK4,sK3(sK4,sK6,sK8),sK8) ),
    inference(instantiation,[status(thm)],[c_7154]) ).

cnf(c_12141,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_12140,c_8969,c_447,c_442,c_82,c_83]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET797+4 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12  % 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 20:37:36 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.17/0.44  Running first-order theorem proving
% 0.17/0.44  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
% 7.86/1.63  % SZS status Started for theBenchmark.p
% 7.86/1.63  % SZS status Theorem for theBenchmark.p
% 7.86/1.63  
% 7.86/1.63  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.86/1.63  
% 7.86/1.63  ------  iProver source info
% 7.86/1.63  
% 7.86/1.63  git: date: 2024-05-02 19:28:25 +0000
% 7.86/1.63  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.86/1.63  git: non_committed_changes: false
% 7.86/1.63  
% 7.86/1.63  ------ Parsing...
% 7.86/1.63  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.86/1.63  
% 7.86/1.63  ------ 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 
% 7.86/1.63  
% 7.86/1.63  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.86/1.63  
% 7.86/1.63  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.86/1.63  ------ Proving...
% 7.86/1.63  ------ Problem Properties 
% 7.86/1.63  
% 7.86/1.63  
% 7.86/1.63  clauses                                 37
% 7.86/1.63  conjectures                             5
% 7.86/1.63  EPR                                     11
% 7.86/1.63  Horn                                    31
% 7.86/1.63  unary                                   9
% 7.86/1.63  binary                                  18
% 7.86/1.63  lits                                    80
% 7.86/1.63  lits eq                                 4
% 7.86/1.63  fd_pure                                 0
% 7.86/1.63  fd_pseudo                               0
% 7.86/1.63  fd_cond                                 0
% 7.86/1.63  fd_pseudo_cond                          3
% 7.86/1.63  AC symbols                              0
% 7.86/1.63  
% 7.86/1.63  ------ Input Options Time Limit: Unbounded
% 7.86/1.63  
% 7.86/1.63  
% 7.86/1.63  ------ 
% 7.86/1.63  Current options:
% 7.86/1.63  ------ 
% 7.86/1.63  
% 7.86/1.63  
% 7.86/1.63  
% 7.86/1.63  
% 7.86/1.63  ------ Proving...
% 7.86/1.63  
% 7.86/1.63  
% 7.86/1.63  % SZS status Theorem for theBenchmark.p
% 7.86/1.63  
% 7.86/1.63  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.86/1.63  
% 7.86/1.64  
%------------------------------------------------------------------------------