TSTP Solution File: KRS261+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : KRS261+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n019.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 02:34:01 EDT 2024

% Result   : Theorem 3.51s 1.14s
% Output   : CNFRefutation 3.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   65 (  10 unt;   0 def)
%            Number of atoms       :  268 (   0 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  321 ( 118   ~; 120   |;  63   &)
%                                         (   8 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :  172 (  12 sgn  79   !;  51   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( model(X2,X0)
         => model(X2,X1) )
    <=> status(X0,X1,thm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ( ! [X4] :
            ( model(X4,X0)
          <=> model(X4,X1) )
        & ? [X3] : ~ model(X3,X0)
        & ? [X2] : model(X2,X0) )
    <=> status(X0,X1,eth) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eth) ).

fof(f20,axiom,
    ! [X6,X7] :
      ( ? [X0,X1] :
          ( status(X0,X1,X7)
          & status(X0,X1,X6) )
    <=> mighta(X6,X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mighta) ).

fof(f31,axiom,
    ? [X0,X1] :
      ( ? [X5] : ~ model(X5,X1)
      & ? [X4] :
          ( model(X4,X1)
          & ~ model(X4,X0) )
      & ! [X3] :
          ( model(X3,X0)
         => model(X3,X1) )
      & ? [X2] : model(X2,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mixed_pair) ).

fof(f33,conjecture,
    mighta(eth,thm),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mighta_eth_thm) ).

fof(f34,negated_conjecture,
    ~ mighta(eth,thm),
    inference(negated_conjecture,[],[f33]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( model(X2,X0)
          <=> model(X2,X1) )
        & ? [X3] : ~ model(X3,X0)
        & ? [X4] : model(X4,X0) )
    <=> status(X0,X1,eth) ),
    inference(rectify,[],[f9]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( status(X2,X3,X1)
          & status(X2,X3,X0) )
    <=> mighta(X0,X1) ),
    inference(rectify,[],[f20]) ).

fof(f57,plain,
    ? [X0,X1] :
      ( ? [X2] : ~ model(X2,X1)
      & ? [X3] :
          ( model(X3,X1)
          & ~ model(X3,X0) )
      & ! [X4] :
          ( model(X4,X0)
         => model(X4,X1) )
      & ? [X5] : model(X5,X0) ),
    inference(rectify,[],[f31]) ).

fof(f59,plain,
    ~ mighta(eth,thm),
    inference(flattening,[],[f34]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( status(X2,X3,X1)
          & status(X2,X3,X0) )
     => mighta(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f46]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( model(X2,X1)
          | ~ model(X2,X0) )
    <=> status(X0,X1,thm) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( mighta(X0,X1)
      | ! [X2,X3] :
          ( ~ status(X2,X3,X1)
          | ~ status(X2,X3,X0) ) ),
    inference(ennf_transformation,[],[f60]) ).

fof(f71,plain,
    ? [X0,X1] :
      ( ? [X2] : ~ model(X2,X1)
      & ? [X3] :
          ( model(X3,X1)
          & ~ model(X3,X0) )
      & ! [X4] :
          ( model(X4,X1)
          | ~ model(X4,X0) )
      & ? [X5] : model(X5,X0) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( model(X2,X1)
            | ~ model(X2,X0) )
        | ~ status(X0,X1,thm) )
      & ( status(X0,X1,thm)
        | ? [X2] :
            ( ~ model(X2,X1)
            & model(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( model(X2,X1)
            | ~ model(X2,X0) )
        | ~ status(X0,X1,thm) )
      & ( status(X0,X1,thm)
        | ? [X3] :
            ( ~ model(X3,X1)
            & model(X3,X0) ) ) ),
    inference(rectify,[],[f95]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ model(X3,X1)
          & model(X3,X0) )
     => ( ~ model(sK9(X0,X1),X1)
        & model(sK9(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( model(X2,X1)
            | ~ model(X2,X0) )
        | ~ status(X0,X1,thm) )
      & ( status(X0,X1,thm)
        | ( ~ model(sK9(X0,X1),X1)
          & model(sK9(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f96,f97]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ( ( ! [X2] :
              ( ( model(X2,X0)
                | ~ model(X2,X1) )
              & ( model(X2,X1)
                | ~ model(X2,X0) ) )
          & ? [X3] : ~ model(X3,X0)
          & ? [X4] : model(X4,X0) )
        | ~ status(X0,X1,eth) )
      & ( status(X0,X1,eth)
        | ? [X2] :
            ( ( ~ model(X2,X1)
              | ~ model(X2,X0) )
            & ( model(X2,X1)
              | model(X2,X0) ) )
        | ! [X3] : model(X3,X0)
        | ! [X4] : ~ model(X4,X0) ) ),
    inference(nnf_transformation,[],[f38]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( ( ( ! [X2] :
              ( ( model(X2,X0)
                | ~ model(X2,X1) )
              & ( model(X2,X1)
                | ~ model(X2,X0) ) )
          & ? [X3] : ~ model(X3,X0)
          & ? [X4] : model(X4,X0) )
        | ~ status(X0,X1,eth) )
      & ( status(X0,X1,eth)
        | ? [X2] :
            ( ( ~ model(X2,X1)
              | ~ model(X2,X0) )
            & ( model(X2,X1)
              | model(X2,X0) ) )
        | ! [X3] : model(X3,X0)
        | ! [X4] : ~ model(X4,X0) ) ),
    inference(flattening,[],[f118]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ( ( ! [X2] :
              ( ( model(X2,X0)
                | ~ model(X2,X1) )
              & ( model(X2,X1)
                | ~ model(X2,X0) ) )
          & ? [X3] : ~ model(X3,X0)
          & ? [X4] : model(X4,X0) )
        | ~ status(X0,X1,eth) )
      & ( status(X0,X1,eth)
        | ? [X5] :
            ( ( ~ model(X5,X1)
              | ~ model(X5,X0) )
            & ( model(X5,X1)
              | model(X5,X0) ) )
        | ! [X6] : model(X6,X0)
        | ! [X7] : ~ model(X7,X0) ) ),
    inference(rectify,[],[f119]) ).

fof(f121,plain,
    ! [X0] :
      ( ? [X3] : ~ model(X3,X0)
     => ~ model(sK17(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f122,plain,
    ! [X0] :
      ( ? [X4] : model(X4,X0)
     => model(sK18(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( ( ~ model(X5,X1)
            | ~ model(X5,X0) )
          & ( model(X5,X1)
            | model(X5,X0) ) )
     => ( ( ~ model(sK19(X0,X1),X1)
          | ~ model(sK19(X0,X1),X0) )
        & ( model(sK19(X0,X1),X1)
          | model(sK19(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ( ( ! [X2] :
              ( ( model(X2,X0)
                | ~ model(X2,X1) )
              & ( model(X2,X1)
                | ~ model(X2,X0) ) )
          & ~ model(sK17(X0),X0)
          & model(sK18(X0),X0) )
        | ~ status(X0,X1,eth) )
      & ( status(X0,X1,eth)
        | ( ( ~ model(sK19(X0,X1),X1)
            | ~ model(sK19(X0,X1),X0) )
          & ( model(sK19(X0,X1),X1)
            | model(sK19(X0,X1),X0) ) )
        | ! [X6] : model(X6,X0)
        | ! [X7] : ~ model(X7,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f120,f123,f122,f121]) ).

fof(f197,plain,
    ( ? [X0,X1] :
        ( ? [X2] : ~ model(X2,X1)
        & ? [X3] :
            ( model(X3,X1)
            & ~ model(X3,X0) )
        & ! [X4] :
            ( model(X4,X1)
            | ~ model(X4,X0) )
        & ? [X5] : model(X5,X0) )
   => ( ? [X2] : ~ model(X2,sK51)
      & ? [X3] :
          ( model(X3,sK51)
          & ~ model(X3,sK50) )
      & ! [X4] :
          ( model(X4,sK51)
          | ~ model(X4,sK50) )
      & ? [X5] : model(X5,sK50) ) ),
    introduced(choice_axiom,[]) ).

fof(f198,plain,
    ( ? [X2] : ~ model(X2,sK51)
   => ~ model(sK52,sK51) ),
    introduced(choice_axiom,[]) ).

fof(f199,plain,
    ( ? [X3] :
        ( model(X3,sK51)
        & ~ model(X3,sK50) )
   => ( model(sK53,sK51)
      & ~ model(sK53,sK50) ) ),
    introduced(choice_axiom,[]) ).

fof(f200,plain,
    ( ? [X5] : model(X5,sK50)
   => model(sK54,sK50) ),
    introduced(choice_axiom,[]) ).

fof(f201,plain,
    ( ~ model(sK52,sK51)
    & model(sK53,sK51)
    & ~ model(sK53,sK50)
    & ! [X4] :
        ( model(X4,sK51)
        | ~ model(X4,sK50) )
    & model(sK54,sK50) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51,sK52,sK53,sK54])],[f71,f200,f199,f198,f197]) ).

fof(f218,plain,
    ! [X0,X1] :
      ( status(X0,X1,thm)
      | model(sK9(X0,X1),X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f219,plain,
    ! [X0,X1] :
      ( status(X0,X1,thm)
      | ~ model(sK9(X0,X1),X1) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f235,plain,
    ! [X0,X1,X6,X7] :
      ( status(X0,X1,eth)
      | model(sK19(X0,X1),X1)
      | model(sK19(X0,X1),X0)
      | model(X6,X0)
      | ~ model(X7,X0) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f236,plain,
    ! [X0,X1,X6,X7] :
      ( status(X0,X1,eth)
      | ~ model(sK19(X0,X1),X1)
      | ~ model(sK19(X0,X1),X0)
      | model(X6,X0)
      | ~ model(X7,X0) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f278,plain,
    ! [X2,X3,X0,X1] :
      ( mighta(X0,X1)
      | ~ status(X2,X3,X1)
      | ~ status(X2,X3,X0) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f290,plain,
    model(sK54,sK50),
    inference(cnf_transformation,[],[f201]) ).

fof(f292,plain,
    ~ model(sK53,sK50),
    inference(cnf_transformation,[],[f201]) ).

fof(f298,plain,
    ~ mighta(eth,thm),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_63,plain,
    ( ~ model(sK9(X0,X1),X1)
    | status(X0,X1,thm) ),
    inference(cnf_transformation,[],[f219]) ).

cnf(c_64,plain,
    ( model(sK9(X0,X1),X0)
    | status(X0,X1,thm) ),
    inference(cnf_transformation,[],[f218]) ).

cnf(c_83,plain,
    ( ~ model(sK19(X0,X1),X0)
    | ~ model(sK19(X0,X1),X1)
    | ~ model(X2,X0)
    | status(X0,X1,eth)
    | model(X3,X0) ),
    inference(cnf_transformation,[],[f236]) ).

cnf(c_84,plain,
    ( ~ model(X0,X1)
    | model(sK19(X1,X2),X1)
    | model(sK19(X1,X2),X2)
    | status(X1,X2,eth)
    | model(X3,X1) ),
    inference(cnf_transformation,[],[f235]) ).

cnf(c_122,plain,
    ( ~ status(X0,X1,X2)
    | ~ status(X0,X1,X3)
    | mighta(X3,X2) ),
    inference(cnf_transformation,[],[f278]) ).

cnf(c_136,plain,
    ~ model(sK53,sK50),
    inference(cnf_transformation,[],[f292]) ).

cnf(c_138,plain,
    model(sK54,sK50),
    inference(cnf_transformation,[],[f290]) ).

cnf(c_142,negated_conjecture,
    ~ mighta(eth,thm),
    inference(cnf_transformation,[],[f298]) ).

cnf(c_974,plain,
    ( ~ status(X0,X1,thm)
    | ~ status(X0,X1,eth) ),
    inference(resolution,[status(thm)],[c_122,c_142]) ).

cnf(c_1020,plain,
    ( ~ status(X0,X1,thm)
    | ~ status(X0,X1,eth) ),
    inference(prop_impl_just,[status(thm)],[c_974]) ).

cnf(c_1750,plain,
    ( ~ status(X0_13,X1_13,thm)
    | ~ status(X0_13,X1_13,eth) ),
    inference(subtyping,[status(esa)],[c_1020]) ).

cnf(c_1805,plain,
    ( ~ model(X0_15,X0_13)
    | model(sK19(X0_13,X1_13),X0_13)
    | model(sK19(X0_13,X1_13),X1_13)
    | status(X0_13,X1_13,eth)
    | model(X1_15,X0_13) ),
    inference(subtyping,[status(esa)],[c_84]) ).

cnf(c_1806,plain,
    ( ~ model(sK19(X0_13,X1_13),X0_13)
    | ~ model(sK19(X0_13,X1_13),X1_13)
    | ~ model(X0_15,X0_13)
    | status(X0_13,X1_13,eth)
    | model(X1_15,X0_13) ),
    inference(subtyping,[status(esa)],[c_83]) ).

cnf(c_1825,plain,
    ( model(sK9(X0_13,X1_13),X0_13)
    | status(X0_13,X1_13,thm) ),
    inference(subtyping,[status(esa)],[c_64]) ).

cnf(c_1826,plain,
    ( ~ model(sK9(X0_13,X1_13),X1_13)
    | status(X0_13,X1_13,thm) ),
    inference(subtyping,[status(esa)],[c_63]) ).

cnf(c_1869,plain,
    ( model(sK9(sK50,sK50),sK50)
    | status(sK50,sK50,thm) ),
    inference(instantiation,[status(thm)],[c_1825]) ).

cnf(c_1870,plain,
    ( ~ status(sK50,sK50,thm)
    | ~ status(sK50,sK50,eth) ),
    inference(instantiation,[status(thm)],[c_1750]) ).

cnf(c_1880,plain,
    ( ~ model(sK9(sK50,sK50),sK50)
    | status(sK50,sK50,thm) ),
    inference(instantiation,[status(thm)],[c_1826]) ).

cnf(c_2122,plain,
    ( ~ model(sK19(sK50,X0_13),X0_13)
    | ~ model(sK19(sK50,X0_13),sK50)
    | ~ model(sK54,sK50)
    | status(sK50,X0_13,eth)
    | model(X0_15,sK50) ),
    inference(instantiation,[status(thm)],[c_1806]) ).

cnf(c_2123,plain,
    ( ~ model(sK54,sK50)
    | model(sK19(sK50,X0_13),X0_13)
    | model(sK19(sK50,X0_13),sK50)
    | status(sK50,X0_13,eth)
    | model(X0_15,sK50) ),
    inference(instantiation,[status(thm)],[c_1805]) ).

cnf(c_2126,plain,
    ( ~ model(sK54,sK50)
    | model(sK19(sK50,sK50),sK50)
    | status(sK50,sK50,eth)
    | model(sK48,sK50) ),
    inference(instantiation,[status(thm)],[c_2123]) ).

cnf(c_2127,plain,
    ( ~ model(sK19(sK50,sK50),sK50)
    | ~ model(sK54,sK50)
    | status(sK50,sK50,eth)
    | model(sK48,sK50) ),
    inference(instantiation,[status(thm)],[c_2122]) ).

cnf(c_2879,plain,
    ( ~ model(X0_15,sK50)
    | model(sK19(sK50,X0_13),X0_13)
    | model(sK19(sK50,X0_13),sK50)
    | status(sK50,X0_13,eth)
    | model(sK53,sK50) ),
    inference(instantiation,[status(thm)],[c_1805]) ).

cnf(c_2880,plain,
    ( ~ model(sK48,sK50)
    | model(sK19(sK50,sK50),sK50)
    | status(sK50,sK50,eth)
    | model(sK53,sK50) ),
    inference(instantiation,[status(thm)],[c_2879]) ).

cnf(c_2965,plain,
    ( ~ model(sK19(sK50,X0_13),X0_13)
    | ~ model(sK19(sK50,X0_13),sK50)
    | ~ model(X0_15,sK50)
    | status(sK50,X0_13,eth)
    | model(sK53,sK50) ),
    inference(instantiation,[status(thm)],[c_1806]) ).

cnf(c_2966,plain,
    ( ~ model(sK19(sK50,sK50),sK50)
    | ~ model(sK48,sK50)
    | status(sK50,sK50,eth)
    | model(sK53,sK50) ),
    inference(instantiation,[status(thm)],[c_2965]) ).

cnf(c_4322,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_2966,c_2880,c_2127,c_2126,c_1880,c_1870,c_1869,c_136,c_138]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KRS261+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.33  % Computer : n019.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 22:41:14 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.18/0.45  Running first-order theorem proving
% 0.18/0.45  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
% 3.51/1.14  % SZS status Started for theBenchmark.p
% 3.51/1.14  % SZS status Theorem for theBenchmark.p
% 3.51/1.14  
% 3.51/1.14  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.51/1.14  
% 3.51/1.14  ------  iProver source info
% 3.51/1.14  
% 3.51/1.14  git: date: 2024-05-02 19:28:25 +0000
% 3.51/1.14  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.51/1.14  git: non_committed_changes: false
% 3.51/1.14  
% 3.51/1.14  ------ Parsing...
% 3.51/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.51/1.14  
% 3.51/1.14  ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe:1:0s pe_e  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 3.51/1.14  
% 3.51/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.51/1.14  ------ Proving...
% 3.51/1.14  ------ Problem Properties 
% 3.51/1.14  
% 3.51/1.14  
% 3.51/1.14  clauses                                 91
% 3.51/1.14  conjectures                             0
% 3.51/1.14  EPR                                     39
% 3.51/1.14  Horn                                    72
% 3.51/1.14  unary                                   13
% 3.51/1.14  binary                                  47
% 3.51/1.14  lits                                    220
% 3.51/1.14  lits eq                                 0
% 3.51/1.14  fd_pure                                 0
% 3.51/1.14  fd_pseudo                               0
% 3.51/1.14  fd_cond                                 0
% 3.51/1.14  fd_pseudo_cond                          0
% 3.51/1.14  AC symbols                              0
% 3.51/1.14  
% 3.51/1.14  ------ Input Options Time Limit: Unbounded
% 3.51/1.14  
% 3.51/1.14  
% 3.51/1.14  ------ 
% 3.51/1.14  Current options:
% 3.51/1.14  ------ 
% 3.51/1.14  
% 3.51/1.14  
% 3.51/1.14  
% 3.51/1.14  
% 3.51/1.14  ------ Proving...
% 3.51/1.14  
% 3.51/1.14  
% 3.51/1.14  % SZS status Theorem for theBenchmark.p
% 3.51/1.14  
% 3.51/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.51/1.14  
% 3.51/1.14  
%------------------------------------------------------------------------------