TSTP Solution File: KRS203+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : KRS203+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n023.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 02:33:56 EDT 2024

% Result   : Theorem 4.01s 1.19s
% Output   : CNFRefutation 4.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   66 (  21 unt;   0 def)
%            Number of atoms       :  187 (   0 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  200 (  79   ~;  59   |;  46   &)
%                                         (   5 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :  150 (   7 sgn  64   !;  42   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0,X1] :
      ( ? [X2] :
          ( model(X2,X1)
          & model(X2,X0) )
    <=> status(X0,X1,sat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sat) ).

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

fof(f22,axiom,
    ! [X6,X7] :
      ( ? [X0,X1] :
          ( ~ status(X0,X1,X7)
          & status(X0,X1,X6) )
    <=> nota(X6,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nota) ).

fof(f27,axiom,
    ? [X9] :
    ! [X8] : model(X8,X9),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tautology) ).

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/sandbox/benchmark/theBenchmark.p',mixed_pair) ).

fof(f33,conjecture,
    nota(sat,thm),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nota_sat_thm) ).

fof(f34,negated_conjecture,
    ~ nota(sat,thm),
    inference(negated_conjecture,[],[f33]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( ~ status(X2,X3,X1)
          & status(X2,X3,X0) )
    <=> nota(X0,X1) ),
    inference(rectify,[],[f22]) ).

fof(f53,plain,
    ? [X0] :
    ! [X1] : model(X1,X0),
    inference(rectify,[],[f27]) ).

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,
    ~ nota(sat,thm),
    inference(flattening,[],[f34]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( ~ status(X2,X3,X1)
          & status(X2,X3,X0) )
     => nota(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f48]) ).

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] :
      ( nota(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(f91,plain,
    ! [X0,X1] :
      ( ( ? [X2] :
            ( model(X2,X1)
            & model(X2,X0) )
        | ~ status(X0,X1,sat) )
      & ( status(X0,X1,sat)
        | ! [X2] :
            ( ~ model(X2,X1)
            | ~ model(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ( ? [X2] :
            ( model(X2,X1)
            & model(X2,X0) )
        | ~ status(X0,X1,sat) )
      & ( status(X0,X1,sat)
        | ! [X3] :
            ( ~ model(X3,X1)
            | ~ model(X3,X0) ) ) ),
    inference(rectify,[],[f91]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( model(X2,X1)
          & model(X2,X0) )
     => ( model(sK8(X0,X1),X1)
        & model(sK8(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ( ( model(sK8(X0,X1),X1)
          & model(sK8(X0,X1),X0) )
        | ~ status(X0,X1,sat) )
      & ( status(X0,X1,sat)
        | ! [X3] :
            ( ~ model(X3,X1)
            | ~ model(X3,X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f92,f93]) ).

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(f185,plain,
    ( ? [X0] :
      ! [X1] : model(X1,X0)
   => ! [X1] : model(X1,sK41) ),
    introduced(choice_axiom,[]) ).

fof(f186,plain,
    ! [X1] : model(X1,sK41),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f53,f185]) ).

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(f215,plain,
    ! [X3,X0,X1] :
      ( status(X0,X1,sat)
      | ~ model(X3,X1)
      | ~ model(X3,X0) ),
    inference(cnf_transformation,[],[f94]) ).

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

fof(f220,plain,
    ! [X2,X0,X1] :
      ( model(X2,X1)
      | ~ model(X2,X0)
      | ~ status(X0,X1,thm) ),
    inference(cnf_transformation,[],[f98]) ).

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

fof(f283,plain,
    ! [X1] : model(X1,sK41),
    inference(cnf_transformation,[],[f186]) ).

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

fof(f293,plain,
    model(sK53,sK51),
    inference(cnf_transformation,[],[f201]) ).

fof(f294,plain,
    ~ model(sK52,sK51),
    inference(cnf_transformation,[],[f201]) ).

fof(f298,plain,
    ~ nota(sat,thm),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_61,plain,
    ( ~ model(X0,X1)
    | ~ model(X0,X2)
    | status(X2,X1,sat) ),
    inference(cnf_transformation,[],[f215]) ).

cnf(c_62,plain,
    ( ~ status(X0,X1,thm)
    | ~ model(X2,X0)
    | model(X2,X1) ),
    inference(cnf_transformation,[],[f220]) ).

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

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

cnf(c_127,plain,
    model(X0,sK41),
    inference(cnf_transformation,[],[f283]) ).

cnf(c_134,plain,
    ~ model(sK52,sK51),
    inference(cnf_transformation,[],[f294]) ).

cnf(c_135,plain,
    model(sK53,sK51),
    inference(cnf_transformation,[],[f293]) ).

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

cnf(c_142,negated_conjecture,
    ~ nota(sat,thm),
    inference(cnf_transformation,[],[f298]) ).

cnf(c_973,plain,
    ( ~ status(X0,X1,sat)
    | status(X0,X1,thm) ),
    inference(resolution,[status(thm)],[c_122,c_142]) ).

cnf(c_1019,plain,
    ( ~ status(X0,X1,sat)
    | status(X0,X1,thm) ),
    inference(prop_impl_just,[status(thm)],[c_973]) ).

cnf(c_1749,plain,
    ( ~ status(X0_13,X1_13,sat)
    | status(X0_13,X1_13,thm) ),
    inference(subtyping,[status(esa)],[c_1019]) ).

cnf(c_1759,plain,
    ~ model(sK52,sK51),
    inference(subtyping,[status(esa)],[c_134]) ).

cnf(c_1766,plain,
    model(X0_15,sK41),
    inference(subtyping,[status(esa)],[c_127]) ).

cnf(c_1824,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,
    ( ~ status(X0_13,X1_13,thm)
    | ~ model(X0_15,X0_13)
    | model(X0_15,X1_13) ),
    inference(subtyping,[status(esa)],[c_62]) ).

cnf(c_1827,plain,
    ( ~ model(X0_15,X0_13)
    | ~ model(X0_15,X1_13)
    | status(X0_13,X1_13,sat) ),
    inference(subtyping,[status(esa)],[c_61]) ).

cnf(c_2510,plain,
    ( ~ status(sK51,X0_13,thm)
    | ~ model(sK53,sK51)
    | model(sK53,X0_13) ),
    inference(instantiation,[status(thm)],[c_1826]) ).

cnf(c_2511,plain,
    ( ~ status(sK51,sK50,thm)
    | ~ model(sK53,sK51)
    | model(sK53,sK50) ),
    inference(instantiation,[status(thm)],[c_2510]) ).

cnf(c_3074,plain,
    ( ~ model(sK9(X0_13,X1_13),X2_13)
    | status(X0_13,X1_13,thm)
    | status(X2_13,X0_13,sat) ),
    inference(resolution,[status(thm)],[c_1827,c_1824]) ).

cnf(c_3119,plain,
    ( ~ status(X0_13,X1_13,sat)
    | ~ model(X0_15,X0_13)
    | model(X0_15,X1_13) ),
    inference(resolution,[status(thm)],[c_1749,c_1826]) ).

cnf(c_3735,plain,
    ( status(X0_13,X1_13,thm)
    | status(sK41,X0_13,sat) ),
    inference(resolution,[status(thm)],[c_1766,c_3074]) ).

cnf(c_4794,plain,
    ( ~ model(X0_15,sK41)
    | status(X0_13,X1_13,thm)
    | model(X0_15,X0_13) ),
    inference(resolution,[status(thm)],[c_3735,c_3119]) ).

cnf(c_7123,plain,
    ( status(X0_13,X1_13,thm)
    | model(X0_15,X0_13) ),
    inference(global_subsumption_just,[status(thm)],[c_4794,c_1766,c_4794]) ).

cnf(c_7137,plain,
    status(sK51,X0_13,thm),
    inference(resolution,[status(thm)],[c_7123,c_1759]) ).

cnf(c_7138,plain,
    status(sK51,sK50,thm),
    inference(instantiation,[status(thm)],[c_7137]) ).

cnf(c_7139,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_7138,c_2511,c_136,c_135]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : KRS203+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.11/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n023.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May  2 22:54:54 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.01/1.19  % SZS status Started for theBenchmark.p
% 4.01/1.19  % SZS status Theorem for theBenchmark.p
% 4.01/1.19  
% 4.01/1.19  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.01/1.19  
% 4.01/1.19  ------  iProver source info
% 4.01/1.19  
% 4.01/1.19  git: date: 2024-05-02 19:28:25 +0000
% 4.01/1.19  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.01/1.19  git: non_committed_changes: false
% 4.01/1.19  
% 4.01/1.19  ------ Parsing...
% 4.01/1.19  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.01/1.19  
% 4.01/1.19  ------ 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 
% 4.01/1.19  
% 4.01/1.19  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.01/1.19  ------ Proving...
% 4.01/1.19  ------ Problem Properties 
% 4.01/1.19  
% 4.01/1.19  
% 4.01/1.19  clauses                                 91
% 4.01/1.19  conjectures                             0
% 4.01/1.19  EPR                                     39
% 4.01/1.19  Horn                                    72
% 4.01/1.19  unary                                   13
% 4.01/1.19  binary                                  47
% 4.01/1.19  lits                                    220
% 4.01/1.19  lits eq                                 0
% 4.01/1.19  fd_pure                                 0
% 4.01/1.19  fd_pseudo                               0
% 4.01/1.19  fd_cond                                 0
% 4.01/1.19  fd_pseudo_cond                          0
% 4.01/1.19  AC symbols                              0
% 4.01/1.19  
% 4.01/1.19  ------ Input Options Time Limit: Unbounded
% 4.01/1.19  
% 4.01/1.19  
% 4.01/1.19  ------ 
% 4.01/1.19  Current options:
% 4.01/1.19  ------ 
% 4.01/1.19  
% 4.01/1.19  
% 4.01/1.19  
% 4.01/1.19  
% 4.01/1.19  ------ Proving...
% 4.01/1.19  
% 4.01/1.19  
% 4.01/1.19  % SZS status Theorem for theBenchmark.p
% 4.01/1.19  
% 4.01/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.01/1.19  
% 4.01/1.19  
%------------------------------------------------------------------------------