TSTP Solution File: KRS268+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : KRS268+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n029.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 02:34:02 EDT 2024

% Result   : Theorem 3.55s 1.17s
% Output   : CNFRefutation 3.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   71 (  18 unt;   0 def)
%            Number of atoms       :  215 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  244 ( 100   ~;  63   |;  58   &)
%                                         (   9 <=>;  14  =>;   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    :   14 (  14 usr;   9 con; 0-2 aty)
%            Number of variables   :  200 (  17 sgn 102   !;  62   ?)

% 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(f13,axiom,
    ! [X0,X1] :
      ( ~ ? [X2] : model(X2,X0)
    <=> status(X0,X1,cax) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cax) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( ( ? [X4] : ~ model(X4,X1)
        & ? [X3] : model(X3,X1)
        & ~ ? [X2] : model(X2,X0) )
    <=> status(X0,X1,wca) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wca) ).

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(f29,axiom,
    ? [X9] :
    ! [X8] : ~ model(X8,X9),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contradiction) ).

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(wca,thm),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mighta_wca_thm) ).

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

fof(f43,plain,
    ! [X0,X1] :
      ( ( ? [X2] : ~ model(X2,X1)
        & ? [X3] : model(X3,X1)
        & ~ ? [X4] : model(X4,X0) )
    <=> status(X0,X1,wca) ),
    inference(rectify,[],[f16]) ).

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

fof(f55,plain,
    ? [X0] :
    ! [X1] : ~ model(X1,X0),
    inference(rectify,[],[f29]) ).

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(wca,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(f66,plain,
    ! [X0,X1] :
      ( ! [X2] : ~ model(X2,X0)
    <=> status(X0,X1,cax) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ( ? [X2] : ~ model(X2,X1)
        & ? [X3] : model(X3,X1)
        & ! [X4] : ~ model(X4,X0) )
    <=> status(X0,X1,wca) ),
    inference(ennf_transformation,[],[f43]) ).

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(f144,plain,
    ! [X0,X1] :
      ( ( ! [X2] : ~ model(X2,X0)
        | ~ status(X0,X1,cax) )
      & ( status(X0,X1,cax)
        | ? [X2] : model(X2,X0) ) ),
    inference(nnf_transformation,[],[f66]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( ( ! [X2] : ~ model(X2,X0)
        | ~ status(X0,X1,cax) )
      & ( status(X0,X1,cax)
        | ? [X3] : model(X3,X0) ) ),
    inference(rectify,[],[f144]) ).

fof(f146,plain,
    ! [X0] :
      ( ? [X3] : model(X3,X0)
     => model(sK28(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ( ! [X2] : ~ model(X2,X0)
        | ~ status(X0,X1,cax) )
      & ( status(X0,X1,cax)
        | model(sK28(X0),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f145,f146]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( ( ( ? [X2] : ~ model(X2,X1)
          & ? [X3] : model(X3,X1)
          & ! [X4] : ~ model(X4,X0) )
        | ~ status(X0,X1,wca) )
      & ( status(X0,X1,wca)
        | ! [X2] : model(X2,X1)
        | ! [X3] : ~ model(X3,X1)
        | ? [X4] : model(X4,X0) ) ),
    inference(nnf_transformation,[],[f69]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( ( ( ? [X2] : ~ model(X2,X1)
          & ? [X3] : model(X3,X1)
          & ! [X4] : ~ model(X4,X0) )
        | ~ status(X0,X1,wca) )
      & ( status(X0,X1,wca)
        | ! [X2] : model(X2,X1)
        | ! [X3] : ~ model(X3,X1)
        | ? [X4] : model(X4,X0) ) ),
    inference(flattening,[],[f160]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( ( ( ? [X2] : ~ model(X2,X1)
          & ? [X3] : model(X3,X1)
          & ! [X4] : ~ model(X4,X0) )
        | ~ status(X0,X1,wca) )
      & ( status(X0,X1,wca)
        | ! [X5] : model(X5,X1)
        | ! [X6] : ~ model(X6,X1)
        | ? [X7] : model(X7,X0) ) ),
    inference(rectify,[],[f161]) ).

fof(f163,plain,
    ! [X1] :
      ( ? [X2] : ~ model(X2,X1)
     => ~ model(sK33(X1),X1) ),
    introduced(choice_axiom,[]) ).

fof(f164,plain,
    ! [X1] :
      ( ? [X3] : model(X3,X1)
     => model(sK34(X1),X1) ),
    introduced(choice_axiom,[]) ).

fof(f165,plain,
    ! [X0] :
      ( ? [X7] : model(X7,X0)
     => model(sK35(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( ( ( ~ model(sK33(X1),X1)
          & model(sK34(X1),X1)
          & ! [X4] : ~ model(X4,X0) )
        | ~ status(X0,X1,wca) )
      & ( status(X0,X1,wca)
        | ! [X5] : model(X5,X1)
        | ! [X6] : ~ model(X6,X1)
        | model(sK35(X0),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35])],[f162,f165,f164,f163]) ).

fof(f191,plain,
    ( ? [X0] :
      ! [X1] : ~ model(X1,X0)
   => ! [X1] : ~ model(X1,sK45) ),
    introduced(choice_axiom,[]) ).

fof(f192,plain,
    ! [X1] : ~ model(X1,sK45),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f55,f191]) ).

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(f255,plain,
    ! [X0,X1] :
      ( status(X0,X1,cax)
      | model(sK28(X0),X0) ),
    inference(cnf_transformation,[],[f147]) ).

fof(f256,plain,
    ! [X2,X0,X1] :
      ( ~ model(X2,X0)
      | ~ status(X0,X1,cax) ),
    inference(cnf_transformation,[],[f147]) ).

fof(f263,plain,
    ! [X0,X1,X6,X5] :
      ( status(X0,X1,wca)
      | model(X5,X1)
      | ~ model(X6,X1)
      | model(sK35(X0),X0) ),
    inference(cnf_transformation,[],[f166]) ).

fof(f264,plain,
    ! [X0,X1,X4] :
      ( ~ model(X4,X0)
      | ~ status(X0,X1,wca) ),
    inference(cnf_transformation,[],[f166]) ).

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

fof(f286,plain,
    ! [X1] : ~ model(X1,sK45),
    inference(cnf_transformation,[],[f192]) ).

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

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

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

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

cnf(c_99,plain,
    ( ~ status(X0,X1,cax)
    | ~ model(X2,X0) ),
    inference(cnf_transformation,[],[f256]) ).

cnf(c_100,plain,
    ( model(sK28(X0),X0)
    | status(X0,X1,cax) ),
    inference(cnf_transformation,[],[f255]) ).

cnf(c_109,plain,
    ( ~ status(X0,X1,wca)
    | ~ model(X2,X0) ),
    inference(cnf_transformation,[],[f264]) ).

cnf(c_110,plain,
    ( ~ model(X0,X1)
    | model(sK35(X2),X2)
    | status(X2,X1,wca)
    | model(X3,X1) ),
    inference(cnf_transformation,[],[f263]) ).

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

cnf(c_130,plain,
    ~ model(X0,sK45),
    inference(cnf_transformation,[],[f286]) ).

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(wca,thm),
    inference(cnf_transformation,[],[f298]) ).

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

cnf(c_1921,plain,
    ( ~ model(sK28(X0),X0)
    | ~ status(X0,X1,wca) ),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_3389,plain,
    ( ~ model(X0,X1)
    | model(sK28(X1),X1) ),
    inference(superposition,[status(thm)],[c_100,c_99]) ).

cnf(c_3524,plain,
    ( model(sK28(X0),X0)
    | status(X0,X1,thm) ),
    inference(superposition,[status(thm)],[c_64,c_3389]) ).

cnf(c_3532,plain,
    model(sK28(sK50),sK50),
    inference(superposition,[status(thm)],[c_138,c_3389]) ).

cnf(c_3708,plain,
    ~ status(X0,X1,wca),
    inference(global_subsumption_just,[status(thm)],[c_109,c_974,c_1921,c_3524]) ).

cnf(c_4005,plain,
    ( ~ model(X0,X1)
    | model(sK35(X2),X2)
    | model(X3,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_110,c_3708]) ).

cnf(c_4031,plain,
    ( model(sK35(X0),X0)
    | model(X1,sK50) ),
    inference(superposition,[status(thm)],[c_3532,c_4005]) ).

cnf(c_5192,plain,
    model(X0,sK50),
    inference(superposition,[status(thm)],[c_4031,c_130]) ).

cnf(c_5196,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_136,c_5192]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : KRS268+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.03/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May  2 22:57:52 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  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
% 3.55/1.17  % SZS status Started for theBenchmark.p
% 3.55/1.17  % SZS status Theorem for theBenchmark.p
% 3.55/1.17  
% 3.55/1.17  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.55/1.17  
% 3.55/1.17  ------  iProver source info
% 3.55/1.17  
% 3.55/1.17  git: date: 2024-05-02 19:28:25 +0000
% 3.55/1.17  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.55/1.17  git: non_committed_changes: false
% 3.55/1.17  
% 3.55/1.17  ------ Parsing...
% 3.55/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.55/1.17  
% 3.55/1.17  ------ 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 
% 3.55/1.17  
% 3.55/1.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.55/1.17  ------ Proving...
% 3.55/1.17  ------ Problem Properties 
% 3.55/1.17  
% 3.55/1.17  
% 3.55/1.17  clauses                                 91
% 3.55/1.17  conjectures                             0
% 3.55/1.17  EPR                                     39
% 3.55/1.17  Horn                                    72
% 3.55/1.17  unary                                   13
% 3.55/1.17  binary                                  47
% 3.55/1.17  lits                                    220
% 3.55/1.17  lits eq                                 0
% 3.55/1.17  fd_pure                                 0
% 3.55/1.17  fd_pseudo                               0
% 3.55/1.17  fd_cond                                 0
% 3.55/1.17  fd_pseudo_cond                          0
% 3.55/1.17  AC symbols                              0
% 3.55/1.17  
% 3.55/1.17  ------ Schedule dynamic 5 is on 
% 3.55/1.17  
% 3.55/1.17  ------ no conjectures: strip conj schedule 
% 3.55/1.17  
% 3.55/1.17  ------ no equalities: superposition off 
% 3.55/1.17  
% 3.55/1.17  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.55/1.17  
% 3.55/1.17  
% 3.55/1.17  ------ 
% 3.55/1.17  Current options:
% 3.55/1.17  ------ 
% 3.55/1.17  
% 3.55/1.17  
% 3.55/1.17  
% 3.55/1.17  
% 3.55/1.17  ------ Proving...
% 3.55/1.17  
% 3.55/1.17  
% 3.55/1.17  % SZS status Theorem for theBenchmark.p
% 3.55/1.17  
% 3.55/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.55/1.17  
% 3.55/1.18  
%------------------------------------------------------------------------------