TSTP Solution File: RNG125+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : RNG125+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n014.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 02:57:46 EDT 2024

% Result   : Theorem 3.50s 1.13s
% Output   : CNFRefutation 3.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   55 (  18 unt;   0 def)
%            Number of atoms       :  206 (  11 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  244 (  93   ~;  77   |;  56   &)
%                                         (   5 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :   76 (   0 sgn  51   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f20,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aElementOf0(X1,X0)
         => aElement0(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).

fof(f24,axiom,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( aElementOf0(X1,X0)
           => ( ! [X2] :
                  ( aElement0(X2)
                 => aElementOf0(sdtasdt0(X2,X1),X0) )
              & ! [X2] :
                  ( aElementOf0(X2,X0)
                 => aElementOf0(sdtpldt0(X1,X2),X0) ) ) )
        & aSet0(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).

fof(f34,axiom,
    ! [X0] :
      ( aElement0(X0)
     => ! [X1] :
          ( aDivisorOf0(X1,X0)
        <=> ( doDivides0(X1,X0)
            & aElement0(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDvs) ).

fof(f39,axiom,
    ( aElement0(xb)
    & aElement0(xa) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).

fof(f42,axiom,
    ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))
    & aIdeal0(xI) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).

fof(f45,axiom,
    ( ! [X0] :
        ( ( sz00 != X0
          & aElementOf0(X0,xI) )
       => ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu)) )
    & sz00 != xu
    & aElementOf0(xu,xI) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).

fof(f46,axiom,
    ~ ( aDivisorOf0(xu,xb)
      & aDivisorOf0(xu,xa) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2383) ).

fof(f48,axiom,
    doDivides0(xu,xa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2479) ).

fof(f49,axiom,
    doDivides0(xu,xb),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).

fof(f55,plain,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( aElementOf0(X1,X0)
           => ( ! [X2] :
                  ( aElement0(X2)
                 => aElementOf0(sdtasdt0(X2,X1),X0) )
              & ! [X3] :
                  ( aElementOf0(X3,X0)
                 => aElementOf0(sdtpldt0(X1,X3),X0) ) ) )
        & aSet0(X0) ) ),
    inference(rectify,[],[f24]) ).

fof(f83,plain,
    ! [X0] :
      ( ! [X1] :
          ( aElement0(X1)
          | ~ aElementOf0(X1,X0) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f90,plain,
    ! [X0] :
      ( aIdeal0(X0)
    <=> ( ! [X1] :
            ( ( ! [X2] :
                  ( aElementOf0(sdtasdt0(X2,X1),X0)
                  | ~ aElement0(X2) )
              & ! [X3] :
                  ( aElementOf0(sdtpldt0(X1,X3),X0)
                  | ~ aElementOf0(X3,X0) ) )
            | ~ aElementOf0(X1,X0) )
        & aSet0(X0) ) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f103,plain,
    ! [X0] :
      ( ! [X1] :
          ( aDivisorOf0(X1,X0)
        <=> ( doDivides0(X1,X0)
            & aElement0(X1) ) )
      | ~ aElement0(X0) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f110,plain,
    ( ! [X0] :
        ( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
        | sz00 = X0
        | ~ aElementOf0(X0,xI) )
    & sz00 != xu
    & aElementOf0(xu,xI) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f111,plain,
    ( ! [X0] :
        ( ~ iLess0(sbrdtbr0(X0),sbrdtbr0(xu))
        | sz00 = X0
        | ~ aElementOf0(X0,xI) )
    & sz00 != xu
    & aElementOf0(xu,xI) ),
    inference(flattening,[],[f110]) ).

fof(f112,plain,
    ( ~ aDivisorOf0(xu,xb)
    | ~ aDivisorOf0(xu,xa) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f132,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                  & aElement0(X2) )
              | ? [X3] :
                  ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                  & aElementOf0(X3,X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X1] :
              ( ( ! [X2] :
                    ( aElementOf0(sdtasdt0(X2,X1),X0)
                    | ~ aElement0(X2) )
                & ! [X3] :
                    ( aElementOf0(sdtpldt0(X1,X3),X0)
                    | ~ aElementOf0(X3,X0) ) )
              | ~ aElementOf0(X1,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(nnf_transformation,[],[f90]) ).

fof(f133,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                  & aElement0(X2) )
              | ? [X3] :
                  ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                  & aElementOf0(X3,X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X1] :
              ( ( ! [X2] :
                    ( aElementOf0(sdtasdt0(X2,X1),X0)
                    | ~ aElement0(X2) )
                & ! [X3] :
                    ( aElementOf0(sdtpldt0(X1,X3),X0)
                    | ~ aElementOf0(X3,X0) ) )
              | ~ aElementOf0(X1,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(flattening,[],[f132]) ).

fof(f134,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ? [X1] :
            ( ( ? [X2] :
                  ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                  & aElement0(X2) )
              | ? [X3] :
                  ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                  & aElementOf0(X3,X0) ) )
            & aElementOf0(X1,X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X4] :
              ( ( ! [X5] :
                    ( aElementOf0(sdtasdt0(X5,X4),X0)
                    | ~ aElement0(X5) )
                & ! [X6] :
                    ( aElementOf0(sdtpldt0(X4,X6),X0)
                    | ~ aElementOf0(X6,X0) ) )
              | ~ aElementOf0(X4,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(rectify,[],[f133]) ).

fof(f135,plain,
    ! [X0] :
      ( ? [X1] :
          ( ( ? [X2] :
                ( ~ aElementOf0(sdtasdt0(X2,X1),X0)
                & aElement0(X2) )
            | ? [X3] :
                ( ~ aElementOf0(sdtpldt0(X1,X3),X0)
                & aElementOf0(X3,X0) ) )
          & aElementOf0(X1,X0) )
     => ( ( ? [X2] :
              ( ~ aElementOf0(sdtasdt0(X2,sK10(X0)),X0)
              & aElement0(X2) )
          | ? [X3] :
              ( ~ aElementOf0(sdtpldt0(sK10(X0),X3),X0)
              & aElementOf0(X3,X0) ) )
        & aElementOf0(sK10(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ! [X0] :
      ( ? [X2] :
          ( ~ aElementOf0(sdtasdt0(X2,sK10(X0)),X0)
          & aElement0(X2) )
     => ( ~ aElementOf0(sdtasdt0(sK11(X0),sK10(X0)),X0)
        & aElement0(sK11(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f137,plain,
    ! [X0] :
      ( ? [X3] :
          ( ~ aElementOf0(sdtpldt0(sK10(X0),X3),X0)
          & aElementOf0(X3,X0) )
     => ( ~ aElementOf0(sdtpldt0(sK10(X0),sK12(X0)),X0)
        & aElementOf0(sK12(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f138,plain,
    ! [X0] :
      ( ( aIdeal0(X0)
        | ( ( ( ~ aElementOf0(sdtasdt0(sK11(X0),sK10(X0)),X0)
              & aElement0(sK11(X0)) )
            | ( ~ aElementOf0(sdtpldt0(sK10(X0),sK12(X0)),X0)
              & aElementOf0(sK12(X0),X0) ) )
          & aElementOf0(sK10(X0),X0) )
        | ~ aSet0(X0) )
      & ( ( ! [X4] :
              ( ( ! [X5] :
                    ( aElementOf0(sdtasdt0(X5,X4),X0)
                    | ~ aElement0(X5) )
                & ! [X6] :
                    ( aElementOf0(sdtpldt0(X4,X6),X0)
                    | ~ aElementOf0(X6,X0) ) )
              | ~ aElementOf0(X4,X0) )
          & aSet0(X0) )
        | ~ aIdeal0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f134,f137,f136,f135]) ).

fof(f150,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aDivisorOf0(X1,X0)
            | ~ doDivides0(X1,X0)
            | ~ aElement0(X1) )
          & ( ( doDivides0(X1,X0)
              & aElement0(X1) )
            | ~ aDivisorOf0(X1,X0) ) )
      | ~ aElement0(X0) ),
    inference(nnf_transformation,[],[f103]) ).

fof(f151,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aDivisorOf0(X1,X0)
            | ~ doDivides0(X1,X0)
            | ~ aElement0(X1) )
          & ( ( doDivides0(X1,X0)
              & aElement0(X1) )
            | ~ aDivisorOf0(X1,X0) ) )
      | ~ aElement0(X0) ),
    inference(flattening,[],[f150]) ).

fof(f192,plain,
    ! [X0,X1] :
      ( aElement0(X1)
      | ~ aElementOf0(X1,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f216,plain,
    ! [X0] :
      ( aSet0(X0)
      | ~ aIdeal0(X0) ),
    inference(cnf_transformation,[],[f138]) ).

fof(f243,plain,
    ! [X0,X1] :
      ( aDivisorOf0(X1,X0)
      | ~ doDivides0(X1,X0)
      | ~ aElement0(X1)
      | ~ aElement0(X0) ),
    inference(cnf_transformation,[],[f151]) ).

fof(f260,plain,
    aElement0(xa),
    inference(cnf_transformation,[],[f39]) ).

fof(f261,plain,
    aElement0(xb),
    inference(cnf_transformation,[],[f39]) ).

fof(f264,plain,
    aIdeal0(xI),
    inference(cnf_transformation,[],[f42]) ).

fof(f272,plain,
    aElementOf0(xu,xI),
    inference(cnf_transformation,[],[f111]) ).

fof(f275,plain,
    ( ~ aDivisorOf0(xu,xb)
    | ~ aDivisorOf0(xu,xa) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f279,plain,
    doDivides0(xu,xa),
    inference(cnf_transformation,[],[f48]) ).

fof(f280,plain,
    doDivides0(xu,xb),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_72,plain,
    ( ~ aElementOf0(X0,X1)
    | ~ aSet0(X1)
    | aElement0(X0) ),
    inference(cnf_transformation,[],[f192]) ).

cnf(c_103,plain,
    ( ~ aIdeal0(X0)
    | aSet0(X0) ),
    inference(cnf_transformation,[],[f216]) ).

cnf(c_121,plain,
    ( ~ doDivides0(X0,X1)
    | ~ aElement0(X0)
    | ~ aElement0(X1)
    | aDivisorOf0(X0,X1) ),
    inference(cnf_transformation,[],[f243]) ).

cnf(c_140,plain,
    aElement0(xb),
    inference(cnf_transformation,[],[f261]) ).

cnf(c_141,plain,
    aElement0(xa),
    inference(cnf_transformation,[],[f260]) ).

cnf(c_145,plain,
    aIdeal0(xI),
    inference(cnf_transformation,[],[f264]) ).

cnf(c_154,plain,
    aElementOf0(xu,xI),
    inference(cnf_transformation,[],[f272]) ).

cnf(c_155,plain,
    ( ~ aDivisorOf0(xu,xb)
    | ~ aDivisorOf0(xu,xa) ),
    inference(cnf_transformation,[],[f275]) ).

cnf(c_159,plain,
    doDivides0(xu,xa),
    inference(cnf_transformation,[],[f279]) ).

cnf(c_160,plain,
    doDivides0(xu,xb),
    inference(cnf_transformation,[],[f280]) ).

cnf(c_2240,plain,
    ( X0 != xu
    | X1 != xa
    | ~ aElement0(X0)
    | ~ aElement0(X1)
    | aDivisorOf0(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_121,c_159]) ).

cnf(c_2241,plain,
    ( ~ aElement0(xa)
    | ~ aElement0(xu)
    | aDivisorOf0(xu,xa) ),
    inference(unflattening,[status(thm)],[c_2240]) ).

cnf(c_2242,plain,
    ( ~ aElement0(xu)
    | aDivisorOf0(xu,xa) ),
    inference(global_subsumption_just,[status(thm)],[c_2241,c_141,c_2241]) ).

cnf(c_2270,plain,
    ( X0 != xu
    | X1 != xb
    | ~ aElement0(X0)
    | ~ aElement0(X1)
    | aDivisorOf0(X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_121,c_160]) ).

cnf(c_2271,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(xu)
    | aDivisorOf0(xu,xb) ),
    inference(unflattening,[status(thm)],[c_2270]) ).

cnf(c_2272,plain,
    ~ aElement0(xu),
    inference(global_subsumption_just,[status(thm)],[c_2271,c_140,c_155,c_2242,c_2271]) ).

cnf(c_7213,plain,
    aSet0(xI),
    inference(superposition,[status(thm)],[c_145,c_103]) ).

cnf(c_7333,plain,
    ( ~ aSet0(xI)
    | aElement0(xu) ),
    inference(superposition,[status(thm)],[c_154,c_72]) ).

cnf(c_7336,plain,
    aElement0(xu),
    inference(forward_subsumption_resolution,[status(thm)],[c_7333,c_7213]) ).

cnf(c_7337,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_7336,c_2272]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : RNG125+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n014.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 21:10:32 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.17/0.43  Running first-order theorem proving
% 0.17/0.43  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
% 3.50/1.13  % SZS status Started for theBenchmark.p
% 3.50/1.13  % SZS status Theorem for theBenchmark.p
% 3.50/1.13  
% 3.50/1.13  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.50/1.13  
% 3.50/1.13  ------  iProver source info
% 3.50/1.13  
% 3.50/1.13  git: date: 2024-05-02 19:28:25 +0000
% 3.50/1.13  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.50/1.13  git: non_committed_changes: false
% 3.50/1.13  
% 3.50/1.13  ------ Parsing...
% 3.50/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.50/1.13  
% 3.50/1.13  ------ Preprocessing... sup_sim: 1  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 3.50/1.13  
% 3.50/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.50/1.13  
% 3.50/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.50/1.13  ------ Proving...
% 3.50/1.13  ------ Problem Properties 
% 3.50/1.13  
% 3.50/1.13  
% 3.50/1.13  clauses                                 107
% 3.50/1.13  conjectures                             0
% 3.50/1.13  EPR                                     26
% 3.50/1.13  Horn                                    83
% 3.50/1.13  unary                                   21
% 3.50/1.13  binary                                  17
% 3.50/1.13  lits                                    351
% 3.50/1.13  lits eq                                 51
% 3.50/1.13  fd_pure                                 0
% 3.50/1.13  fd_pseudo                               0
% 3.50/1.13  fd_cond                                 5
% 3.50/1.13  fd_pseudo_cond                          11
% 3.50/1.13  AC symbols                              0
% 3.50/1.13  
% 3.50/1.13  ------ Schedule dynamic 5 is on 
% 3.50/1.13  
% 3.50/1.13  ------ no conjectures: strip conj schedule 
% 3.50/1.13  
% 3.50/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.50/1.13  
% 3.50/1.13  
% 3.50/1.13  ------ 
% 3.50/1.13  Current options:
% 3.50/1.13  ------ 
% 3.50/1.13  
% 3.50/1.13  
% 3.50/1.13  
% 3.50/1.13  
% 3.50/1.13  ------ Proving...
% 3.50/1.13  
% 3.50/1.13  
% 3.50/1.13  % SZS status Theorem for theBenchmark.p
% 3.50/1.13  
% 3.50/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.50/1.13  
% 3.50/1.13  
%------------------------------------------------------------------------------