TSTP Solution File: NUM504+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM504+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n004.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 02:49:37 EDT 2024

% Result   : Theorem 3.75s 1.14s
% Output   : CNFRefutation 3.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   59 (  24 unt;   0 def)
%            Number of atoms       :  217 (  76 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  228 (  70   ~;  56   |;  91   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;  12 con; 0-2 aty)
%            Number of variables   :   57 (   0 sgn  32   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

fof(f21,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X0)
          & sdtlseqdt0(X0,X1) )
       => X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).

fof(f45,axiom,
    ( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & aNaturalNumber0(xk) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).

fof(f48,axiom,
    ( isPrime0(xr)
    & ! [X0] :
        ( ( ( doDivides0(X0,xr)
            | ? [X1] :
                ( sdtasdt0(X0,X1) = xr
                & aNaturalNumber0(X1) ) )
          & aNaturalNumber0(X0) )
       => ( xr = X0
          | sz10 = X0 ) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & ? [X0] :
        ( xk = sdtasdt0(xr,X0)
        & aNaturalNumber0(X0) )
    & aNaturalNumber0(xr) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).

fof(f49,axiom,
    ( doDivides0(xr,sdtasdt0(xn,xm))
    & ? [X0] :
        ( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
        & aNaturalNumber0(X0) )
    & ? [X0] :
        ( xk = sdtpldt0(xr,X0)
        & aNaturalNumber0(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).

fof(f51,axiom,
    ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    & ? [X0] :
        ( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X0)
        & aNaturalNumber0(X0) )
    & sdtasdt0(xp,xk) != sdtasdt0(xp,xm)
    & sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    & ? [X0] :
        ( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),X0)
        & aNaturalNumber0(X0) )
    & sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2414) ).

fof(f59,plain,
    ( isPrime0(xr)
    & ! [X0] :
        ( ( ( doDivides0(X0,xr)
            | ? [X1] :
                ( sdtasdt0(X0,X1) = xr
                & aNaturalNumber0(X1) ) )
          & aNaturalNumber0(X0) )
       => ( xr = X0
          | sz10 = X0 ) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & ? [X2] :
        ( xk = sdtasdt0(xr,X2)
        & aNaturalNumber0(X2) )
    & aNaturalNumber0(xr) ),
    inference(rectify,[],[f48]) ).

fof(f60,plain,
    ( doDivides0(xr,sdtasdt0(xn,xm))
    & ? [X0] :
        ( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
        & aNaturalNumber0(X0) )
    & ? [X1] :
        ( xk = sdtpldt0(xr,X1)
        & aNaturalNumber0(X1) ) ),
    inference(rectify,[],[f49]) ).

fof(f61,plain,
    ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    & ? [X0] :
        ( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X0)
        & aNaturalNumber0(X0) )
    & sdtasdt0(xp,xk) != sdtasdt0(xp,xm)
    & sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    & ? [X1] :
        ( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),X1)
        & aNaturalNumber0(X1) )
    & sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
    inference(rectify,[],[f51]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f63]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f65]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f93]) ).

fof(f134,plain,
    ( isPrime0(xr)
    & ! [X0] :
        ( xr = X0
        | sz10 = X0
        | ( ~ doDivides0(X0,xr)
          & ! [X1] :
              ( sdtasdt0(X0,X1) != xr
              | ~ aNaturalNumber0(X1) ) )
        | ~ aNaturalNumber0(X0) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & ? [X2] :
        ( xk = sdtasdt0(xr,X2)
        & aNaturalNumber0(X2) )
    & aNaturalNumber0(xr) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f135,plain,
    ( isPrime0(xr)
    & ! [X0] :
        ( xr = X0
        | sz10 = X0
        | ( ~ doDivides0(X0,xr)
          & ! [X1] :
              ( sdtasdt0(X0,X1) != xr
              | ~ aNaturalNumber0(X1) ) )
        | ~ aNaturalNumber0(X0) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & ? [X2] :
        ( xk = sdtasdt0(xr,X2)
        & aNaturalNumber0(X2) )
    & aNaturalNumber0(xr) ),
    inference(flattening,[],[f134]) ).

fof(f175,plain,
    ( ? [X2] :
        ( xk = sdtasdt0(xr,X2)
        & aNaturalNumber0(X2) )
   => ( xk = sdtasdt0(xr,sK13)
      & aNaturalNumber0(sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f176,plain,
    ( isPrime0(xr)
    & ! [X0] :
        ( xr = X0
        | sz10 = X0
        | ( ~ doDivides0(X0,xr)
          & ! [X1] :
              ( sdtasdt0(X0,X1) != xr
              | ~ aNaturalNumber0(X1) ) )
        | ~ aNaturalNumber0(X0) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & xk = sdtasdt0(xr,sK13)
    & aNaturalNumber0(sK13)
    & aNaturalNumber0(xr) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f135,f175]) ).

fof(f177,plain,
    ( ? [X0] :
        ( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
        & aNaturalNumber0(X0) )
   => ( sdtasdt0(xn,xm) = sdtasdt0(xr,sK14)
      & aNaturalNumber0(sK14) ) ),
    introduced(choice_axiom,[]) ).

fof(f178,plain,
    ( ? [X1] :
        ( xk = sdtpldt0(xr,X1)
        & aNaturalNumber0(X1) )
   => ( xk = sdtpldt0(xr,sK15)
      & aNaturalNumber0(sK15) ) ),
    introduced(choice_axiom,[]) ).

fof(f179,plain,
    ( doDivides0(xr,sdtasdt0(xn,xm))
    & sdtasdt0(xn,xm) = sdtasdt0(xr,sK14)
    & aNaturalNumber0(sK14)
    & xk = sdtpldt0(xr,sK15)
    & aNaturalNumber0(sK15) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f60,f178,f177]) ).

fof(f182,plain,
    ( ? [X0] :
        ( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X0)
        & aNaturalNumber0(X0) )
   => ( sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),sK17)
      & aNaturalNumber0(sK17) ) ),
    introduced(choice_axiom,[]) ).

fof(f183,plain,
    ( ? [X1] :
        ( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),X1)
        & aNaturalNumber0(X1) )
   => ( sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),sK18)
      & aNaturalNumber0(sK18) ) ),
    introduced(choice_axiom,[]) ).

fof(f184,plain,
    ( sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    & sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),sK17)
    & aNaturalNumber0(sK17)
    & sdtasdt0(xp,xk) != sdtasdt0(xp,xm)
    & sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    & sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),sK18)
    & aNaturalNumber0(sK18)
    & sdtasdt0(xn,xm) != sdtasdt0(xp,xm) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f61,f183,f182]) ).

fof(f188,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtasdt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f216,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f293,plain,
    sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
    inference(cnf_transformation,[],[f45]) ).

fof(f299,plain,
    aNaturalNumber0(xr),
    inference(cnf_transformation,[],[f176]) ).

fof(f310,plain,
    aNaturalNumber0(sK14),
    inference(cnf_transformation,[],[f179]) ).

fof(f311,plain,
    sdtasdt0(xn,xm) = sdtasdt0(xr,sK14),
    inference(cnf_transformation,[],[f179]) ).

fof(f317,plain,
    aNaturalNumber0(sK18),
    inference(cnf_transformation,[],[f184]) ).

fof(f318,plain,
    sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),sK18),
    inference(cnf_transformation,[],[f184]) ).

fof(f319,plain,
    sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
    inference(cnf_transformation,[],[f184]) ).

fof(f320,plain,
    sdtasdt0(xp,xk) != sdtasdt0(xp,xm),
    inference(cnf_transformation,[],[f184]) ).

fof(f323,plain,
    sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
    inference(cnf_transformation,[],[f184]) ).

cnf(c_52,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(sdtpldt0(X0,X1)) ),
    inference(cnf_transformation,[],[f188]) ).

cnf(c_53,plain,
    ( ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | aNaturalNumber0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f189]) ).

cnf(c_80,plain,
    ( ~ sdtlseqdt0(X0,X1)
    | ~ sdtlseqdt0(X1,X0)
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = X1 ),
    inference(cnf_transformation,[],[f216]) ).

cnf(c_156,plain,
    sdtasdt0(xp,xk) = sdtasdt0(xn,xm),
    inference(cnf_transformation,[],[f293]) ).

cnf(c_170,plain,
    aNaturalNumber0(xr),
    inference(cnf_transformation,[],[f299]) ).

cnf(c_172,plain,
    sdtasdt0(xn,xm) = sdtasdt0(xr,sK14),
    inference(cnf_transformation,[],[f311]) ).

cnf(c_173,plain,
    aNaturalNumber0(sK14),
    inference(cnf_transformation,[],[f310]) ).

cnf(c_179,plain,
    sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
    inference(cnf_transformation,[],[f323]) ).

cnf(c_182,plain,
    sdtasdt0(xp,xm) != sdtasdt0(xp,xk),
    inference(cnf_transformation,[],[f320]) ).

cnf(c_183,plain,
    sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
    inference(cnf_transformation,[],[f319]) ).

cnf(c_184,plain,
    sdtpldt0(sdtasdt0(xn,xm),sK18) = sdtasdt0(xp,xm),
    inference(cnf_transformation,[],[f318]) ).

cnf(c_185,plain,
    aNaturalNumber0(sK18),
    inference(cnf_transformation,[],[f317]) ).

cnf(c_1091,plain,
    sdtasdt0(xp,xk) = sdtasdt0(xr,sK14),
    inference(demodulation,[status(thm)],[c_172,c_156]) ).

cnf(c_1092,plain,
    sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)),
    inference(demodulation,[status(thm)],[c_183,c_156]) ).

cnf(c_1126,plain,
    sdtpldt0(sdtasdt0(xp,xk),sK18) = sdtasdt0(xp,xm),
    inference(light_normalisation,[status(thm)],[c_184,c_156]) ).

cnf(c_11071,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(sK14)
    | aNaturalNumber0(sdtasdt0(xp,xk)) ),
    inference(superposition,[status(thm)],[c_1091,c_53]) ).

cnf(c_11078,plain,
    aNaturalNumber0(sdtasdt0(xp,xk)),
    inference(forward_subsumption_resolution,[status(thm)],[c_11071,c_173,c_170]) ).

cnf(c_11130,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xp,xk))
    | ~ aNaturalNumber0(sK18)
    | aNaturalNumber0(sdtasdt0(xp,xm)) ),
    inference(superposition,[status(thm)],[c_1126,c_52]) ).

cnf(c_11131,plain,
    aNaturalNumber0(sdtasdt0(xp,xm)),
    inference(forward_subsumption_resolution,[status(thm)],[c_11130,c_185,c_11078]) ).

cnf(c_11500,plain,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
    | ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(sdtasdt0(xp,xm))
    | ~ aNaturalNumber0(sdtasdt0(xp,xk))
    | sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
    inference(instantiation,[status(thm)],[c_80]) ).

cnf(c_11501,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_11500,c_11131,c_11078,c_1092,c_182,c_179]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM504+3 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n004.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May  2 19:15:03 EDT 2024
% 0.12/0.33  % 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
% 3.75/1.14  % SZS status Started for theBenchmark.p
% 3.75/1.14  % SZS status Theorem for theBenchmark.p
% 3.75/1.14  
% 3.75/1.14  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.75/1.14  
% 3.75/1.14  ------  iProver source info
% 3.75/1.14  
% 3.75/1.14  git: date: 2024-05-02 19:28:25 +0000
% 3.75/1.14  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.75/1.14  git: non_committed_changes: false
% 3.75/1.14  
% 3.75/1.14  ------ Parsing...
% 3.75/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.75/1.14  
% 3.75/1.14  ------ Preprocessing... sup_sim: 9  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.75/1.14  
% 3.75/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.75/1.14  
% 3.75/1.14  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.75/1.14  ------ Proving...
% 3.75/1.14  ------ Problem Properties 
% 3.75/1.14  
% 3.75/1.14  
% 3.75/1.14  clauses                                 130
% 3.75/1.14  conjectures                             0
% 3.75/1.14  EPR                                     48
% 3.75/1.14  Horn                                    90
% 3.75/1.14  unary                                   51
% 3.75/1.14  binary                                  13
% 3.75/1.14  lits                                    401
% 3.75/1.14  lits eq                                 124
% 3.75/1.14  fd_pure                                 0
% 3.75/1.14  fd_pseudo                               0
% 3.75/1.14  fd_cond                                 24
% 3.75/1.14  fd_pseudo_cond                          11
% 3.75/1.14  AC symbols                              0
% 3.75/1.14  
% 3.75/1.14  ------ Schedule dynamic 5 is on 
% 3.75/1.14  
% 3.75/1.14  ------ no conjectures: strip conj schedule 
% 3.75/1.14  
% 3.75/1.14  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.75/1.14  
% 3.75/1.14  
% 3.75/1.14  ------ 
% 3.75/1.14  Current options:
% 3.75/1.14  ------ 
% 3.75/1.14  
% 3.75/1.14  
% 3.75/1.14  
% 3.75/1.14  
% 3.75/1.14  ------ Proving...
% 3.75/1.14  
% 3.75/1.14  
% 3.75/1.14  % SZS status Theorem for theBenchmark.p
% 3.75/1.14  
% 3.75/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.75/1.14  
% 3.75/1.15  
%------------------------------------------------------------------------------