TSTP Solution File: NUM590+3 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM590+3 : TPTP v8.1.2. Released v4.0.0.
% 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 02:50:05 EDT 2024

% Result   : Theorem 8.06s 1.70s
% Output   : CNFRefutation 8.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   40 (  11 unt;   0 def)
%            Number of atoms       :  175 (  17 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  201 (  66   ~;  54   |;  66   &)
%                                         (   5 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   56 (   0 sgn  41   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f10,axiom,
    ! [X0] :
      ( aSet0(X0)
     => ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( ! [X2] :
                ( aElementOf0(X2,X1)
               => aElementOf0(X2,X0) )
            & aSet0(X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).

fof(f23,axiom,
    ( isCountable0(szNzAzT0)
    & aSet0(szNzAzT0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).

fof(f82,axiom,
    ! [X0] :
      ( aElementOf0(X0,szNzAzT0)
     => ( isCountable0(sdtlpdtrp0(xN,X0))
        & aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
        & ! [X1] :
            ( aElementOf0(X1,sdtlpdtrp0(xN,X0))
           => aElementOf0(X1,szNzAzT0) )
        & aSet0(sdtlpdtrp0(xN,X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3671) ).

fof(f90,axiom,
    aElementOf0(xi,szNzAzT0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4448) ).

fof(f91,axiom,
    ( xd = sdtlpdtrp0(xC,xi)
    & xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
    & ! [X0] :
        ( aElementOf0(X0,xY)
      <=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X0
          & aElementOf0(X0,sdtlpdtrp0(xN,xi))
          & aElement0(X0) ) )
    & aSet0(xY)
    & ! [X0] :
        ( aElementOf0(X0,sdtlpdtrp0(xN,xi))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X0) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4448_02) ).

fof(f92,conjecture,
    ( aSubsetOf0(xY,szNzAzT0)
    | ! [X0] :
        ( aElementOf0(X0,xY)
       => aElementOf0(X0,szNzAzT0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f93,negated_conjecture,
    ~ ( aSubsetOf0(xY,szNzAzT0)
      | ! [X0] :
          ( aElementOf0(X0,xY)
         => aElementOf0(X0,szNzAzT0) ) ),
    inference(negated_conjecture,[],[f92]) ).

fof(f109,plain,
    ( xd = sdtlpdtrp0(xC,xi)
    & xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
    & ! [X0] :
        ( aElementOf0(X0,xY)
      <=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X0
          & aElementOf0(X0,sdtlpdtrp0(xN,xi))
          & aElement0(X0) ) )
    & aSet0(xY)
    & ! [X1] :
        ( aElementOf0(X1,sdtlpdtrp0(xN,xi))
       => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(rectify,[],[f91]) ).

fof(f116,plain,
    ! [X0] :
      ( ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( ! [X2] :
                ( aElementOf0(X2,X0)
                | ~ aElementOf0(X2,X1) )
            & aSet0(X1) ) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f216,plain,
    ! [X0] :
      ( ( isCountable0(sdtlpdtrp0(xN,X0))
        & aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
        & ! [X1] :
            ( aElementOf0(X1,szNzAzT0)
            | ~ aElementOf0(X1,sdtlpdtrp0(xN,X0)) )
        & aSet0(sdtlpdtrp0(xN,X0)) )
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(ennf_transformation,[],[f82]) ).

fof(f228,plain,
    ( xd = sdtlpdtrp0(xC,xi)
    & xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
    & ! [X0] :
        ( aElementOf0(X0,xY)
      <=> ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X0
          & aElementOf0(X0,sdtlpdtrp0(xN,xi))
          & aElement0(X0) ) )
    & aSet0(xY)
    & ! [X1] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1)
        | ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(ennf_transformation,[],[f109]) ).

fof(f229,plain,
    ( ~ aSubsetOf0(xY,szNzAzT0)
    & ? [X0] :
        ( ~ aElementOf0(X0,szNzAzT0)
        & aElementOf0(X0,xY) ) ),
    inference(ennf_transformation,[],[f93]) ).

fof(f264,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( aElementOf0(X2,X0)
                  | ~ aElementOf0(X2,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(nnf_transformation,[],[f116]) ).

fof(f265,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X2] :
                  ( aElementOf0(X2,X0)
                  | ~ aElementOf0(X2,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(flattening,[],[f264]) ).

fof(f266,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ? [X2] :
                ( ~ aElementOf0(X2,X0)
                & aElementOf0(X2,X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X3] :
                  ( aElementOf0(X3,X0)
                  | ~ aElementOf0(X3,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(rectify,[],[f265]) ).

fof(f267,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,X0)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK23(X0,X1),X0)
        & aElementOf0(sK23(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f268,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ( ~ aElementOf0(sK23(X0,X1),X0)
              & aElementOf0(sK23(X0,X1),X1) )
            | ~ aSet0(X1) )
          & ( ( ! [X3] :
                  ( aElementOf0(X3,X0)
                  | ~ aElementOf0(X3,X1) )
              & aSet0(X1) )
            | ~ aSubsetOf0(X1,X0) ) )
      | ~ aSet0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f266,f267]) ).

fof(f418,plain,
    ( xd = sdtlpdtrp0(xC,xi)
    & xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
    & ! [X0] :
        ( ( aElementOf0(X0,xY)
          | szmzizndt0(sdtlpdtrp0(xN,xi)) = X0
          | ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
          | ~ aElement0(X0) )
        & ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X0
            & aElementOf0(X0,sdtlpdtrp0(xN,xi))
            & aElement0(X0) )
          | ~ aElementOf0(X0,xY) ) )
    & aSet0(xY)
    & ! [X1] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1)
        | ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(nnf_transformation,[],[f228]) ).

fof(f419,plain,
    ( xd = sdtlpdtrp0(xC,xi)
    & xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))
    & ! [X0] :
        ( ( aElementOf0(X0,xY)
          | szmzizndt0(sdtlpdtrp0(xN,xi)) = X0
          | ~ aElementOf0(X0,sdtlpdtrp0(xN,xi))
          | ~ aElement0(X0) )
        & ( ( szmzizndt0(sdtlpdtrp0(xN,xi)) != X0
            & aElementOf0(X0,sdtlpdtrp0(xN,xi))
            & aElement0(X0) )
          | ~ aElementOf0(X0,xY) ) )
    & aSet0(xY)
    & ! [X1] :
        ( sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xi)),X1)
        | ~ aElementOf0(X1,sdtlpdtrp0(xN,xi)) )
    & aElementOf0(szmzizndt0(sdtlpdtrp0(xN,xi)),sdtlpdtrp0(xN,xi)) ),
    inference(flattening,[],[f418]) ).

fof(f420,plain,
    ( ? [X0] :
        ( ~ aElementOf0(X0,szNzAzT0)
        & aElementOf0(X0,xY) )
   => ( ~ aElementOf0(sK59,szNzAzT0)
      & aElementOf0(sK59,xY) ) ),
    introduced(choice_axiom,[]) ).

fof(f421,plain,
    ( ~ aSubsetOf0(xY,szNzAzT0)
    & ~ aElementOf0(sK59,szNzAzT0)
    & aElementOf0(sK59,xY) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f229,f420]) ).

fof(f430,plain,
    ! [X3,X0,X1] :
      ( aElementOf0(X3,X0)
      | ~ aElementOf0(X3,X1)
      | ~ aSubsetOf0(X1,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f268]) ).

fof(f467,plain,
    aSet0(szNzAzT0),
    inference(cnf_transformation,[],[f23]) ).

fof(f642,plain,
    ! [X0] :
      ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
      | ~ aElementOf0(X0,szNzAzT0) ),
    inference(cnf_transformation,[],[f216]) ).

fof(f748,plain,
    aElementOf0(xi,szNzAzT0),
    inference(cnf_transformation,[],[f90]) ).

fof(f753,plain,
    ! [X0] :
      ( aElementOf0(X0,sdtlpdtrp0(xN,xi))
      | ~ aElementOf0(X0,xY) ),
    inference(cnf_transformation,[],[f419]) ).

fof(f758,plain,
    aElementOf0(sK59,xY),
    inference(cnf_transformation,[],[f421]) ).

fof(f759,plain,
    ~ aElementOf0(sK59,szNzAzT0),
    inference(cnf_transformation,[],[f421]) ).

cnf(c_58,plain,
    ( ~ aElementOf0(X0,X1)
    | ~ aSubsetOf0(X1,X2)
    | ~ aSet0(X2)
    | aElementOf0(X0,X2) ),
    inference(cnf_transformation,[],[f430]) ).

cnf(c_95,plain,
    aSet0(szNzAzT0),
    inference(cnf_transformation,[],[f467]) ).

cnf(c_268,plain,
    ( ~ aElementOf0(X0,szNzAzT0)
    | aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
    inference(cnf_transformation,[],[f642]) ).

cnf(c_375,plain,
    aElementOf0(xi,szNzAzT0),
    inference(cnf_transformation,[],[f748]) ).

cnf(c_380,plain,
    ( ~ aElementOf0(X0,xY)
    | aElementOf0(X0,sdtlpdtrp0(xN,xi)) ),
    inference(cnf_transformation,[],[f753]) ).

cnf(c_386,negated_conjecture,
    ~ aElementOf0(sK59,szNzAzT0),
    inference(cnf_transformation,[],[f759]) ).

cnf(c_387,negated_conjecture,
    aElementOf0(sK59,xY),
    inference(cnf_transformation,[],[f758]) ).

cnf(c_18052,plain,
    ( ~ aSubsetOf0(sdtlpdtrp0(xN,xi),X0)
    | ~ aElementOf0(X1,xY)
    | ~ aSet0(X0)
    | aElementOf0(X1,X0) ),
    inference(superposition,[status(thm)],[c_380,c_58]) ).

cnf(c_18111,plain,
    ( ~ aElementOf0(X0,xY)
    | ~ aElementOf0(xi,szNzAzT0)
    | ~ aSet0(szNzAzT0)
    | aElementOf0(X0,szNzAzT0) ),
    inference(superposition,[status(thm)],[c_268,c_18052]) ).

cnf(c_18134,plain,
    ( ~ aElementOf0(X0,xY)
    | aElementOf0(X0,szNzAzT0) ),
    inference(global_subsumption_just,[status(thm)],[c_18111,c_95,c_375,c_18111]) ).

cnf(c_18141,plain,
    aElementOf0(sK59,szNzAzT0),
    inference(superposition,[status(thm)],[c_387,c_18134]) ).

cnf(c_18142,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_386,c_18141]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : NUM590+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n019.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 19:34:59 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  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
% 8.06/1.70  % SZS status Started for theBenchmark.p
% 8.06/1.70  % SZS status Theorem for theBenchmark.p
% 8.06/1.70  
% 8.06/1.70  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 8.06/1.70  
% 8.06/1.70  ------  iProver source info
% 8.06/1.70  
% 8.06/1.70  git: date: 2024-05-02 19:28:25 +0000
% 8.06/1.70  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 8.06/1.70  git: non_committed_changes: false
% 8.06/1.70  
% 8.06/1.70  ------ Parsing...
% 8.06/1.70  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 8.06/1.70  
% 8.06/1.70  ------ Preprocessing... sup_sim: 1  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e 
% 8.06/1.70  
% 8.06/1.70  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 8.06/1.70  
% 8.06/1.70  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 8.06/1.70  ------ Proving...
% 8.06/1.70  ------ Problem Properties 
% 8.06/1.70  
% 8.06/1.70  
% 8.06/1.70  clauses                                 316
% 8.06/1.70  conjectures                             3
% 8.06/1.70  EPR                                     56
% 8.06/1.70  Horn                                    244
% 8.06/1.70  unary                                   37
% 8.06/1.70  binary                                  75
% 8.06/1.70  lits                                    1039
% 8.06/1.70  lits eq                                 128
% 8.06/1.70  fd_pure                                 0
% 8.06/1.70  fd_pseudo                               0
% 8.06/1.70  fd_cond                                 11
% 8.06/1.70  fd_pseudo_cond                          39
% 8.06/1.70  AC symbols                              0
% 8.06/1.70  
% 8.06/1.70  ------ Input Options Time Limit: Unbounded
% 8.06/1.70  
% 8.06/1.70  
% 8.06/1.70  ------ 
% 8.06/1.70  Current options:
% 8.06/1.70  ------ 
% 8.06/1.70  
% 8.06/1.70  
% 8.06/1.70  
% 8.06/1.70  
% 8.06/1.70  ------ Proving...
% 8.06/1.70  
% 8.06/1.70  
% 8.06/1.70  % SZS status Theorem for theBenchmark.p
% 8.06/1.70  
% 8.06/1.70  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.06/1.70  
% 8.06/1.70  
%------------------------------------------------------------------------------