TSTP Solution File: NUM552+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUM552+1 : 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 : Thu Aug 31 11:31:23 EDT 2023

% Result   : Theorem 3.91s 1.13s
% Output   : CNFRefutation 3.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   54 (  16 unt;   0 def)
%            Number of atoms       :  241 (  38 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  308 ( 121   ~; 117   |;  55   &)
%                                         (   8 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   8 con; 0-3 aty)
%            Number of variables   :   85 (   0 sgn;  66   !;   8   ?)

% 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(f57,axiom,
    ! [X0,X1] :
      ( ( aElementOf0(X1,szNzAzT0)
        & aSet0(X0) )
     => ! [X2] :
          ( slbdtsldtrb0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( sbrdtbr0(X3) = X1
                  & aSubsetOf0(X3,X0) ) )
            & aSet0(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).

fof(f61,axiom,
    aElementOf0(xk,szNzAzT0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202) ).

fof(f62,axiom,
    ( sz00 != xk
    & aSet0(xT)
    & aSet0(xS) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).

fof(f63,axiom,
    ( slcrc0 != slbdtsldtrb0(xS,xk)
    & aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2227) ).

fof(f65,axiom,
    aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).

fof(f68,conjecture,
    ( aElementOf0(xx,xQ)
   => aElementOf0(xx,xT) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f69,negated_conjecture,
    ~ ( aElementOf0(xx,xQ)
     => aElementOf0(xx,xT) ),
    inference(negated_conjecture,[],[f68]) ).

fof(f83,plain,
    ! [X0] :
      ( ! [X1] :
          ( aSubsetOf0(X1,X0)
        <=> ( ! [X2] :
                ( aElementOf0(X2,X0)
                | ~ aElementOf0(X2,X1) )
            & aSet0(X1) ) )
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f150,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( slbdtsldtrb0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( sbrdtbr0(X3) = X1
                  & aSubsetOf0(X3,X0) ) )
            & aSet0(X2) ) )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f151,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( slbdtsldtrb0(X0,X1) = X2
        <=> ( ! [X3] :
                ( aElementOf0(X3,X2)
              <=> ( sbrdtbr0(X3) = X1
                  & aSubsetOf0(X3,X0) ) )
            & aSet0(X2) ) )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f150]) ).

fof(f158,plain,
    ( ~ aElementOf0(xx,xT)
    & aElementOf0(xx,xQ) ),
    inference(ennf_transformation,[],[f69]) ).

fof(f170,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,[],[f83]) ).

fof(f171,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,[],[f170]) ).

fof(f172,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,[],[f171]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ aElementOf0(X2,X0)
          & aElementOf0(X2,X1) )
     => ( ~ aElementOf0(sK5(X0,X1),X0)
        & aElementOf0(sK5(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f174,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aSubsetOf0(X1,X0)
            | ( ~ aElementOf0(sK5(X0,X1),X0)
              & aElementOf0(sK5(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,[sK5])],[f172,f173]) ).

fof(f214,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( slbdtsldtrb0(X0,X1) = X2
            | ? [X3] :
                ( ( sbrdtbr0(X3) != X1
                  | ~ aSubsetOf0(X3,X0)
                  | ~ aElementOf0(X3,X2) )
                & ( ( sbrdtbr0(X3) = X1
                    & aSubsetOf0(X3,X0) )
                  | aElementOf0(X3,X2) ) )
            | ~ aSet0(X2) )
          & ( ( ! [X3] :
                  ( ( aElementOf0(X3,X2)
                    | sbrdtbr0(X3) != X1
                    | ~ aSubsetOf0(X3,X0) )
                  & ( ( sbrdtbr0(X3) = X1
                      & aSubsetOf0(X3,X0) )
                    | ~ aElementOf0(X3,X2) ) )
              & aSet0(X2) )
            | slbdtsldtrb0(X0,X1) != X2 ) )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(nnf_transformation,[],[f151]) ).

fof(f215,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( slbdtsldtrb0(X0,X1) = X2
            | ? [X3] :
                ( ( sbrdtbr0(X3) != X1
                  | ~ aSubsetOf0(X3,X0)
                  | ~ aElementOf0(X3,X2) )
                & ( ( sbrdtbr0(X3) = X1
                    & aSubsetOf0(X3,X0) )
                  | aElementOf0(X3,X2) ) )
            | ~ aSet0(X2) )
          & ( ( ! [X3] :
                  ( ( aElementOf0(X3,X2)
                    | sbrdtbr0(X3) != X1
                    | ~ aSubsetOf0(X3,X0) )
                  & ( ( sbrdtbr0(X3) = X1
                      & aSubsetOf0(X3,X0) )
                    | ~ aElementOf0(X3,X2) ) )
              & aSet0(X2) )
            | slbdtsldtrb0(X0,X1) != X2 ) )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(flattening,[],[f214]) ).

fof(f216,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( slbdtsldtrb0(X0,X1) = X2
            | ? [X3] :
                ( ( sbrdtbr0(X3) != X1
                  | ~ aSubsetOf0(X3,X0)
                  | ~ aElementOf0(X3,X2) )
                & ( ( sbrdtbr0(X3) = X1
                    & aSubsetOf0(X3,X0) )
                  | aElementOf0(X3,X2) ) )
            | ~ aSet0(X2) )
          & ( ( ! [X4] :
                  ( ( aElementOf0(X4,X2)
                    | sbrdtbr0(X4) != X1
                    | ~ aSubsetOf0(X4,X0) )
                  & ( ( sbrdtbr0(X4) = X1
                      & aSubsetOf0(X4,X0) )
                    | ~ aElementOf0(X4,X2) ) )
              & aSet0(X2) )
            | slbdtsldtrb0(X0,X1) != X2 ) )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(rectify,[],[f215]) ).

fof(f217,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( sbrdtbr0(X3) != X1
            | ~ aSubsetOf0(X3,X0)
            | ~ aElementOf0(X3,X2) )
          & ( ( sbrdtbr0(X3) = X1
              & aSubsetOf0(X3,X0) )
            | aElementOf0(X3,X2) ) )
     => ( ( sbrdtbr0(sK14(X0,X1,X2)) != X1
          | ~ aSubsetOf0(sK14(X0,X1,X2),X0)
          | ~ aElementOf0(sK14(X0,X1,X2),X2) )
        & ( ( sbrdtbr0(sK14(X0,X1,X2)) = X1
            & aSubsetOf0(sK14(X0,X1,X2),X0) )
          | aElementOf0(sK14(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f218,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( slbdtsldtrb0(X0,X1) = X2
            | ( ( sbrdtbr0(sK14(X0,X1,X2)) != X1
                | ~ aSubsetOf0(sK14(X0,X1,X2),X0)
                | ~ aElementOf0(sK14(X0,X1,X2),X2) )
              & ( ( sbrdtbr0(sK14(X0,X1,X2)) = X1
                  & aSubsetOf0(sK14(X0,X1,X2),X0) )
                | aElementOf0(sK14(X0,X1,X2),X2) ) )
            | ~ aSet0(X2) )
          & ( ( ! [X4] :
                  ( ( aElementOf0(X4,X2)
                    | sbrdtbr0(X4) != X1
                    | ~ aSubsetOf0(X4,X0) )
                  & ( ( sbrdtbr0(X4) = X1
                      & aSubsetOf0(X4,X0) )
                    | ~ aElementOf0(X4,X2) ) )
              & aSet0(X2) )
            | slbdtsldtrb0(X0,X1) != X2 ) )
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f216,f217]) ).

fof(f227,plain,
    ! [X3,X0,X1] :
      ( aElementOf0(X3,X0)
      | ~ aElementOf0(X3,X1)
      | ~ aSubsetOf0(X1,X0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f174]) ).

fof(f318,plain,
    ! [X2,X0,X1] :
      ( aSet0(X2)
      | slbdtsldtrb0(X0,X1) != X2
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f218]) ).

fof(f319,plain,
    ! [X2,X0,X1,X4] :
      ( aSubsetOf0(X4,X0)
      | ~ aElementOf0(X4,X2)
      | slbdtsldtrb0(X0,X1) != X2
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(cnf_transformation,[],[f218]) ).

fof(f328,plain,
    aElementOf0(xk,szNzAzT0),
    inference(cnf_transformation,[],[f61]) ).

fof(f330,plain,
    aSet0(xT),
    inference(cnf_transformation,[],[f62]) ).

fof(f332,plain,
    aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
    inference(cnf_transformation,[],[f63]) ).

fof(f335,plain,
    aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
    inference(cnf_transformation,[],[f65]) ).

fof(f341,plain,
    aElementOf0(xx,xQ),
    inference(cnf_transformation,[],[f158]) ).

fof(f342,plain,
    ~ aElementOf0(xx,xT),
    inference(cnf_transformation,[],[f158]) ).

fof(f363,plain,
    ! [X0,X1,X4] :
      ( aSubsetOf0(X4,X0)
      | ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(equality_resolution,[],[f319]) ).

fof(f364,plain,
    ! [X0,X1] :
      ( aSet0(slbdtsldtrb0(X0,X1))
      | ~ aElementOf0(X1,szNzAzT0)
      | ~ aSet0(X0) ),
    inference(equality_resolution,[],[f318]) ).

cnf(c_58,plain,
    ( ~ aElementOf0(X0,X1)
    | ~ aSubsetOf0(X1,X2)
    | ~ aSet0(X2)
    | aElementOf0(X0,X2) ),
    inference(cnf_transformation,[],[f227]) ).

cnf(c_153,plain,
    ( ~ aElementOf0(X0,slbdtsldtrb0(X1,X2))
    | ~ aElementOf0(X2,szNzAzT0)
    | ~ aSet0(X1)
    | aSubsetOf0(X0,X1) ),
    inference(cnf_transformation,[],[f363]) ).

cnf(c_154,plain,
    ( ~ aElementOf0(X0,szNzAzT0)
    | ~ aSet0(X1)
    | aSet0(slbdtsldtrb0(X1,X0)) ),
    inference(cnf_transformation,[],[f364]) ).

cnf(c_158,plain,
    aElementOf0(xk,szNzAzT0),
    inference(cnf_transformation,[],[f328]) ).

cnf(c_160,plain,
    aSet0(xT),
    inference(cnf_transformation,[],[f330]) ).

cnf(c_163,plain,
    aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
    inference(cnf_transformation,[],[f332]) ).

cnf(c_165,plain,
    aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
    inference(cnf_transformation,[],[f335]) ).

cnf(c_171,negated_conjecture,
    ~ aElementOf0(xx,xT),
    inference(cnf_transformation,[],[f342]) ).

cnf(c_172,negated_conjecture,
    aElementOf0(xx,xQ),
    inference(cnf_transformation,[],[f341]) ).

cnf(c_11479,plain,
    ( ~ aSubsetOf0(slbdtsldtrb0(xS,xk),X0)
    | ~ aSet0(X0)
    | aElementOf0(xQ,X0) ),
    inference(superposition,[status(thm)],[c_165,c_58]) ).

cnf(c_11789,plain,
    ( ~ aSet0(slbdtsldtrb0(xT,xk))
    | aElementOf0(xQ,slbdtsldtrb0(xT,xk)) ),
    inference(superposition,[status(thm)],[c_163,c_11479]) ).

cnf(c_11925,plain,
    ( ~ aSubsetOf0(slbdtsldtrb0(xS,xk),X0)
    | ~ aSet0(X0)
    | aElementOf0(xQ,X0) ),
    inference(superposition,[status(thm)],[c_165,c_58]) ).

cnf(c_11926,plain,
    ( ~ aSubsetOf0(xQ,X0)
    | ~ aSet0(X0)
    | aElementOf0(xx,X0) ),
    inference(superposition,[status(thm)],[c_172,c_58]) ).

cnf(c_12607,plain,
    ( ~ aSet0(slbdtsldtrb0(xT,xk))
    | aElementOf0(xQ,slbdtsldtrb0(xT,xk)) ),
    inference(superposition,[status(thm)],[c_163,c_11925]) ).

cnf(c_12694,plain,
    ( ~ aSet0(slbdtsldtrb0(xT,xk))
    | ~ aElementOf0(xk,szNzAzT0)
    | ~ aSet0(xT)
    | aSubsetOf0(xQ,xT) ),
    inference(superposition,[status(thm)],[c_11789,c_153]) ).

cnf(c_14395,plain,
    ( ~ aSet0(slbdtsldtrb0(xT,xk))
    | aSubsetOf0(xQ,xT) ),
    inference(global_subsumption_just,[status(thm)],[c_12694,c_160,c_158,c_12694]) ).

cnf(c_14401,plain,
    ( ~ aElementOf0(xk,szNzAzT0)
    | ~ aSet0(xT)
    | aSubsetOf0(xQ,xT) ),
    inference(superposition,[status(thm)],[c_154,c_14395]) ).

cnf(c_14508,plain,
    ( ~ aSet0(slbdtsldtrb0(xT,xk))
    | ~ aElementOf0(xk,szNzAzT0)
    | ~ aSet0(xT)
    | aSubsetOf0(xQ,xT) ),
    inference(superposition,[status(thm)],[c_12607,c_153]) ).

cnf(c_16955,plain,
    aSubsetOf0(xQ,xT),
    inference(global_subsumption_just,[status(thm)],[c_14508,c_160,c_158,c_14401]) ).

cnf(c_16965,plain,
    ( ~ aSet0(xT)
    | aElementOf0(xx,xT) ),
    inference(superposition,[status(thm)],[c_16955,c_11926]) ).

cnf(c_16966,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_16965,c_171,c_160]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM552+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.34  % Computer : n004.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri Aug 25 15:51:23 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.91/1.13  % SZS status Started for theBenchmark.p
% 3.91/1.13  % SZS status Theorem for theBenchmark.p
% 3.91/1.13  
% 3.91/1.13  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.91/1.13  
% 3.91/1.13  ------  iProver source info
% 3.91/1.13  
% 3.91/1.13  git: date: 2023-05-31 18:12:56 +0000
% 3.91/1.13  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.91/1.13  git: non_committed_changes: false
% 3.91/1.13  git: last_make_outside_of_git: false
% 3.91/1.13  
% 3.91/1.13  ------ Parsing...
% 3.91/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.91/1.13  
% 3.91/1.13  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.91/1.13  
% 3.91/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.91/1.13  
% 3.91/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.91/1.13  ------ Proving...
% 3.91/1.13  ------ Problem Properties 
% 3.91/1.13  
% 3.91/1.13  
% 3.91/1.13  clauses                                 122
% 3.91/1.13  conjectures                             2
% 3.91/1.13  EPR                                     40
% 3.91/1.13  Horn                                    92
% 3.91/1.13  unary                                   24
% 3.91/1.13  binary                                  16
% 3.91/1.13  lits                                    392
% 3.91/1.13  lits eq                                 58
% 3.91/1.13  fd_pure                                 0
% 3.91/1.13  fd_pseudo                               0
% 3.91/1.13  fd_cond                                 9
% 3.91/1.13  fd_pseudo_cond                          18
% 3.91/1.13  AC symbols                              0
% 3.91/1.13  
% 3.91/1.13  ------ Input Options Time Limit: Unbounded
% 3.91/1.13  
% 3.91/1.13  
% 3.91/1.13  ------ 
% 3.91/1.13  Current options:
% 3.91/1.13  ------ 
% 3.91/1.13  
% 3.91/1.13  
% 3.91/1.13  
% 3.91/1.13  
% 3.91/1.13  ------ Proving...
% 3.91/1.13  
% 3.91/1.13  
% 3.91/1.13  ------ Proving...
% 3.91/1.13  
% 3.91/1.13  
% 3.91/1.13  ------ Proving...
% 3.91/1.13  
% 3.91/1.13  
% 3.91/1.13  % SZS status Theorem for theBenchmark.p
% 3.91/1.13  
% 3.91/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.91/1.13  
% 3.91/1.13  
%------------------------------------------------------------------------------