%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SYN399+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n009.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 Sep  1 03:06:53 EDT 2023

% Result   : Theorem 0.49s 1.18s
% Output   : CNFRefutation 0.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   20 (   1 unt;   0 def)
%            Number of atoms       :   69 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   78 (  29   ~;  27   |;  13   &)
%                                         (   5 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   2 prp; 0-1 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   24 (   3 sgn;  17   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ( ! [X0] :
        ( f(X0)
      <=> p )
   => ( ! [X1] : f(X1)
    <=> p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish223) ).

fof(f2,negated_conjecture,
    ~ ( ! [X0] :
          ( f(X0)
        <=> p )
     => ( ! [X1] : f(X1)
      <=> p ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f3,plain,
    ( ( ! [X1] : f(X1)
    <~> p )
    & ! [X0] :
        ( f(X0)
      <=> p ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f4,plain,
    ( ( ~ p
      | ? [X1] : ~ f(X1) )
    & ( p
      | ! [X1] : f(X1) )
    & ! [X0] :
        ( ( f(X0)
          | ~ p )
        & ( p
          | ~ f(X0) ) ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f5,plain,
    ( ( ~ p
      | ? [X1] : ~ f(X1) )
    & ( p
      | ! [X1] : f(X1) )
    & ! [X0] :
        ( ( f(X0)
          | ~ p )
        & ( p
          | ~ f(X0) ) ) ),
    inference(flattening,[],[f4]) ).

fof(f6,plain,
    ( ( ~ p
      | ? [X0] : ~ f(X0) )
    & ( p
      | ! [X1] : f(X1) )
    & ! [X2] :
        ( ( f(X2)
          | ~ p )
        & ( p
          | ~ f(X2) ) ) ),
    inference(rectify,[],[f5]) ).

fof(f7,plain,
    ( ? [X0] : ~ f(X0)
   => ~ f(sK0) ),
    introduced(choice_axiom,[]) ).

fof(f8,plain,
    ( ( ~ p
      | ~ f(sK0) )
    & ( p
      | ! [X1] : f(X1) )
    & ! [X2] :
        ( ( f(X2)
          | ~ p )
        & ( p
          | ~ f(X2) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).

fof(f9,plain,
    ! [X2] :
      ( p
      | ~ f(X2) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f10,plain,
    ! [X2] :
      ( f(X2)
      | ~ p ),
    inference(cnf_transformation,[],[f8]) ).

fof(f11,plain,
    ! [X1] :
      ( p
      | f(X1) ),
    inference(cnf_transformation,[],[f8]) ).

fof(f12,plain,
    ( ~ p
    | ~ f(sK0) ),
    inference(cnf_transformation,[],[f8]) ).

cnf(c_49,negated_conjecture,
    ( ~ f(sK0)
    | ~ p ),
    inference(cnf_transformation,[],[f12]) ).

cnf(c_50,negated_conjecture,
    ( f(X0)
    | p ),
    inference(cnf_transformation,[],[f11]) ).

cnf(c_51,negated_conjecture,
    ( ~ p
    | f(X0) ),
    inference(cnf_transformation,[],[f10]) ).

cnf(c_52,negated_conjecture,
    ( ~ f(X0)
    | p ),
    inference(cnf_transformation,[],[f9]) ).

cnf(c_53,plain,
    ( f(sK0)
    | p ),
    inference(instantiation,[status(thm)],[c_50]) ).

cnf(c_54,plain,
    ( ~ f(sK0)
    | p ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_55,plain,
    ( ~ p
    | f(sK0) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_56,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_49,c_55,c_54,c_53]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SYN399+1 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n009.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 : Sat Aug 26 17:20:20 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.45  Running first-order theorem proving
% 0.18/0.45  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.49/1.18  % SZS status Started for theBenchmark.p
% 0.49/1.18  % SZS status Theorem for theBenchmark.p
% 0.49/1.18  
% 0.49/1.18  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.49/1.18  
% 0.49/1.18  ------  iProver source info
% 0.49/1.18  
% 0.49/1.18  git: date: 2023-05-31 18:12:56 +0000
% 0.49/1.18  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.49/1.18  git: non_committed_changes: false
% 0.49/1.18  git: last_make_outside_of_git: false
% 0.49/1.18  
% 0.49/1.18  ------ Parsing...
% 0.49/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...------  preprocesses with Option_epr_non_horn_non_eq
% 0.49/1.18  
% 0.49/1.18  
% 0.49/1.18  ------ Preprocessing...
% 0.49/1.18  
% 0.49/1.18  % SZS status Theorem for theBenchmark.p
% 0.49/1.18  
% 0.49/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.49/1.18  
% 0.49/1.18  
%------------------------------------------------------------------------------