TSTP Solution File: LCL539+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : LCL539+1 : TPTP v8.1.2. Released v3.3.0.
% 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 02:38:09 EDT 2024

% Result   : Theorem 13.24s 2.68s
% Output   : CNFRefutation 13.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  104 (  44 unt;   0 def)
%            Number of atoms       :  190 (  26 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  148 (  62   ~;  57   |;   6   &)
%                                         (   7 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   12 (  10 usr;  10 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-2 aty)
%            Number of variables   :  113 (   6 sgn  62   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ( modus_ponens
  <=> ! [X0,X1] :
        ( ( is_a_theorem(implies(X0,X1))
          & is_a_theorem(X0) )
       => is_a_theorem(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).

fof(f2,axiom,
    ( substitution_of_equivalents
  <=> ! [X0,X1] :
        ( is_a_theorem(equiv(X0,X1))
       => X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).

fof(f7,axiom,
    ( and_1
  <=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).

fof(f8,axiom,
    ( and_2
  <=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).

fof(f15,axiom,
    ( equivalence_3
  <=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_3) ).

fof(f35,axiom,
    modus_ponens,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).

fof(f40,axiom,
    and_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).

fof(f41,axiom,
    and_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).

fof(f48,axiom,
    equivalence_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).

fof(f49,axiom,
    substitution_of_equivalents,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).

fof(f53,axiom,
    ( substitution_strict_equiv
  <=> ! [X0,X1] :
        ( is_a_theorem(strict_equiv(X0,X1))
       => X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_strict_equiv) ).

fof(f55,axiom,
    ( axiom_M
  <=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).

fof(f75,axiom,
    ( op_strict_implies
   => ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).

fof(f76,axiom,
    ( op_strict_equiv
   => ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_equiv) ).

fof(f80,axiom,
    axiom_M,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_M) ).

fof(f86,axiom,
    op_strict_implies,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).

fof(f88,axiom,
    op_strict_equiv,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).

fof(f89,conjecture,
    substitution_strict_equiv,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).

fof(f90,negated_conjecture,
    ~ substitution_strict_equiv,
    inference(negated_conjecture,[],[f89]) ).

fof(f105,plain,
    ~ substitution_strict_equiv,
    inference(flattening,[],[f90]) ).

fof(f108,plain,
    ( axiom_M
   => ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
    inference(unused_predicate_definition_removal,[],[f55]) ).

fof(f110,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(strict_equiv(X0,X1))
       => X0 = X1 )
   => substitution_strict_equiv ),
    inference(unused_predicate_definition_removal,[],[f53]) ).

fof(f112,plain,
    ( equivalence_3
   => ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
    inference(unused_predicate_definition_removal,[],[f15]) ).

fof(f119,plain,
    ( and_2
   => ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
    inference(unused_predicate_definition_removal,[],[f8]) ).

fof(f120,plain,
    ( and_1
   => ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(unused_predicate_definition_removal,[],[f7]) ).

fof(f125,plain,
    ( substitution_of_equivalents
   => ! [X0,X1] :
        ( is_a_theorem(equiv(X0,X1))
       => X0 = X1 ) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f126,plain,
    ( modus_ponens
   => ! [X0,X1] :
        ( ( is_a_theorem(implies(X0,X1))
          & is_a_theorem(X0) )
       => is_a_theorem(X1) ) ),
    inference(unused_predicate_definition_removal,[],[f1]) ).

fof(f131,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f126]) ).

fof(f132,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f131]) ).

fof(f133,plain,
    ( ! [X0,X1] :
        ( X0 = X1
        | ~ is_a_theorem(equiv(X0,X1)) )
    | ~ substitution_of_equivalents ),
    inference(ennf_transformation,[],[f125]) ).

fof(f138,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
    | ~ and_1 ),
    inference(ennf_transformation,[],[f120]) ).

fof(f139,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
    | ~ and_2 ),
    inference(ennf_transformation,[],[f119]) ).

fof(f146,plain,
    ( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
    | ~ equivalence_3 ),
    inference(ennf_transformation,[],[f112]) ).

fof(f151,plain,
    ( substitution_strict_equiv
    | ? [X0,X1] :
        ( X0 != X1
        & is_a_theorem(strict_equiv(X0,X1)) ) ),
    inference(ennf_transformation,[],[f110]) ).

fof(f153,plain,
    ( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
    | ~ axiom_M ),
    inference(ennf_transformation,[],[f108]) ).

fof(f157,plain,
    ( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
    | ~ op_strict_implies ),
    inference(ennf_transformation,[],[f75]) ).

fof(f158,plain,
    ( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
    | ~ op_strict_equiv ),
    inference(ennf_transformation,[],[f76]) ).

fof(f159,plain,
    ( ? [X0,X1] :
        ( X0 != X1
        & is_a_theorem(strict_equiv(X0,X1)) )
   => ( sK0 != sK1
      & is_a_theorem(strict_equiv(sK0,sK1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f160,plain,
    ( substitution_strict_equiv
    | ( sK0 != sK1
      & is_a_theorem(strict_equiv(sK0,sK1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f151,f159]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[],[f132]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ is_a_theorem(equiv(X0,X1))
      | ~ substitution_of_equivalents ),
    inference(cnf_transformation,[],[f133]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(and(X0,X1),X0))
      | ~ and_1 ),
    inference(cnf_transformation,[],[f138]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(and(X0,X1),X1))
      | ~ and_2 ),
    inference(cnf_transformation,[],[f139]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
      | ~ equivalence_3 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f182,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f187,plain,
    and_1,
    inference(cnf_transformation,[],[f40]) ).

fof(f188,plain,
    and_2,
    inference(cnf_transformation,[],[f41]) ).

fof(f195,plain,
    equivalence_3,
    inference(cnf_transformation,[],[f48]) ).

fof(f196,plain,
    substitution_of_equivalents,
    inference(cnf_transformation,[],[f49]) ).

fof(f198,plain,
    ( substitution_strict_equiv
    | is_a_theorem(strict_equiv(sK0,sK1)) ),
    inference(cnf_transformation,[],[f160]) ).

fof(f199,plain,
    ( substitution_strict_equiv
    | sK0 != sK1 ),
    inference(cnf_transformation,[],[f160]) ).

fof(f201,plain,
    ! [X0] :
      ( is_a_theorem(implies(necessarily(X0),X0))
      | ~ axiom_M ),
    inference(cnf_transformation,[],[f153]) ).

fof(f205,plain,
    ! [X0,X1] :
      ( strict_implies(X0,X1) = necessarily(implies(X0,X1))
      | ~ op_strict_implies ),
    inference(cnf_transformation,[],[f157]) ).

fof(f206,plain,
    ! [X0,X1] :
      ( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
      | ~ op_strict_equiv ),
    inference(cnf_transformation,[],[f158]) ).

fof(f210,plain,
    axiom_M,
    inference(cnf_transformation,[],[f80]) ).

fof(f215,plain,
    op_strict_implies,
    inference(cnf_transformation,[],[f86]) ).

fof(f217,plain,
    op_strict_equiv,
    inference(cnf_transformation,[],[f88]) ).

fof(f218,plain,
    ~ substitution_strict_equiv,
    inference(cnf_transformation,[],[f105]) ).

cnf(c_49,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | ~ modus_ponens
    | is_a_theorem(X1) ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_50,plain,
    ( ~ is_a_theorem(equiv(X0,X1))
    | ~ substitution_of_equivalents
    | X0 = X1 ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_55,plain,
    ( ~ and_1
    | is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(cnf_transformation,[],[f167]) ).

cnf(c_56,plain,
    ( ~ and_2
    | is_a_theorem(implies(and(X0,X1),X1)) ),
    inference(cnf_transformation,[],[f168]) ).

cnf(c_63,plain,
    ( ~ equivalence_3
    | is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
    inference(cnf_transformation,[],[f175]) ).

cnf(c_70,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f182]) ).

cnf(c_75,plain,
    and_1,
    inference(cnf_transformation,[],[f187]) ).

cnf(c_76,plain,
    and_2,
    inference(cnf_transformation,[],[f188]) ).

cnf(c_83,plain,
    equivalence_3,
    inference(cnf_transformation,[],[f195]) ).

cnf(c_84,plain,
    substitution_of_equivalents,
    inference(cnf_transformation,[],[f196]) ).

cnf(c_86,plain,
    ( sK0 != sK1
    | substitution_strict_equiv ),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_87,plain,
    ( is_a_theorem(strict_equiv(sK0,sK1))
    | substitution_strict_equiv ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_89,plain,
    ( ~ axiom_M
    | is_a_theorem(implies(necessarily(X0),X0)) ),
    inference(cnf_transformation,[],[f201]) ).

cnf(c_93,plain,
    ( ~ op_strict_implies
    | necessarily(implies(X0,X1)) = strict_implies(X0,X1) ),
    inference(cnf_transformation,[],[f205]) ).

cnf(c_94,plain,
    ( ~ op_strict_equiv
    | and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1) ),
    inference(cnf_transformation,[],[f206]) ).

cnf(c_98,plain,
    axiom_M,
    inference(cnf_transformation,[],[f210]) ).

cnf(c_103,plain,
    op_strict_implies,
    inference(cnf_transformation,[],[f215]) ).

cnf(c_105,plain,
    op_strict_equiv,
    inference(cnf_transformation,[],[f217]) ).

cnf(c_106,negated_conjecture,
    ~ substitution_strict_equiv,
    inference(cnf_transformation,[],[f218]) ).

cnf(c_132,plain,
    is_a_theorem(strict_equiv(sK0,sK1)),
    inference(global_subsumption_just,[status(thm)],[c_87,c_106,c_87]) ).

cnf(c_134,plain,
    sK0 != sK1,
    inference(global_subsumption_just,[status(thm)],[c_86,c_106,c_86]) ).

cnf(c_136,plain,
    is_a_theorem(implies(necessarily(X0),X0)),
    inference(global_subsumption_just,[status(thm)],[c_89,c_98,c_89]) ).

cnf(c_150,plain,
    is_a_theorem(implies(and(X0,X1),X1)),
    inference(global_subsumption_just,[status(thm)],[c_56,c_76,c_56]) ).

cnf(c_153,plain,
    is_a_theorem(implies(and(X0,X1),X0)),
    inference(global_subsumption_just,[status(thm)],[c_55,c_75,c_55]) ).

cnf(c_172,plain,
    necessarily(implies(X0,X1)) = strict_implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_93,c_103,c_93]) ).

cnf(c_175,plain,
    ( ~ is_a_theorem(equiv(X0,X1))
    | X0 = X1 ),
    inference(global_subsumption_just,[status(thm)],[c_50,c_84,c_50]) ).

cnf(c_187,plain,
    ( ~ is_a_theorem(X0)
    | ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_70,c_49]) ).

cnf(c_188,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | is_a_theorem(X1) ),
    inference(renaming,[status(thm)],[c_187]) ).

cnf(c_195,plain,
    and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_94,c_105,c_94]) ).

cnf(c_201,plain,
    is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
    inference(global_subsumption_just,[status(thm)],[c_63,c_83,c_63]) ).

cnf(c_2286,plain,
    ( ~ is_a_theorem(and(X0,X1))
    | is_a_theorem(X0) ),
    inference(superposition,[status(thm)],[c_153,c_188]) ).

cnf(c_2287,plain,
    ( ~ is_a_theorem(and(X0,X1))
    | is_a_theorem(X1) ),
    inference(superposition,[status(thm)],[c_150,c_188]) ).

cnf(c_2293,plain,
    ( ~ is_a_theorem(necessarily(X0))
    | is_a_theorem(X0) ),
    inference(superposition,[status(thm)],[c_136,c_188]) ).

cnf(c_2302,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(implies(implies(X1,X0),equiv(X0,X1))) ),
    inference(superposition,[status(thm)],[c_201,c_188]) ).

cnf(c_2308,plain,
    ( ~ is_a_theorem(strict_implies(X0,X1))
    | is_a_theorem(implies(X0,X1)) ),
    inference(superposition,[status(thm)],[c_172,c_2293]) ).

cnf(c_2315,plain,
    ( ~ is_a_theorem(strict_equiv(X0,X1))
    | is_a_theorem(strict_implies(X0,X1)) ),
    inference(superposition,[status(thm)],[c_195,c_2286]) ).

cnf(c_2319,plain,
    ( ~ is_a_theorem(strict_equiv(X0,X1))
    | is_a_theorem(strict_implies(X1,X0)) ),
    inference(superposition,[status(thm)],[c_195,c_2287]) ).

cnf(c_2518,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(implies(X1,X0))
    | is_a_theorem(equiv(X0,X1)) ),
    inference(superposition,[status(thm)],[c_2302,c_188]) ).

cnf(c_2546,plain,
    is_a_theorem(strict_implies(sK0,sK1)),
    inference(superposition,[status(thm)],[c_132,c_2315]) ).

cnf(c_2549,plain,
    is_a_theorem(strict_implies(sK1,sK0)),
    inference(superposition,[status(thm)],[c_132,c_2319]) ).

cnf(c_2693,plain,
    is_a_theorem(implies(sK0,sK1)),
    inference(superposition,[status(thm)],[c_2546,c_2308]) ).

cnf(c_2694,plain,
    is_a_theorem(implies(sK1,sK0)),
    inference(superposition,[status(thm)],[c_2549,c_2308]) ).

cnf(c_8627,plain,
    ( ~ is_a_theorem(implies(sK0,sK1))
    | is_a_theorem(equiv(sK0,sK1)) ),
    inference(superposition,[status(thm)],[c_2694,c_2518]) ).

cnf(c_8649,plain,
    is_a_theorem(equiv(sK0,sK1)),
    inference(forward_subsumption_resolution,[status(thm)],[c_8627,c_2693]) ).

cnf(c_9545,plain,
    sK0 = sK1,
    inference(superposition,[status(thm)],[c_8649,c_175]) ).

cnf(c_9546,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_9545,c_134]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : LCL539+1 : TPTP v8.1.2. Released v3.3.0.
% 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 19:08:14 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  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
% 13.24/2.68  % SZS status Started for theBenchmark.p
% 13.24/2.68  % SZS status Theorem for theBenchmark.p
% 13.24/2.68  
% 13.24/2.68  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 13.24/2.68  
% 13.24/2.68  ------  iProver source info
% 13.24/2.68  
% 13.24/2.68  git: date: 2024-05-02 19:28:25 +0000
% 13.24/2.68  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 13.24/2.68  git: non_committed_changes: false
% 13.24/2.68  
% 13.24/2.68  ------ Parsing...
% 13.24/2.68  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 13.24/2.68  
% 13.24/2.68  ------ Preprocessing... sup_sim: 2  sf_s  rm: 28 0s  sf_e  pe_s  pe_e  sup_sim: 1  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 13.24/2.68  
% 13.24/2.68  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 13.24/2.68  
% 13.24/2.68  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 13.24/2.68  ------ Proving...
% 13.24/2.68  ------ Problem Properties 
% 13.24/2.68  
% 13.24/2.68  
% 13.24/2.68  clauses                                 28
% 13.24/2.68  conjectures                             0
% 13.24/2.68  EPR                                     1
% 13.24/2.68  Horn                                    28
% 13.24/2.68  unary                                   25
% 13.24/2.68  binary                                  2
% 13.24/2.68  lits                                    32
% 13.24/2.68  lits eq                                 8
% 13.24/2.68  fd_pure                                 0
% 13.24/2.68  fd_pseudo                               0
% 13.24/2.68  fd_cond                                 0
% 13.24/2.68  fd_pseudo_cond                          1
% 13.24/2.68  AC symbols                              0
% 13.24/2.68  
% 13.24/2.68  ------ Input Options Time Limit: Unbounded
% 13.24/2.68  
% 13.24/2.68  
% 13.24/2.68  ------ 
% 13.24/2.68  Current options:
% 13.24/2.68  ------ 
% 13.24/2.68  
% 13.24/2.68  
% 13.24/2.68  
% 13.24/2.68  
% 13.24/2.68  ------ Proving...
% 13.24/2.68  
% 13.24/2.68  
% 13.24/2.68  % SZS status Theorem for theBenchmark.p
% 13.24/2.68  
% 13.24/2.68  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 13.24/2.68  
% 13.24/2.68  
%------------------------------------------------------------------------------