TSTP Solution File: LCL454+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : LCL454+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n011.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 02:37:57 EDT 2024

% Result   : Theorem 1.47s 1.10s
% Output   : CNFRefutation 1.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   57 (  21 unt;   0 def)
%            Number of atoms       :  107 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   90 (  40   ~;  34   |;   2   &)
%                                         (   6 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    7 (   6 usr;   6 prp; 0-1 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   67 (   1 sgn  41   !;   2   ?)

% 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/sandbox/benchmark/theBenchmark.p',modus_ponens) ).

fof(f4,axiom,
    ( implies_1
  <=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_1) ).

fof(f5,axiom,
    ( implies_2
  <=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).

fof(f12,axiom,
    ( or_3
  <=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_3) ).

fof(f22,axiom,
    ( r1
  <=> ! [X3] : is_a_theorem(implies(or(X3,X3),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).

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

fof(f37,axiom,
    implies_1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).

fof(f38,axiom,
    implies_2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).

fof(f45,axiom,
    or_3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_3) ).

fof(f53,conjecture,
    r1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r1) ).

fof(f54,negated_conjecture,
    ~ r1,
    inference(negated_conjecture,[],[f53]) ).

fof(f61,plain,
    ( r1
  <=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
    inference(rectify,[],[f22]) ).

fof(f66,plain,
    ~ r1,
    inference(flattening,[],[f54]) ).

fof(f67,plain,
    ( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
   => r1 ),
    inference(unused_predicate_definition_removal,[],[f61]) ).

fof(f71,plain,
    ( or_3
   => ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
    inference(unused_predicate_definition_removal,[],[f12]) ).

fof(f78,plain,
    ( implies_2
   => ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f5]) ).

fof(f79,plain,
    ( implies_1
   => ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
    inference(unused_predicate_definition_removal,[],[f4]) ).

fof(f82,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(f83,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f82]) ).

fof(f84,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f83]) ).

fof(f87,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0)))
    | ~ implies_1 ),
    inference(ennf_transformation,[],[f79]) ).

fof(f88,plain,
    ( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
    | ~ implies_2 ),
    inference(ennf_transformation,[],[f78]) ).

fof(f95,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
    | ~ or_3 ),
    inference(ennf_transformation,[],[f71]) ).

fof(f99,plain,
    ( r1
    | ? [X0] : ~ is_a_theorem(implies(or(X0,X0),X0)) ),
    inference(ennf_transformation,[],[f67]) ).

fof(f105,plain,
    ( ? [X0] : ~ is_a_theorem(implies(or(X0,X0),X0))
   => ~ is_a_theorem(implies(or(sK0,sK0),sK0)) ),
    introduced(choice_axiom,[]) ).

fof(f106,plain,
    ( r1
    | ~ is_a_theorem(implies(or(sK0,sK0),sK0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f99,f105]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[],[f84]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X0,implies(X1,X0)))
      | ~ implies_1 ),
    inference(cnf_transformation,[],[f87]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
      | ~ implies_2 ),
    inference(cnf_transformation,[],[f88]) ).

fof(f118,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2))))
      | ~ or_3 ),
    inference(cnf_transformation,[],[f95]) ).

fof(f122,plain,
    ( r1
    | ~ is_a_theorem(implies(or(sK0,sK0),sK0)) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f131,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f133,plain,
    implies_1,
    inference(cnf_transformation,[],[f37]) ).

fof(f134,plain,
    implies_2,
    inference(cnf_transformation,[],[f38]) ).

fof(f141,plain,
    or_3,
    inference(cnf_transformation,[],[f45]) ).

fof(f149,plain,
    ~ r1,
    inference(cnf_transformation,[],[f66]) ).

cnf(c_49,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | ~ modus_ponens
    | is_a_theorem(X1) ),
    inference(cnf_transformation,[],[f107]) ).

cnf(c_52,plain,
    ( ~ implies_1
    | is_a_theorem(implies(X0,implies(X1,X0))) ),
    inference(cnf_transformation,[],[f110]) ).

cnf(c_53,plain,
    ( ~ implies_2
    | is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
    inference(cnf_transformation,[],[f111]) ).

cnf(c_60,plain,
    ( ~ or_3
    | is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))) ),
    inference(cnf_transformation,[],[f118]) ).

cnf(c_64,plain,
    ( ~ is_a_theorem(implies(or(sK0,sK0),sK0))
    | r1 ),
    inference(cnf_transformation,[],[f122]) ).

cnf(c_73,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f131]) ).

cnf(c_75,plain,
    implies_1,
    inference(cnf_transformation,[],[f133]) ).

cnf(c_76,plain,
    implies_2,
    inference(cnf_transformation,[],[f134]) ).

cnf(c_83,plain,
    or_3,
    inference(cnf_transformation,[],[f141]) ).

cnf(c_91,negated_conjecture,
    ~ r1,
    inference(cnf_transformation,[],[f149]) ).

cnf(c_96,plain,
    ( ~ implies_1
    | is_a_theorem(implies(sK0,implies(sK0,sK0))) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_143,plain,
    is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
    inference(global_subsumption_just,[status(thm)],[c_53,c_76,c_53]) ).

cnf(c_149,plain,
    ( ~ is_a_theorem(X0)
    | ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_73,c_49]) ).

cnf(c_150,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | is_a_theorem(X1) ),
    inference(renaming,[status(thm)],[c_149]) ).

cnf(c_166,plain,
    is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),
    inference(global_subsumption_just,[status(thm)],[c_60,c_83,c_60]) ).

cnf(c_715,plain,
    ( ~ is_a_theorem(implies(X0,implies(X0,X1)))
    | is_a_theorem(implies(X0,X1)) ),
    inference(superposition,[status(thm)],[c_143,c_150]) ).

cnf(c_778,plain,
    ( ~ is_a_theorem(implies(sK0,implies(sK0,sK0)))
    | is_a_theorem(implies(sK0,sK0)) ),
    inference(instantiation,[status(thm)],[c_715]) ).

cnf(c_2467,plain,
    is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))),
    inference(superposition,[status(thm)],[c_166,c_715]) ).

cnf(c_3307,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(implies(or(X0,X0),X1)) ),
    inference(superposition,[status(thm)],[c_2467,c_150]) ).

cnf(c_3314,plain,
    ( ~ is_a_theorem(implies(sK0,sK0))
    | is_a_theorem(implies(or(sK0,sK0),sK0)) ),
    inference(instantiation,[status(thm)],[c_3307]) ).

cnf(c_3315,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_3314,c_778,c_96,c_64,c_91,c_75]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : LCL454+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.10  % Command  : run_iprover %s %d THM
% 0.10/0.30  % Computer : n011.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Thu May  2 19:14:48 EDT 2024
% 0.10/0.30  % CPUTime  : 
% 0.15/0.40  Running first-order theorem proving
% 0.15/0.40  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
% 1.47/1.10  % SZS status Started for theBenchmark.p
% 1.47/1.10  % SZS status Theorem for theBenchmark.p
% 1.47/1.10  
% 1.47/1.10  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.47/1.10  
% 1.47/1.10  ------  iProver source info
% 1.47/1.10  
% 1.47/1.10  git: date: 2024-05-02 19:28:25 +0000
% 1.47/1.10  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 1.47/1.10  git: non_committed_changes: false
% 1.47/1.10  
% 1.47/1.10  ------ Parsing...
% 1.47/1.10  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.47/1.10  
% 1.47/1.10  ------ Preprocessing... sup_sim: 3  sf_s  rm: 22 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 1.47/1.10  
% 1.47/1.10  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.47/1.10  
% 1.47/1.10  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.47/1.10  ------ Proving...
% 1.47/1.10  ------ Problem Properties 
% 1.47/1.10  
% 1.47/1.10  
% 1.47/1.10  clauses                                 21
% 1.47/1.10  conjectures                             0
% 1.47/1.10  EPR                                     0
% 1.47/1.10  Horn                                    21
% 1.47/1.10  unary                                   19
% 1.47/1.10  binary                                  1
% 1.47/1.10  lits                                    24
% 1.47/1.10  lits eq                                 6
% 1.47/1.10  fd_pure                                 0
% 1.47/1.10  fd_pseudo                               0
% 1.47/1.10  fd_cond                                 0
% 1.47/1.10  fd_pseudo_cond                          1
% 1.47/1.10  AC symbols                              0
% 1.47/1.10  
% 1.47/1.10  ------ Schedule dynamic 5 is on 
% 1.47/1.10  
% 1.47/1.10  ------ no conjectures: strip conj schedule 
% 1.47/1.10  
% 1.47/1.10  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.47/1.10  
% 1.47/1.10  
% 1.47/1.10  ------ 
% 1.47/1.10  Current options:
% 1.47/1.10  ------ 
% 1.47/1.10  
% 1.47/1.10  
% 1.47/1.10  
% 1.47/1.10  
% 1.47/1.10  ------ Proving...
% 1.47/1.10  
% 1.47/1.10  
% 1.47/1.10  % SZS status Theorem for theBenchmark.p
% 1.47/1.10  
% 1.47/1.10  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.47/1.10  
% 1.47/1.11  
%------------------------------------------------------------------------------