TSTP Solution File: LCL496+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : LCL496+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n003.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 07:44:45 EDT 2023

% Result   : Theorem 30.36s 5.23s
% Output   : CNFRefutation 30.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   62 (  29 unt;   0 def)
%            Number of atoms       :  109 (   5 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   84 (  37   ~;  30   |;   2   &)
%                                         (   7 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    8 (   6 usr;   6 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  107 (   0 sgn;  55   !;   6   ?)

% 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(f19,axiom,
    ( cn1
  <=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn1) ).

fof(f25,axiom,
    ( r4
  <=> ! [X3,X4,X5] : is_a_theorem(implies(or(X3,or(X4,X5)),or(X4,or(X3,X5)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).

fof(f26,axiom,
    ( r5
  <=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X4,X5),implies(or(X3,X4),or(X3,X5)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).

fof(f30,axiom,
    ( op_implies_or
   => ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).

fof(f32,axiom,
    op_implies_or,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).

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

fof(f39,axiom,
    r4,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r4) ).

fof(f40,axiom,
    r5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r5) ).

fof(f45,conjecture,
    cn1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn1) ).

fof(f46,negated_conjecture,
    ~ cn1,
    inference(negated_conjecture,[],[f45]) ).

fof(f50,plain,
    ( cn1
  <=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
    inference(rectify,[],[f19]) ).

fof(f56,plain,
    ( r4
  <=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
    inference(rectify,[],[f25]) ).

fof(f57,plain,
    ( r5
  <=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
    inference(rectify,[],[f26]) ).

fof(f58,plain,
    ~ cn1,
    inference(flattening,[],[f46]) ).

fof(f59,plain,
    ( r5
   => ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
    inference(unused_predicate_definition_removal,[],[f57]) ).

fof(f60,plain,
    ( r4
   => ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
    inference(unused_predicate_definition_removal,[],[f56]) ).

fof(f64,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
   => cn1 ),
    inference(unused_predicate_definition_removal,[],[f50]) ).

fof(f66,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(f69,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f66]) ).

fof(f70,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f69]) ).

fof(f72,plain,
    ( cn1
    | ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f76,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
    | ~ r4 ),
    inference(ennf_transformation,[],[f60]) ).

fof(f77,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
    | ~ r5 ),
    inference(ennf_transformation,[],[f59]) ).

fof(f80,plain,
    ( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
    | ~ op_implies_or ),
    inference(ennf_transformation,[],[f30]) ).

fof(f82,plain,
    ( ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
   => ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
    introduced(choice_axiom,[]) ).

fof(f83,plain,
    ( cn1
    | ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f72,f82]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[],[f70]) ).

fof(f86,plain,
    ( cn1
    | ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f90,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
      | ~ r4 ),
    inference(cnf_transformation,[],[f76]) ).

fof(f91,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
      | ~ r5 ),
    inference(cnf_transformation,[],[f77]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = or(not(X0),X1)
      | ~ op_implies_or ),
    inference(cnf_transformation,[],[f80]) ).

fof(f96,plain,
    op_implies_or,
    inference(cnf_transformation,[],[f32]) ).

fof(f99,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f103,plain,
    r4,
    inference(cnf_transformation,[],[f39]) ).

fof(f104,plain,
    r5,
    inference(cnf_transformation,[],[f40]) ).

fof(f108,plain,
    ~ cn1,
    inference(cnf_transformation,[],[f58]) ).

cnf(c_49,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | ~ modus_ponens
    | is_a_theorem(X1) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_51,plain,
    ( ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
    | cn1 ),
    inference(cnf_transformation,[],[f86]) ).

cnf(c_55,plain,
    ( ~ r4
    | is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
    inference(cnf_transformation,[],[f90]) ).

cnf(c_56,plain,
    ( ~ r5
    | is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_59,plain,
    ( ~ op_implies_or
    | or(not(X0),X1) = implies(X0,X1) ),
    inference(cnf_transformation,[],[f94]) ).

cnf(c_61,plain,
    op_implies_or,
    inference(cnf_transformation,[],[f96]) ).

cnf(c_64,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f99]) ).

cnf(c_68,plain,
    r4,
    inference(cnf_transformation,[],[f103]) ).

cnf(c_69,plain,
    r5,
    inference(cnf_transformation,[],[f104]) ).

cnf(c_73,negated_conjecture,
    ~ cn1,
    inference(cnf_transformation,[],[f108]) ).

cnf(c_93,plain,
    or(not(X0),X1) = implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_59,c_61,c_59]) ).

cnf(c_99,plain,
    ( ~ is_a_theorem(X0)
    | ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_64,c_49]) ).

cnf(c_100,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | is_a_theorem(X1) ),
    inference(renaming,[status(thm)],[c_99]) ).

cnf(c_110,plain,
    is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
    inference(global_subsumption_just,[status(thm)],[c_56,c_69,c_56]) ).

cnf(c_113,plain,
    is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
    inference(global_subsumption_just,[status(thm)],[c_55,c_68,c_55]) ).

cnf(c_116,plain,
    ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))),
    inference(global_subsumption_just,[status(thm)],[c_51,c_73,c_51]) ).

cnf(c_1246,plain,
    is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
    inference(superposition,[status(thm)],[c_93,c_110]) ).

cnf(c_1327,plain,
    is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))),
    inference(superposition,[status(thm)],[c_93,c_113]) ).

cnf(c_1732,plain,
    is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))),
    inference(demodulation,[status(thm)],[c_1327,c_93]) ).

cnf(c_1734,plain,
    is_a_theorem(implies(implies(X0,implies(X1,X2)),or(not(X1),implies(X0,X2)))),
    inference(superposition,[status(thm)],[c_93,c_1732]) ).

cnf(c_5618,plain,
    is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
    inference(demodulation,[status(thm)],[c_1246,c_93]) ).

cnf(c_5945,plain,
    is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))),
    inference(demodulation,[status(thm)],[c_1734,c_93]) ).

cnf(c_5953,plain,
    ( ~ is_a_theorem(implies(X0,implies(X1,X2)))
    | is_a_theorem(implies(X1,implies(X0,X2))) ),
    inference(superposition,[status(thm)],[c_5945,c_100]) ).

cnf(c_6684,plain,
    is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
    inference(superposition,[status(thm)],[c_5618,c_5953]) ).

cnf(c_6697,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_116,c_6684]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL496+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug 24 17:45:38 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.18/0.47  Running first-order theorem proving
% 0.18/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 30.36/5.23  % SZS status Started for theBenchmark.p
% 30.36/5.23  % SZS status Theorem for theBenchmark.p
% 30.36/5.23  
% 30.36/5.23  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 30.36/5.23  
% 30.36/5.23  ------  iProver source info
% 30.36/5.23  
% 30.36/5.23  git: date: 2023-05-31 18:12:56 +0000
% 30.36/5.23  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 30.36/5.23  git: non_committed_changes: false
% 30.36/5.23  git: last_make_outside_of_git: false
% 30.36/5.23  
% 30.36/5.23  ------ Parsing...
% 30.36/5.23  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 30.36/5.23  
% 30.36/5.23  ------ Preprocessing... sup_sim: 1  sf_s  rm: 13 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 30.36/5.23  
% 30.36/5.23  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 30.36/5.23  
% 30.36/5.23  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 30.36/5.23  ------ Proving...
% 30.36/5.23  ------ Problem Properties 
% 30.36/5.23  
% 30.36/5.23  
% 30.36/5.23  clauses                                 12
% 30.36/5.23  conjectures                             0
% 30.36/5.23  EPR                                     0
% 30.36/5.23  Horn                                    12
% 30.36/5.23  unary                                   10
% 30.36/5.23  binary                                  1
% 30.36/5.23  lits                                    15
% 30.36/5.23  lits eq                                 5
% 30.36/5.23  fd_pure                                 0
% 30.36/5.23  fd_pseudo                               0
% 30.36/5.23  fd_cond                                 0
% 30.36/5.23  fd_pseudo_cond                          1
% 30.36/5.23  AC symbols                              0
% 30.36/5.23  
% 30.36/5.23  ------ Input Options Time Limit: Unbounded
% 30.36/5.23  
% 30.36/5.23  
% 30.36/5.23  ------ 
% 30.36/5.23  Current options:
% 30.36/5.23  ------ 
% 30.36/5.23  
% 30.36/5.23  
% 30.36/5.23  
% 30.36/5.23  
% 30.36/5.23  ------ Proving...
% 30.36/5.23  
% 30.36/5.23  
% 30.36/5.23  % SZS status Theorem for theBenchmark.p
% 30.36/5.23  
% 30.36/5.23  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 30.36/5.23  
% 30.36/5.24  
%------------------------------------------------------------------------------