TSTP Solution File: LCL494+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : LCL494+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 02:38:01 EDT 2024

% Result   : Theorem 3.88s 1.18s
% Output   : CNFRefutation 3.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   94 (  46 unt;   0 def)
%            Number of atoms       :  156 (  28 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  111 (  49   ~;  42   |;   2   &)
%                                         (   6 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   12 (  10 usr;  10 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :  121 (   6 sgn  64   !;   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/sandbox/benchmark/theBenchmark.p',modus_ponens) ).

fof(f14,axiom,
    ( equivalence_2
  <=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_2) ).

fof(f23,axiom,
    ( r2
  <=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).

fof(f24,axiom,
    ( r3
  <=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).

fof(f27,axiom,
    ( op_or
   => ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).

fof(f28,axiom,
    ( op_and
   => ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).

fof(f29,axiom,
    ( op_implies_and
   => ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).

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(f31,axiom,
    ( op_equiv
   => ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).

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

fof(f33,axiom,
    op_and,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).

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

fof(f37,axiom,
    r2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).

fof(f38,axiom,
    r3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).

fof(f42,axiom,
    op_or,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).

fof(f43,axiom,
    op_implies_and,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).

fof(f44,axiom,
    op_equiv,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).

fof(f45,conjecture,
    equivalence_2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).

fof(f46,negated_conjecture,
    ~ equivalence_2,
    inference(negated_conjecture,[],[f45]) ).

fof(f54,plain,
    ( r2
  <=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    inference(rectify,[],[f23]) ).

fof(f55,plain,
    ( r3
  <=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(rectify,[],[f24]) ).

fof(f58,plain,
    ~ equivalence_2,
    inference(flattening,[],[f46]) ).

fof(f61,plain,
    ( r3
   => ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(unused_predicate_definition_removal,[],[f55]) ).

fof(f62,plain,
    ( r2
   => ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f54]) ).

fof(f64,plain,
    ( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
   => equivalence_2 ),
    inference(unused_predicate_definition_removal,[],[f14]) ).

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(f67,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f66]) ).

fof(f68,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f67]) ).

fof(f70,plain,
    ( equivalence_2
    | ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f72,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
    | ~ r2 ),
    inference(ennf_transformation,[],[f62]) ).

fof(f73,plain,
    ( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
    | ~ r3 ),
    inference(ennf_transformation,[],[f61]) ).

fof(f76,plain,
    ( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
    | ~ op_or ),
    inference(ennf_transformation,[],[f27]) ).

fof(f77,plain,
    ( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
    | ~ op_and ),
    inference(ennf_transformation,[],[f28]) ).

fof(f78,plain,
    ( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
    | ~ op_implies_and ),
    inference(ennf_transformation,[],[f29]) ).

fof(f79,plain,
    ( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
    | ~ op_implies_or ),
    inference(ennf_transformation,[],[f30]) ).

fof(f80,plain,
    ( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
    | ~ op_equiv ),
    inference(ennf_transformation,[],[f31]) ).

fof(f81,plain,
    ( ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
   => ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))) ),
    introduced(choice_axiom,[]) ).

fof(f82,plain,
    ( equivalence_2
    | ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f70,f81]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[],[f68]) ).

fof(f85,plain,
    ( equivalence_2
    | ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X1,or(X0,X1)))
      | ~ r2 ),
    inference(cnf_transformation,[],[f72]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
      | ~ r3 ),
    inference(cnf_transformation,[],[f73]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( or(X0,X1) = not(and(not(X0),not(X1)))
      | ~ op_or ),
    inference(cnf_transformation,[],[f76]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( and(X0,X1) = not(or(not(X0),not(X1)))
      | ~ op_and ),
    inference(cnf_transformation,[],[f77]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = not(and(X0,not(X1)))
      | ~ op_implies_and ),
    inference(cnf_transformation,[],[f78]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = or(not(X0),X1)
      | ~ op_implies_or ),
    inference(cnf_transformation,[],[f79]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
      | ~ op_equiv ),
    inference(cnf_transformation,[],[f80]) ).

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

fof(f97,plain,
    op_and,
    inference(cnf_transformation,[],[f33]) ).

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

fof(f101,plain,
    r2,
    inference(cnf_transformation,[],[f37]) ).

fof(f102,plain,
    r3,
    inference(cnf_transformation,[],[f38]) ).

fof(f106,plain,
    op_or,
    inference(cnf_transformation,[],[f42]) ).

fof(f107,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f43]) ).

fof(f108,plain,
    op_equiv,
    inference(cnf_transformation,[],[f44]) ).

fof(f109,plain,
    ~ equivalence_2,
    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,[],[f83]) ).

cnf(c_51,plain,
    ( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0)))
    | equivalence_2 ),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_53,plain,
    ( ~ r2
    | is_a_theorem(implies(X0,or(X1,X0))) ),
    inference(cnf_transformation,[],[f87]) ).

cnf(c_54,plain,
    ( ~ r3
    | is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_57,plain,
    ( ~ op_or
    | not(and(not(X0),not(X1))) = or(X0,X1) ),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_58,plain,
    ( ~ op_and
    | not(or(not(X0),not(X1))) = and(X0,X1) ),
    inference(cnf_transformation,[],[f92]) ).

cnf(c_59,plain,
    ( ~ op_implies_and
    | not(and(X0,not(X1))) = implies(X0,X1) ),
    inference(cnf_transformation,[],[f93]) ).

cnf(c_60,plain,
    ( ~ op_implies_or
    | or(not(X0),X1) = implies(X0,X1) ),
    inference(cnf_transformation,[],[f94]) ).

cnf(c_61,plain,
    ( ~ op_equiv
    | and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_62,plain,
    op_implies_or,
    inference(cnf_transformation,[],[f96]) ).

cnf(c_63,plain,
    op_and,
    inference(cnf_transformation,[],[f97]) ).

cnf(c_65,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f99]) ).

cnf(c_67,plain,
    r2,
    inference(cnf_transformation,[],[f101]) ).

cnf(c_68,plain,
    r3,
    inference(cnf_transformation,[],[f102]) ).

cnf(c_72,plain,
    op_or,
    inference(cnf_transformation,[],[f106]) ).

cnf(c_73,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f107]) ).

cnf(c_74,plain,
    op_equiv,
    inference(cnf_transformation,[],[f108]) ).

cnf(c_75,negated_conjecture,
    ~ equivalence_2,
    inference(cnf_transformation,[],[f109]) ).

cnf(c_87,plain,
    is_a_theorem(implies(X0,or(X1,X0))),
    inference(global_subsumption_just,[status(thm)],[c_53,c_67,c_53]) ).

cnf(c_93,plain,
    is_a_theorem(implies(or(X0,X1),or(X1,X0))),
    inference(global_subsumption_just,[status(thm)],[c_54,c_68,c_54]) ).

cnf(c_96,plain,
    ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))),
    inference(global_subsumption_just,[status(thm)],[c_51,c_75,c_51]) ).

cnf(c_98,plain,
    or(not(X0),X1) = implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_60,c_62,c_60]) ).

cnf(c_104,plain,
    not(and(X0,not(X1))) = implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_59,c_73,c_59]) ).

cnf(c_107,plain,
    ( ~ is_a_theorem(X0)
    | ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_65,c_49]) ).

cnf(c_108,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | is_a_theorem(X1) ),
    inference(renaming,[status(thm)],[c_107]) ).

cnf(c_109,plain,
    not(or(not(X0),not(X1))) = and(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_58,c_63,c_58]) ).

cnf(c_112,plain,
    not(and(not(X0),not(X1))) = or(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_57,c_72,c_57]) ).

cnf(c_115,plain,
    and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_61,c_74,c_61]) ).

cnf(c_190,plain,
    implies(not(X0),X1) = or(X0,X1),
    inference(demodulation,[status(thm)],[c_112,c_104]) ).

cnf(c_191,plain,
    not(implies(X0,not(X1))) = and(X0,X1),
    inference(demodulation,[status(thm)],[c_109,c_98]) ).

cnf(c_420,plain,
    is_a_theorem(implies(X0,implies(X1,X0))),
    inference(superposition,[status(thm)],[c_98,c_87]) ).

cnf(c_439,plain,
    is_a_theorem(or(X0,implies(X1,not(X0)))),
    inference(superposition,[status(thm)],[c_190,c_420]) ).

cnf(c_449,plain,
    or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
    inference(superposition,[status(thm)],[c_191,c_190]) ).

cnf(c_603,plain,
    ( ~ is_a_theorem(or(X0,X1))
    | is_a_theorem(or(X1,X0)) ),
    inference(superposition,[status(thm)],[c_93,c_108]) ).

cnf(c_744,plain,
    is_a_theorem(or(implies(X0,not(X1)),X1)),
    inference(superposition,[status(thm)],[c_439,c_603]) ).

cnf(c_825,plain,
    is_a_theorem(implies(and(X0,X1),X1)),
    inference(demodulation,[status(thm)],[c_744,c_449]) ).

cnf(c_826,plain,
    is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
    inference(superposition,[status(thm)],[c_115,c_825]) ).

cnf(c_830,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_96,c_826]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : LCL494+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.36  % Computer : n018.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Thu May  2 19:25:31 EDT 2024
% 0.13/0.36  % CPUTime  : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  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
% 3.88/1.18  % SZS status Started for theBenchmark.p
% 3.88/1.18  % SZS status Theorem for theBenchmark.p
% 3.88/1.18  
% 3.88/1.18  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.88/1.18  
% 3.88/1.18  ------  iProver source info
% 3.88/1.18  
% 3.88/1.18  git: date: 2024-05-02 19:28:25 +0000
% 3.88/1.18  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.88/1.18  git: non_committed_changes: false
% 3.88/1.18  
% 3.88/1.18  ------ Parsing...
% 3.88/1.18  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.88/1.18  
% 3.88/1.18  ------ Preprocessing... sup_sim: 2  sf_s  rm: 14 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.88/1.18  
% 3.88/1.18  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.88/1.18  
% 3.88/1.18  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.88/1.18  ------ Proving...
% 3.88/1.18  ------ Problem Properties 
% 3.88/1.18  
% 3.88/1.18  
% 3.88/1.18  clauses                                 13
% 3.88/1.18  conjectures                             0
% 3.88/1.18  EPR                                     0
% 3.88/1.18  Horn                                    13
% 3.88/1.18  unary                                   11
% 3.88/1.18  binary                                  1
% 3.88/1.18  lits                                    16
% 3.88/1.18  lits eq                                 6
% 3.88/1.18  fd_pure                                 0
% 3.88/1.18  fd_pseudo                               0
% 3.88/1.18  fd_cond                                 0
% 3.88/1.18  fd_pseudo_cond                          1
% 3.88/1.18  AC symbols                              0
% 3.88/1.18  
% 3.88/1.18  ------ Schedule dynamic 5 is on 
% 3.88/1.18  
% 3.88/1.18  ------ no conjectures: strip conj schedule 
% 3.88/1.18  
% 3.88/1.18  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.88/1.18  
% 3.88/1.18  
% 3.88/1.18  ------ 
% 3.88/1.18  Current options:
% 3.88/1.18  ------ 
% 3.88/1.18  
% 3.88/1.18  
% 3.88/1.18  
% 3.88/1.18  
% 3.88/1.18  ------ Proving...
% 3.88/1.18  
% 3.88/1.18  
% 3.88/1.18  % SZS status Theorem for theBenchmark.p
% 3.88/1.18  
% 3.88/1.18  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.88/1.18  
% 3.88/1.19  
%------------------------------------------------------------------------------