TSTP Solution File: LCL909+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : LCL909+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n001.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 07:52:57 EDT 2023

% Result   : Satisfiable 1.38s 1.16s
% Output   : Saturation 1.38s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% 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(f22,axiom,
    ( r1
  <=> ! [X3] : is_a_theorem(implies(or(X3,X3),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1) ).

fof(f23,axiom,
    ( r2
  <=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).

fof(f24,axiom,
    ( r3
  <=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3) ).

fof(f25,axiom,
    ( r4
  <=> ! [X3,X4,X5] : is_a_theorem(implies(or(X3,or(X4,X5)),or(X4,or(X3,X5)))) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',r5) ).

fof(f28,axiom,
    ( op_and
   => ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_and) ).

fof(f30,axiom,
    ( op_implies_or
   => ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
    file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',op_equiv) ).

fof(f32,axiom,
    op_implies_or,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).

fof(f33,axiom,
    op_and,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).

fof(f34,axiom,
    op_equiv,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_equiv) ).

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

fof(f36,axiom,
    r1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).

fof(f37,axiom,
    r2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).

fof(f38,axiom,
    r3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).

fof(f39,axiom,
    r4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r4) ).

fof(f40,axiom,
    r5,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r5) ).

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

fof(f48,plain,
    ( r1
  <=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
    inference(rectify,[],[f22]) ).

fof(f49,plain,
    ( r2
  <=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    inference(rectify,[],[f23]) ).

fof(f50,plain,
    ( r3
  <=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(rectify,[],[f24]) ).

fof(f51,plain,
    ( r4
  <=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
    inference(rectify,[],[f25]) ).

fof(f52,plain,
    ( r5
  <=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
    inference(rectify,[],[f26]) ).

fof(f53,plain,
    ( r5
   => ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
    inference(unused_predicate_definition_removal,[],[f52]) ).

fof(f54,plain,
    ( r4
   => ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
    inference(unused_predicate_definition_removal,[],[f51]) ).

fof(f55,plain,
    ( r3
   => ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(unused_predicate_definition_removal,[],[f50]) ).

fof(f56,plain,
    ( r2
   => ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f49]) ).

fof(f57,plain,
    ( r1
   => ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
    inference(unused_predicate_definition_removal,[],[f48]) ).

fof(f58,plain,
    ( substitution_of_equivalents
   => ! [X0,X1] :
        ( is_a_theorem(equiv(X0,X1))
       => X0 = X1 ) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f59,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(f62,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f59]) ).

fof(f63,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f62]) ).

fof(f64,plain,
    ( ! [X0,X1] :
        ( X0 = X1
        | ~ is_a_theorem(equiv(X0,X1)) )
    | ~ substitution_of_equivalents ),
    inference(ennf_transformation,[],[f58]) ).

fof(f65,plain,
    ( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
    | ~ r1 ),
    inference(ennf_transformation,[],[f57]) ).

fof(f66,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
    | ~ r2 ),
    inference(ennf_transformation,[],[f56]) ).

fof(f67,plain,
    ( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
    | ~ r3 ),
    inference(ennf_transformation,[],[f55]) ).

fof(f68,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
    | ~ r4 ),
    inference(ennf_transformation,[],[f54]) ).

fof(f69,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
    | ~ r5 ),
    inference(ennf_transformation,[],[f53]) ).

fof(f70,plain,
    ( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
    | ~ op_and ),
    inference(ennf_transformation,[],[f28]) ).

fof(f71,plain,
    ( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
    | ~ op_implies_or ),
    inference(ennf_transformation,[],[f30]) ).

fof(f72,plain,
    ( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
    | ~ op_equiv ),
    inference(ennf_transformation,[],[f31]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[],[f63]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ is_a_theorem(equiv(X0,X1))
      | ~ substitution_of_equivalents ),
    inference(cnf_transformation,[],[f64]) ).

fof(f75,plain,
    ! [X0] :
      ( is_a_theorem(implies(or(X0,X0),X0))
      | ~ r1 ),
    inference(cnf_transformation,[],[f65]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X1,or(X0,X1)))
      | ~ r2 ),
    inference(cnf_transformation,[],[f66]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
      | ~ r3 ),
    inference(cnf_transformation,[],[f67]) ).

fof(f78,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
      | ~ r4 ),
    inference(cnf_transformation,[],[f68]) ).

fof(f79,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
      | ~ r5 ),
    inference(cnf_transformation,[],[f69]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( and(X0,X1) = not(or(not(X0),not(X1)))
      | ~ op_and ),
    inference(cnf_transformation,[],[f70]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = or(not(X0),X1)
      | ~ op_implies_or ),
    inference(cnf_transformation,[],[f71]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
      | ~ op_equiv ),
    inference(cnf_transformation,[],[f72]) ).

fof(f83,plain,
    op_implies_or,
    inference(cnf_transformation,[],[f32]) ).

fof(f84,plain,
    op_and,
    inference(cnf_transformation,[],[f33]) ).

fof(f85,plain,
    op_equiv,
    inference(cnf_transformation,[],[f34]) ).

fof(f86,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f87,plain,
    r1,
    inference(cnf_transformation,[],[f36]) ).

fof(f88,plain,
    r2,
    inference(cnf_transformation,[],[f37]) ).

fof(f89,plain,
    r3,
    inference(cnf_transformation,[],[f38]) ).

fof(f90,plain,
    r4,
    inference(cnf_transformation,[],[f39]) ).

fof(f91,plain,
    r5,
    inference(cnf_transformation,[],[f40]) ).

fof(f92,plain,
    substitution_of_equivalents,
    inference(cnf_transformation,[],[f41]) ).

cnf(c_49,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | ~ modus_ponens
    | is_a_theorem(X1) ),
    inference(cnf_transformation,[],[f73]) ).

cnf(c_50,plain,
    ( ~ is_a_theorem(equiv(X0,X1))
    | ~ substitution_of_equivalents
    | X0 = X1 ),
    inference(cnf_transformation,[],[f74]) ).

cnf(c_51,plain,
    ( ~ r1
    | is_a_theorem(implies(or(X0,X0),X0)) ),
    inference(cnf_transformation,[],[f75]) ).

cnf(c_52,plain,
    ( ~ r2
    | is_a_theorem(implies(X0,or(X1,X0))) ),
    inference(cnf_transformation,[],[f76]) ).

cnf(c_53,plain,
    ( ~ r3
    | is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(cnf_transformation,[],[f77]) ).

cnf(c_54,plain,
    ( ~ r4
    | is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
    inference(cnf_transformation,[],[f78]) ).

cnf(c_55,plain,
    ( ~ r5
    | is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
    inference(cnf_transformation,[],[f79]) ).

cnf(c_56,plain,
    ( ~ op_and
    | not(or(not(X0),not(X1))) = and(X0,X1) ),
    inference(cnf_transformation,[],[f80]) ).

cnf(c_57,plain,
    ( ~ op_implies_or
    | or(not(X0),X1) = implies(X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_58,plain,
    ( ~ op_equiv
    | and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
    inference(cnf_transformation,[],[f82]) ).

cnf(c_59,plain,
    op_implies_or,
    inference(cnf_transformation,[],[f83]) ).

cnf(c_60,plain,
    op_and,
    inference(cnf_transformation,[],[f84]) ).

cnf(c_61,plain,
    op_equiv,
    inference(cnf_transformation,[],[f85]) ).

cnf(c_62,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f86]) ).

cnf(c_63,plain,
    r1,
    inference(cnf_transformation,[],[f87]) ).

cnf(c_64,plain,
    r2,
    inference(cnf_transformation,[],[f88]) ).

cnf(c_65,plain,
    r3,
    inference(cnf_transformation,[],[f89]) ).

cnf(c_66,plain,
    r4,
    inference(cnf_transformation,[],[f90]) ).

cnf(c_67,plain,
    r5,
    inference(cnf_transformation,[],[f91]) ).

cnf(c_68,plain,
    substitution_of_equivalents,
    inference(cnf_transformation,[],[f92]) ).

cnf(c_78,plain,
    is_a_theorem(implies(X0,or(X1,X0))),
    inference(global_subsumption_just,[status(thm)],[c_52,c_64,c_52]) ).

cnf(c_81,plain,
    is_a_theorem(implies(or(X0,X0),X0)),
    inference(global_subsumption_just,[status(thm)],[c_51,c_63,c_51]) ).

cnf(c_84,plain,
    is_a_theorem(implies(or(X0,X1),or(X1,X0))),
    inference(global_subsumption_just,[status(thm)],[c_53,c_65,c_53]) ).

cnf(c_87,plain,
    or(not(X0),X1) = implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_57,c_59,c_57]) ).

cnf(c_90,plain,
    ( ~ is_a_theorem(equiv(X0,X1))
    | X0 = X1 ),
    inference(global_subsumption_just,[status(thm)],[c_50,c_68,c_50]) ).

cnf(c_93,plain,
    ( ~ is_a_theorem(X0)
    | ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_62,c_49]) ).

cnf(c_94,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | is_a_theorem(X1) ),
    inference(renaming,[status(thm)],[c_93]) ).

cnf(c_95,plain,
    not(or(not(X0),not(X1))) = and(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_56,c_60,c_56]) ).

cnf(c_98,plain,
    and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_58,c_61,c_58]) ).

cnf(c_101,plain,
    is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
    inference(global_subsumption_just,[status(thm)],[c_55,c_67,c_55]) ).

cnf(c_104,plain,
    is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
    inference(global_subsumption_just,[status(thm)],[c_54,c_66,c_54]) ).

cnf(c_161,plain,
    not(implies(X0,not(X1))) = and(X0,X1),
    inference(demodulation,[status(thm)],[c_95,c_87]) ).

cnf(c_162,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_163,plain,
    X0_1 = X0_1,
    theory(equality) ).

cnf(c_164,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_165,plain,
    ( X0 != X1
    | ~ is_a_theorem(X1)
    | is_a_theorem(X0) ),
    theory(equality) ).

cnf(c_166,plain,
    ( X0 != X1
    | X2 != X3
    | implies(X0,X2) = implies(X1,X3) ),
    theory(equality) ).

cnf(c_167,plain,
    ( X0 != X1
    | X2 != X3
    | or(X0,X2) = or(X1,X3) ),
    theory(equality) ).

cnf(c_168,plain,
    ( X0 != X1
    | X2 != X3
    | and(X0,X2) = and(X1,X3) ),
    theory(equality) ).

cnf(c_169,plain,
    ( X0 != X1
    | not(X0) = not(X1) ),
    theory(equality) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL909+1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n001.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 : Fri Aug 25 07:47:13 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.48  Running first-order theorem proving
% 0.19/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.61  WARNING - Could not infer the problem pformat. Setting FOF as default
% 1.38/1.16  % SZS status Started for theBenchmark.p
% 1.38/1.16  % SZS status Satisfiable for theBenchmark.p
% 1.38/1.16  
% 1.38/1.16  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.38/1.16  
% 1.38/1.16  ------  iProver source info
% 1.38/1.16  
% 1.38/1.16  git: date: 2023-05-31 18:12:56 +0000
% 1.38/1.16  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.38/1.16  git: non_committed_changes: false
% 1.38/1.16  git: last_make_outside_of_git: false
% 1.38/1.16  
% 1.38/1.16  ------ Parsing...
% 1.38/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.38/1.16  
% 1.38/1.16  ------ Preprocessing... sup_sim: 1  sf_s  rm: 28 0s  sf_e  pe_s  pe_e  sf_s  rm: 8 0s  sf_e  pe_s  pe_e 
% 1.38/1.16  
% 1.38/1.16  ------ Preprocessing...------  preprocesses with Option_epr_horn
% 1.38/1.16   gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.38/1.16  ------ Proving...
% 1.38/1.16  ------ Problem Properties 
% 1.38/1.16  
% 1.38/1.16  
% 1.38/1.16  clauses                                 0
% 1.38/1.16  conjectures                             0
% 1.38/1.16  EPR                                     0
% 1.38/1.16  Horn                                    0
% 1.38/1.16  unary                                   0
% 1.38/1.16  binary                                  0
% 1.38/1.16  lits                                    0
% 1.38/1.16  lits eq                                 0
% 1.38/1.16  fd_pure                                 0
% 1.38/1.16  fd_pseudo                               0
% 1.38/1.16  fd_cond                                 0
% 1.38/1.16  fd_pseudo_cond                          0
% 1.38/1.16  AC symbols                              0
% 1.38/1.16  
% 1.38/1.16  ------ Schedule EPR Horn non eq is on
% 1.38/1.16  
% 1.38/1.16  ------ no conjectures: strip conj schedule 
% 1.38/1.16  
% 1.38/1.16  ------ no equalities: superposition off 
% 1.38/1.16  
% 1.38/1.16  ------ Option_epr_horn stripped conjectures Time Limit: Unbounded
% 1.38/1.16  
% 1.38/1.16  
% 1.38/1.16  
% 1.38/1.16  
% 1.38/1.16  % SZS status Satisfiable for theBenchmark.p
% 1.38/1.16  
% 1.38/1.16  % SZS output start Saturation for theBenchmark.p
% See solution above
% 1.38/1.16  
% 1.38/1.16  
%------------------------------------------------------------------------------