TSTP Solution File: LCL502+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : LCL502+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n007.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 07:44:47 EDT 2023

% Result   : CounterSatisfiable 236.68s 31.85s
% Output   : Saturation 236.68s
% 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(f3,axiom,
    ( modus_tollens
  <=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_tollens) ).

fof(f16,axiom,
    ( kn1
  <=> ! [X3] : is_a_theorem(implies(X3,and(X3,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn1) ).

fof(f17,axiom,
    ( kn2
  <=> ! [X3,X4] : is_a_theorem(implies(and(X3,X4),X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn2) ).

fof(f18,axiom,
    ( kn3
  <=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(not(and(X4,X5)),not(and(X5,X3))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn3) ).

fof(f27,axiom,
    ( op_or
   => ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).

fof(f29,axiom,
    ( op_implies_and
   => ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and) ).

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_or,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_or) ).

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

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

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

fof(f36,axiom,
    kn1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn1) ).

fof(f37,axiom,
    kn2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).

fof(f38,axiom,
    kn3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn3) ).

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

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

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

fof(f42,axiom,
    op_equiv,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).

fof(f43,conjecture,
    modus_tollens,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_tollens) ).

fof(f44,negated_conjecture,
    ~ modus_tollens,
    inference(negated_conjecture,[],[f43]) ).

fof(f45,plain,
    ( kn1
  <=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
    inference(rectify,[],[f16]) ).

fof(f46,plain,
    ( kn2
  <=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(rectify,[],[f17]) ).

fof(f47,plain,
    ( kn3
  <=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
    inference(rectify,[],[f18]) ).

fof(f56,plain,
    ~ modus_tollens,
    inference(flattening,[],[f44]) ).

fof(f57,plain,
    ( kn3
   => ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
    inference(unused_predicate_definition_removal,[],[f47]) ).

fof(f58,plain,
    ( kn2
   => ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(unused_predicate_definition_removal,[],[f46]) ).

fof(f59,plain,
    ( kn1
   => ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
    inference(unused_predicate_definition_removal,[],[f45]) ).

fof(f60,plain,
    ( ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
   => modus_tollens ),
    inference(unused_predicate_definition_removal,[],[f3]) ).

fof(f61,plain,
    ( substitution_of_equivalents
   => ! [X0,X1] :
        ( is_a_theorem(equiv(X0,X1))
       => X0 = X1 ) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f62,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(f65,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f62]) ).

fof(f66,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f65]) ).

fof(f67,plain,
    ( ! [X0,X1] :
        ( X0 = X1
        | ~ is_a_theorem(equiv(X0,X1)) )
    | ~ substitution_of_equivalents ),
    inference(ennf_transformation,[],[f61]) ).

fof(f68,plain,
    ( modus_tollens
    | ? [X0,X1] : ~ is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
    inference(ennf_transformation,[],[f60]) ).

fof(f69,plain,
    ( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
    | ~ kn1 ),
    inference(ennf_transformation,[],[f59]) ).

fof(f70,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
    | ~ kn2 ),
    inference(ennf_transformation,[],[f58]) ).

fof(f71,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
    | ~ kn3 ),
    inference(ennf_transformation,[],[f57]) ).

fof(f72,plain,
    ( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
    | ~ op_or ),
    inference(ennf_transformation,[],[f27]) ).

fof(f73,plain,
    ( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
    | ~ op_implies_and ),
    inference(ennf_transformation,[],[f29]) ).

fof(f74,plain,
    ( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
    | ~ op_equiv ),
    inference(ennf_transformation,[],[f31]) ).

fof(f75,plain,
    ( ? [X0,X1] : ~ is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
   => ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
    introduced(choice_axiom,[]) ).

fof(f76,plain,
    ( modus_tollens
    | ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f68,f75]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[],[f66]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ is_a_theorem(equiv(X0,X1))
      | ~ substitution_of_equivalents ),
    inference(cnf_transformation,[],[f67]) ).

fof(f79,plain,
    ( modus_tollens
    | ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f80,plain,
    ! [X0] :
      ( is_a_theorem(implies(X0,and(X0,X0)))
      | ~ kn1 ),
    inference(cnf_transformation,[],[f69]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(and(X0,X1),X0))
      | ~ kn2 ),
    inference(cnf_transformation,[],[f70]) ).

fof(f82,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
      | ~ kn3 ),
    inference(cnf_transformation,[],[f71]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( or(X0,X1) = not(and(not(X0),not(X1)))
      | ~ op_or ),
    inference(cnf_transformation,[],[f72]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = not(and(X0,not(X1)))
      | ~ op_implies_and ),
    inference(cnf_transformation,[],[f73]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
      | ~ op_equiv ),
    inference(cnf_transformation,[],[f74]) ).

fof(f86,plain,
    op_or,
    inference(cnf_transformation,[],[f32]) ).

fof(f87,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f33]) ).

fof(f88,plain,
    op_equiv,
    inference(cnf_transformation,[],[f34]) ).

fof(f89,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f90,plain,
    kn1,
    inference(cnf_transformation,[],[f36]) ).

fof(f91,plain,
    kn2,
    inference(cnf_transformation,[],[f37]) ).

fof(f92,plain,
    kn3,
    inference(cnf_transformation,[],[f38]) ).

fof(f93,plain,
    substitution_of_equivalents,
    inference(cnf_transformation,[],[f39]) ).

fof(f94,plain,
    op_or,
    inference(cnf_transformation,[],[f40]) ).

fof(f95,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f41]) ).

fof(f96,plain,
    op_equiv,
    inference(cnf_transformation,[],[f42]) ).

fof(f97,plain,
    ~ modus_tollens,
    inference(cnf_transformation,[],[f56]) ).

cnf(c_49,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | ~ modus_ponens
    | is_a_theorem(X1) ),
    inference(cnf_transformation,[],[f77]) ).

cnf(c_50,plain,
    ( ~ is_a_theorem(equiv(X0,X1))
    | ~ substitution_of_equivalents
    | X0 = X1 ),
    inference(cnf_transformation,[],[f78]) ).

cnf(c_51,plain,
    ( ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1)))
    | modus_tollens ),
    inference(cnf_transformation,[],[f79]) ).

cnf(c_52,plain,
    ( ~ kn1
    | is_a_theorem(implies(X0,and(X0,X0))) ),
    inference(cnf_transformation,[],[f80]) ).

cnf(c_53,plain,
    ( ~ kn2
    | is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_54,plain,
    ( ~ kn3
    | is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
    inference(cnf_transformation,[],[f82]) ).

cnf(c_55,plain,
    ( ~ op_or
    | not(and(not(X0),not(X1))) = or(X0,X1) ),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_56,plain,
    ( ~ op_implies_and
    | not(and(X0,not(X1))) = implies(X0,X1) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_57,plain,
    ( ~ op_equiv
    | and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_58,plain,
    op_or,
    inference(cnf_transformation,[],[f86]) ).

cnf(c_59,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f87]) ).

cnf(c_60,plain,
    op_equiv,
    inference(cnf_transformation,[],[f88]) ).

cnf(c_61,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f89]) ).

cnf(c_62,plain,
    kn1,
    inference(cnf_transformation,[],[f90]) ).

cnf(c_63,plain,
    kn2,
    inference(cnf_transformation,[],[f91]) ).

cnf(c_64,plain,
    kn3,
    inference(cnf_transformation,[],[f92]) ).

cnf(c_65,plain,
    substitution_of_equivalents,
    inference(cnf_transformation,[],[f93]) ).

cnf(c_66,plain,
    op_or,
    inference(cnf_transformation,[],[f94]) ).

cnf(c_67,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f95]) ).

cnf(c_68,plain,
    op_equiv,
    inference(cnf_transformation,[],[f96]) ).

cnf(c_69,negated_conjecture,
    ~ modus_tollens,
    inference(cnf_transformation,[],[f97]) ).

cnf(c_77,plain,
    is_a_theorem(implies(and(X0,X1),X0)),
    inference(global_subsumption_just,[status(thm)],[c_53,c_63,c_53]) ).

cnf(c_80,plain,
    is_a_theorem(implies(X0,and(X0,X0))),
    inference(global_subsumption_just,[status(thm)],[c_52,c_62,c_52]) ).

cnf(c_83,plain,
    ( ~ is_a_theorem(equiv(X0,X1))
    | X0 = X1 ),
    inference(global_subsumption_just,[status(thm)],[c_50,c_65,c_50]) ).

cnf(c_86,plain,
    not(and(X0,not(X1))) = implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_56,c_67,c_56]) ).

cnf(c_89,plain,
    ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))),
    inference(global_subsumption_just,[status(thm)],[c_51,c_69,c_51]) ).

cnf(c_91,plain,
    ( ~ is_a_theorem(X0)
    | ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_61,c_49]) ).

cnf(c_92,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | is_a_theorem(X1) ),
    inference(renaming,[status(thm)],[c_91]) ).

cnf(c_93,plain,
    not(and(not(X0),not(X1))) = or(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_55,c_66,c_55]) ).

cnf(c_96,plain,
    and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_57,c_68,c_57]) ).

cnf(c_99,plain,
    is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
    inference(global_subsumption_just,[status(thm)],[c_54,c_64,c_54]) ).

cnf(c_144,plain,
    implies(not(X0),X1) = or(X0,X1),
    inference(demodulation,[status(thm)],[c_93,c_86]) ).

cnf(c_145,plain,
    ~ is_a_theorem(implies(or(sK1,not(sK0)),implies(sK0,sK1))),
    inference(demodulation,[status(thm)],[c_89,c_144]) ).

cnf(c_146,plain,
    is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
    inference(demodulation,[status(thm)],[c_99,c_144]) ).

cnf(c_190,plain,
    X0_1 = X0_1,
    theory(equality) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL502+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n007.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 06:08:56 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.21/0.46  Running first-order theorem proving
% 0.21/0.46  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 236.68/31.85  % SZS status Started for theBenchmark.p
% 236.68/31.85  % SZS status CounterSatisfiable for theBenchmark.p
% 236.68/31.85  
% 236.68/31.85  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 236.68/31.85  
% 236.68/31.85  ------  iProver source info
% 236.68/31.85  
% 236.68/31.85  git: date: 2023-05-31 18:12:56 +0000
% 236.68/31.85  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 236.68/31.85  git: non_committed_changes: false
% 236.68/31.85  git: last_make_outside_of_git: false
% 236.68/31.85  
% 236.68/31.85  ------ Parsing...
% 236.68/31.85  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 236.68/31.85  
% 236.68/31.85  ------ Preprocessing... sup_sim: 3  sf_s  rm: 10 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 236.68/31.85  
% 236.68/31.85  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 236.68/31.85  
% 236.68/31.85  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 236.68/31.85  ------ Proving...
% 236.68/31.85  ------ Problem Properties 
% 236.68/31.85  
% 236.68/31.85  
% 236.68/31.85  clauses                                 9
% 236.68/31.85  conjectures                             0
% 236.68/31.85  EPR                                     0
% 236.68/31.85  Horn                                    9
% 236.68/31.85  unary                                   7
% 236.68/31.85  binary                                  1
% 236.68/31.85  lits                                    12
% 236.68/31.85  lits eq                                 4
% 236.68/31.85  fd_pure                                 0
% 236.68/31.85  fd_pseudo                               0
% 236.68/31.85  fd_cond                                 0
% 236.68/31.85  fd_pseudo_cond                          1
% 236.68/31.85  AC symbols                              0
% 236.68/31.85  
% 236.68/31.85  ------ Input Options Time Limit: Unbounded
% 236.68/31.85  
% 236.68/31.85  
% 236.68/31.85  ------ 
% 236.68/31.85  Current options:
% 236.68/31.85  ------ 
% 236.68/31.85  
% 236.68/31.85  
% 236.68/31.85  
% 236.68/31.85  
% 236.68/31.85  ------ Proving...
% 236.68/31.85  
% 236.68/31.85  
% 236.68/31.85  % SZS status CounterSatisfiable for theBenchmark.p
% 236.68/31.85  
% 236.68/31.85  % SZS output start Saturation for theBenchmark.p
% See solution above
% 236.68/31.85  
% 236.68/31.86  
%------------------------------------------------------------------------------