TSTP Solution File: LCL500+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : LCL500+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n025.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   : Theorem 96.48s 13.81s
% Output   : CNFRefutation 96.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   29
% Syntax   : Number of formulae    :  155 (  62 unt;   0 def)
%            Number of atoms       :  276 (  56 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  220 (  99   ~;  92   |;   2   &)
%                                         (  13 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   14 (  12 usr;  12 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  254 (   9 sgn;  95   !;   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/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).

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

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(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(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(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(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(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(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(f42,axiom,
    op_or,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_or) ).

fof(f43,axiom,
    op_implies_and,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_implies_and) ).

fof(f45,conjecture,
    kn2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).

fof(f46,negated_conjecture,
    ~ kn2,
    inference(negated_conjecture,[],[f45]) ).

fof(f48,plain,
    ( kn2
  <=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(rectify,[],[f17]) ).

fof(f53,plain,
    ( r1
  <=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
    inference(rectify,[],[f22]) ).

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(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,
    ~ kn2,
    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(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(f63,plain,
    ( r1
   => ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
    inference(unused_predicate_definition_removal,[],[f53]) ).

fof(f64,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
   => kn2 ),
    inference(unused_predicate_definition_removal,[],[f48]) ).

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,
    ( kn2
    | ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f71,plain,
    ( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
    | ~ r1 ),
    inference(ennf_transformation,[],[f63]) ).

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(f74,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
    | ~ r4 ),
    inference(ennf_transformation,[],[f60]) ).

fof(f75,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
    | ~ r5 ),
    inference(ennf_transformation,[],[f59]) ).

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

fof(f82,plain,
    ( kn2
    | ~ is_a_theorem(implies(and(sK0,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,
    ( kn2
    | ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f86,plain,
    ! [X0] :
      ( is_a_theorem(implies(or(X0,X0),X0))
      | ~ r1 ),
    inference(cnf_transformation,[],[f71]) ).

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(f89,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
      | ~ r4 ),
    inference(cnf_transformation,[],[f74]) ).

fof(f90,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
      | ~ r5 ),
    inference(cnf_transformation,[],[f75]) ).

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(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(f100,plain,
    r1,
    inference(cnf_transformation,[],[f36]) ).

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

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

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

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

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

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

fof(f109,plain,
    ~ kn2,
    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(and(sK0,sK1),sK0))
    | kn2 ),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_52,plain,
    ( ~ r1
    | is_a_theorem(implies(or(X0,X0),X0)) ),
    inference(cnf_transformation,[],[f86]) ).

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_55,plain,
    ( ~ r4
    | is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
    inference(cnf_transformation,[],[f89]) ).

cnf(c_56,plain,
    ( ~ r5
    | is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
    inference(cnf_transformation,[],[f90]) ).

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_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_66,plain,
    r1,
    inference(cnf_transformation,[],[f100]) ).

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

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

cnf(c_69,plain,
    r4,
    inference(cnf_transformation,[],[f103]) ).

cnf(c_70,plain,
    r5,
    inference(cnf_transformation,[],[f104]) ).

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

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

cnf(c_75,negated_conjecture,
    ~ kn2,
    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_90,plain,
    is_a_theorem(implies(or(X0,X0),X0)),
    inference(global_subsumption_just,[status(thm)],[c_52,c_66,c_52]) ).

cnf(c_93,plain,
    ~ is_a_theorem(implies(and(sK0,sK1),sK0)),
    inference(global_subsumption_just,[status(thm)],[c_51,c_75,c_51]) ).

cnf(c_95,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_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_118,plain,
    is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
    inference(global_subsumption_just,[status(thm)],[c_56,c_70,c_56]) ).

cnf(c_121,plain,
    is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
    inference(global_subsumption_just,[status(thm)],[c_55,c_69,c_55]) ).

cnf(c_140,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_142,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_143,plain,
    ( X0 != X1
    | ~ is_a_theorem(X1)
    | is_a_theorem(X0) ),
    theory(equality) ).

cnf(c_144,plain,
    ( X0 != X1
    | X2 != X3
    | implies(X0,X2) = implies(X1,X3) ),
    theory(equality) ).

cnf(c_146,plain,
    ( X0 != X1
    | X2 != X3
    | or(X0,X2) = or(X1,X3) ),
    theory(equality) ).

cnf(c_147,plain,
    ( X0 != X1
    | not(X0) = not(X1) ),
    theory(equality) ).

cnf(c_457,plain,
    ( ~ is_a_theorem(or(X0,X0))
    | is_a_theorem(X0) ),
    inference(resolution,[status(thm)],[c_108,c_90]) ).

cnf(c_461,plain,
    ( ~ is_a_theorem(or(X0,X1))
    | is_a_theorem(or(X1,X0)) ),
    inference(resolution,[status(thm)],[c_108,c_95]) ).

cnf(c_512,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(not(and(X0,not(X1)))) ),
    inference(resolution,[status(thm)],[c_143,c_104]) ).

cnf(c_514,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(or(not(X0),X1)) ),
    inference(resolution,[status(thm)],[c_143,c_98]) ).

cnf(c_565,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(implies(or(X2,X0),or(X2,X1))) ),
    inference(resolution,[status(thm)],[c_118,c_108]) ).

cnf(c_572,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(or(X1,not(X0))) ),
    inference(resolution,[status(thm)],[c_514,c_461]) ).

cnf(c_590,plain,
    ( ~ is_a_theorem(or(X0,or(X1,X2)))
    | is_a_theorem(or(X1,or(X0,X2))) ),
    inference(resolution,[status(thm)],[c_121,c_108]) ).

cnf(c_629,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(or(X2,X0))
    | is_a_theorem(or(X2,X1)) ),
    inference(resolution,[status(thm)],[c_565,c_108]) ).

cnf(c_726,plain,
    ( X0 != X1
    | X1 = X0 ),
    inference(resolution,[status(thm)],[c_142,c_140]) ).

cnf(c_727,plain,
    ( X0 != X1
    | X2 != not(X1)
    | not(X0) = X2 ),
    inference(resolution,[status(thm)],[c_142,c_147]) ).

cnf(c_750,plain,
    ( X0 != X1
    | X2 != X3
    | ~ is_a_theorem(implies(X1,X3))
    | is_a_theorem(implies(X0,X2)) ),
    inference(resolution,[status(thm)],[c_144,c_143]) ).

cnf(c_807,plain,
    ( X0 != X1
    | X2 != X3
    | ~ is_a_theorem(or(X1,X3))
    | is_a_theorem(or(X0,X2)) ),
    inference(resolution,[status(thm)],[c_146,c_143]) ).

cnf(c_858,plain,
    or(X0,X1) = not(and(not(X0),not(X1))),
    inference(resolution,[status(thm)],[c_726,c_112]) ).

cnf(c_860,plain,
    and(X0,X1) = not(or(not(X0),not(X1))),
    inference(resolution,[status(thm)],[c_726,c_109]) ).

cnf(c_864,plain,
    implies(X0,X1) = or(not(X0),X1),
    inference(resolution,[status(thm)],[c_726,c_98]) ).

cnf(c_875,plain,
    ( ~ is_a_theorem(or(not(X0),X1))
    | is_a_theorem(implies(X0,X1)) ),
    inference(resolution,[status(thm)],[c_864,c_143]) ).

cnf(c_941,plain,
    ( ~ is_a_theorem(implies(X0,not(X1)))
    | is_a_theorem(implies(X1,not(X0))) ),
    inference(resolution,[status(thm)],[c_875,c_572]) ).

cnf(c_1233,plain,
    ( ~ is_a_theorem(not(and(not(X0),not(X1))))
    | is_a_theorem(or(X0,X1)) ),
    inference(resolution,[status(thm)],[c_858,c_143]) ).

cnf(c_1396,plain,
    ( X0 != or(not(X1),not(X2))
    | not(X0) = and(X1,X2) ),
    inference(resolution,[status(thm)],[c_727,c_860]) ).

cnf(c_1886,plain,
    ( X0 != or(X1,X2)
    | X3 != or(X2,X1)
    | is_a_theorem(implies(X0,X3)) ),
    inference(resolution,[status(thm)],[c_750,c_95]) ).

cnf(c_2022,plain,
    ( X0 != not(X1)
    | X2 != X3
    | ~ is_a_theorem(implies(X1,X3))
    | is_a_theorem(or(X0,X2)) ),
    inference(resolution,[status(thm)],[c_807,c_514]) ).

cnf(c_3420,plain,
    ( ~ is_a_theorem(implies(not(X0),X1))
    | is_a_theorem(or(X0,X1)) ),
    inference(resolution,[status(thm)],[c_1233,c_512]) ).

cnf(c_3430,plain,
    is_a_theorem(or(X0,or(X1,not(X0)))),
    inference(resolution,[status(thm)],[c_3420,c_87]) ).

cnf(c_3472,plain,
    is_a_theorem(or(X0,or(X1,not(X1)))),
    inference(resolution,[status(thm)],[c_3430,c_590]) ).

cnf(c_3555,plain,
    is_a_theorem(or(X0,not(X0))),
    inference(resolution,[status(thm)],[c_3472,c_457]) ).

cnf(c_3633,plain,
    is_a_theorem(or(not(X0),X0)),
    inference(resolution,[status(thm)],[c_3555,c_461]) ).

cnf(c_3698,plain,
    is_a_theorem(implies(X0,X0)),
    inference(resolution,[status(thm)],[c_3633,c_875]) ).

cnf(c_7809,plain,
    ( X0 != or(X1,not(X2))
    | is_a_theorem(implies(X0,implies(X2,X1))) ),
    inference(resolution,[status(thm)],[c_1886,c_864]) ).

cnf(c_10436,plain,
    ( X0 != X1
    | ~ is_a_theorem(implies(X2,X1))
    | is_a_theorem(or(not(X2),X0)) ),
    inference(resolution,[status(thm)],[c_2022,c_140]) ).

cnf(c_22736,plain,
    ( ~ is_a_theorem(implies(or(X0,not(X1)),X2))
    | is_a_theorem(or(X1,X2)) ),
    inference(resolution,[status(thm)],[c_629,c_3430]) ).

cnf(c_34102,plain,
    is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
    inference(resolution,[status(thm)],[c_7809,c_140]) ).

cnf(c_34316,plain,
    ( ~ is_a_theorem(or(X0,not(X1)))
    | is_a_theorem(implies(X1,X0)) ),
    inference(resolution,[status(thm)],[c_34102,c_108]) ).

cnf(c_41435,plain,
    ( X0 != X1
    | is_a_theorem(or(not(X1),X0)) ),
    inference(resolution,[status(thm)],[c_10436,c_3698]) ).

cnf(c_42377,plain,
    ( X0 != X1
    | is_a_theorem(implies(X1,X0)) ),
    inference(resolution,[status(thm)],[c_41435,c_875]) ).

cnf(c_46207,plain,
    not(implies(X0,not(X1))) = and(X0,X1),
    inference(resolution,[status(thm)],[c_1396,c_864]) ).

cnf(c_50841,plain,
    is_a_theorem(implies(and(X0,X1),not(implies(X0,not(X1))))),
    inference(resolution,[status(thm)],[c_46207,c_42377]) ).

cnf(c_52524,plain,
    is_a_theorem(implies(implies(X0,not(X1)),not(and(X0,X1)))),
    inference(resolution,[status(thm)],[c_50841,c_941]) ).

cnf(c_200827,plain,
    is_a_theorem(or(X0,implies(X0,X1))),
    inference(resolution,[status(thm)],[c_22736,c_34102]) ).

cnf(c_201279,plain,
    ( ~ is_a_theorem(implies(implies(X0,X1),X2))
    | is_a_theorem(or(X0,X2)) ),
    inference(resolution,[status(thm)],[c_200827,c_629]) ).

cnf(c_253755,plain,
    is_a_theorem(or(X0,not(and(X0,X1)))),
    inference(resolution,[status(thm)],[c_201279,c_52524]) ).

cnf(c_255462,plain,
    is_a_theorem(implies(and(X0,X1),X0)),
    inference(resolution,[status(thm)],[c_253755,c_34316]) ).

cnf(c_255652,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_93,c_255462]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL500+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.33  % Computer : n025.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Fri Aug 25 04:59:37 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.46  Running first-order theorem proving
% 0.20/0.46  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 96.48/13.81  % SZS status Started for theBenchmark.p
% 96.48/13.81  % SZS status Theorem for theBenchmark.p
% 96.48/13.81  
% 96.48/13.81  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 96.48/13.81  
% 96.48/13.81  ------  iProver source info
% 96.48/13.81  
% 96.48/13.81  git: date: 2023-05-31 18:12:56 +0000
% 96.48/13.81  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 96.48/13.81  git: non_committed_changes: false
% 96.48/13.81  git: last_make_outside_of_git: false
% 96.48/13.81  
% 96.48/13.81  ------ Parsing...
% 96.48/13.81  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 96.48/13.81  
% 96.48/13.81  ------ Preprocessing... sf_s  rm: 14 0s  sf_e  sf_s  rm: 1 0s  sf_e 
% 96.48/13.81  
% 96.48/13.81  ------ Preprocessing...
% 96.48/13.81  
% 96.48/13.81  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 96.48/13.81  ------ Proving...
% 96.48/13.81  ------ Problem Properties 
% 96.48/13.81  
% 96.48/13.81  
% 96.48/13.81  clauses                                 13
% 96.48/13.81  conjectures                             0
% 96.48/13.81  EPR                                     0
% 96.48/13.81  Horn                                    13
% 96.48/13.81  unary                                   11
% 96.48/13.81  binary                                  1
% 96.48/13.81  lits                                    16
% 96.48/13.81  lits eq                                 6
% 96.48/13.81  fd_pure                                 0
% 96.48/13.81  fd_pseudo                               0
% 96.48/13.81  fd_cond                                 0
% 96.48/13.81  fd_pseudo_cond                          1
% 96.48/13.81  AC symbols                              0
% 96.48/13.81  
% 96.48/13.81  ------ Input Options Time Limit: Unbounded
% 96.48/13.81  
% 96.48/13.81  
% 96.48/13.81  ------ 
% 96.48/13.81  Current options:
% 96.48/13.81  ------ 
% 96.48/13.81  
% 96.48/13.81  
% 96.48/13.81  
% 96.48/13.81  
% 96.48/13.81  ------ Proving...
% 96.48/13.81  
% 96.48/13.81  
% 96.48/13.81  % SZS status Theorem for theBenchmark.p
% 96.48/13.81  
% 96.48/13.81  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 96.48/13.81  
% 96.48/13.82  
%------------------------------------------------------------------------------