TSTP Solution File: LCL520+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : LCL520+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.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 07:44:52 EDT 2023

% Result   : Theorem 7.71s 1.67s
% Output   : CNFRefutation 7.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  142 (  56 unt;   0 def)
%            Number of atoms       :  257 (  50 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  225 ( 110   ~;  91   |;   2   &)
%                                         (   9 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   13 (  11 usr;  11 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :  176 (   5 sgn;  76   !;   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(f16,axiom,
    ( kn1
  <=> ! [X3] : is_a_theorem(implies(X3,and(X3,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).

fof(f17,axiom,
    ( kn2
  <=> ! [X3,X4] : is_a_theorem(implies(and(X3,X4),X3)) ),
    file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',kn3) ).

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

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

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

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

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

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

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

fof(f41,axiom,
    op_and,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).

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

fof(f43,conjecture,
    r3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).

fof(f44,negated_conjecture,
    ~ r3,
    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(f53,plain,
    ( r3
  <=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(rectify,[],[f24]) ).

fof(f56,plain,
    ~ r3,
    inference(flattening,[],[f44]) ).

fof(f57,plain,
    ( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
   => r3 ),
    inference(unused_predicate_definition_removal,[],[f53]) ).

fof(f58,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(f59,plain,
    ( kn2
   => ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(unused_predicate_definition_removal,[],[f46]) ).

fof(f60,plain,
    ( kn1
   => ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
    inference(unused_predicate_definition_removal,[],[f45]) ).

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

fof(f64,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f63]) ).

fof(f66,plain,
    ( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
    | ~ kn1 ),
    inference(ennf_transformation,[],[f60]) ).

fof(f67,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
    | ~ kn2 ),
    inference(ennf_transformation,[],[f59]) ).

fof(f68,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
    | ~ kn3 ),
    inference(ennf_transformation,[],[f58]) ).

fof(f69,plain,
    ( r3
    | ? [X0,X1] : ~ is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
    inference(ennf_transformation,[],[f57]) ).

fof(f70,plain,
    ( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
    | ~ op_or ),
    inference(ennf_transformation,[],[f27]) ).

fof(f71,plain,
    ( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
    | ~ op_and ),
    inference(ennf_transformation,[],[f28]) ).

fof(f72,plain,
    ( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
    | ~ op_implies_and ),
    inference(ennf_transformation,[],[f29]) ).

fof(f73,plain,
    ( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
    | ~ op_implies_or ),
    inference(ennf_transformation,[],[f30]) ).

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(or(X0,X1),or(X1,X0)))
   => ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ),
    introduced(choice_axiom,[]) ).

fof(f76,plain,
    ( r3
    | ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f69,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,[],[f64]) ).

fof(f79,plain,
    ! [X0] :
      ( is_a_theorem(implies(X0,and(X0,X0)))
      | ~ kn1 ),
    inference(cnf_transformation,[],[f66]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(and(X0,X1),X0))
      | ~ kn2 ),
    inference(cnf_transformation,[],[f67]) ).

fof(f81,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
      | ~ kn3 ),
    inference(cnf_transformation,[],[f68]) ).

fof(f82,plain,
    ( r3
    | ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( or(X0,X1) = not(and(not(X0),not(X1)))
      | ~ op_or ),
    inference(cnf_transformation,[],[f70]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( and(X0,X1) = not(or(not(X0),not(X1)))
      | ~ op_and ),
    inference(cnf_transformation,[],[f71]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = not(and(X0,not(X1)))
      | ~ op_implies_and ),
    inference(cnf_transformation,[],[f72]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( implies(X0,X1) = or(not(X0),X1)
      | ~ op_implies_or ),
    inference(cnf_transformation,[],[f73]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
      | ~ op_equiv ),
    inference(cnf_transformation,[],[f74]) ).

fof(f88,plain,
    op_or,
    inference(cnf_transformation,[],[f32]) ).

fof(f89,plain,
    op_implies_and,
    inference(cnf_transformation,[],[f33]) ).

fof(f91,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f92,plain,
    kn1,
    inference(cnf_transformation,[],[f36]) ).

fof(f93,plain,
    kn2,
    inference(cnf_transformation,[],[f37]) ).

fof(f94,plain,
    kn3,
    inference(cnf_transformation,[],[f38]) ).

fof(f96,plain,
    op_implies_or,
    inference(cnf_transformation,[],[f40]) ).

fof(f97,plain,
    op_and,
    inference(cnf_transformation,[],[f41]) ).

fof(f98,plain,
    op_equiv,
    inference(cnf_transformation,[],[f42]) ).

fof(f99,plain,
    ~ r3,
    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_51,plain,
    ( ~ kn1
    | is_a_theorem(implies(X0,and(X0,X0))) ),
    inference(cnf_transformation,[],[f79]) ).

cnf(c_52,plain,
    ( ~ kn2
    | is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(cnf_transformation,[],[f80]) ).

cnf(c_53,plain,
    ( ~ kn3
    | is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_54,plain,
    ( ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0)))
    | r3 ),
    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_and
    | not(or(not(X0),not(X1))) = and(X0,X1) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_57,plain,
    ( ~ op_implies_and
    | not(and(X0,not(X1))) = implies(X0,X1) ),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_58,plain,
    ( ~ op_implies_or
    | or(not(X0),X1) = implies(X0,X1) ),
    inference(cnf_transformation,[],[f86]) ).

cnf(c_59,plain,
    ( ~ op_equiv
    | and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
    inference(cnf_transformation,[],[f87]) ).

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

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

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

cnf(c_64,plain,
    kn1,
    inference(cnf_transformation,[],[f92]) ).

cnf(c_65,plain,
    kn2,
    inference(cnf_transformation,[],[f93]) ).

cnf(c_66,plain,
    kn3,
    inference(cnf_transformation,[],[f94]) ).

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

cnf(c_69,plain,
    op_and,
    inference(cnf_transformation,[],[f97]) ).

cnf(c_70,plain,
    op_equiv,
    inference(cnf_transformation,[],[f98]) ).

cnf(c_71,negated_conjecture,
    ~ r3,
    inference(cnf_transformation,[],[f99]) ).

cnf(c_72,plain,
    ( ~ kn2
    | is_a_theorem(implies(and(sK0,sK0),sK0)) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_73,plain,
    ( ~ kn1
    | is_a_theorem(implies(sK0,and(sK0,sK0))) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_81,plain,
    is_a_theorem(implies(and(X0,X1),X0)),
    inference(global_subsumption_just,[status(thm)],[c_52,c_65,c_52]) ).

cnf(c_84,plain,
    is_a_theorem(implies(X0,and(X0,X0))),
    inference(global_subsumption_just,[status(thm)],[c_51,c_64,c_51]) ).

cnf(c_87,plain,
    ~ is_a_theorem(implies(or(sK0,sK1),or(sK1,sK0))),
    inference(global_subsumption_just,[status(thm)],[c_54,c_71,c_54]) ).

cnf(c_89,plain,
    or(not(X0),X1) = implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_58,c_68,c_58]) ).

cnf(c_95,plain,
    not(and(X0,not(X1))) = implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_57,c_61,c_57]) ).

cnf(c_98,plain,
    ( ~ is_a_theorem(X0)
    | ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_63,c_49]) ).

cnf(c_99,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | is_a_theorem(X1) ),
    inference(renaming,[status(thm)],[c_98]) ).

cnf(c_100,plain,
    not(or(not(X0),not(X1))) = and(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_56,c_69,c_56]) ).

cnf(c_103,plain,
    not(and(not(X0),not(X1))) = or(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_55,c_60,c_55]) ).

cnf(c_106,plain,
    and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_59,c_70,c_59]) ).

cnf(c_109,plain,
    is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
    inference(global_subsumption_just,[status(thm)],[c_53,c_66,c_53]) ).

cnf(c_206,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_208,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_209,plain,
    ( X0 != X1
    | ~ is_a_theorem(X1)
    | is_a_theorem(X0) ),
    theory(equality) ).

cnf(c_210,plain,
    ( X0 != X1
    | X2 != X3
    | implies(X0,X2) = implies(X1,X3) ),
    theory(equality) ).

cnf(c_381,plain,
    ( implies(or(sK0,sK1),or(sK1,sK0)) != X0
    | ~ is_a_theorem(X0) ),
    inference(resolution,[status(thm)],[c_209,c_87]) ).

cnf(c_392,plain,
    ( ~ is_a_theorem(implies(implies(X0,and(X0,X0)),X1))
    | ~ is_a_theorem(implies(X0,and(X0,X0)))
    | is_a_theorem(X1) ),
    inference(instantiation,[status(thm)],[c_99]) ).

cnf(c_404,plain,
    ( implies(or(sK0,sK1),or(sK1,sK0)) != X0
    | X1 != X0
    | ~ is_a_theorem(X1) ),
    inference(resolution,[status(thm)],[c_381,c_208]) ).

cnf(c_405,plain,
    ( ~ is_a_theorem(X0)
    | is_a_theorem(and(X0,X0)) ),
    inference(superposition,[status(thm)],[c_84,c_99]) ).

cnf(c_406,plain,
    ( ~ is_a_theorem(and(X0,X1))
    | is_a_theorem(X0) ),
    inference(superposition,[status(thm)],[c_81,c_99]) ).

cnf(c_420,plain,
    ( X0 != implies(and(X1,X2),X1)
    | ~ is_a_theorem(implies(and(X1,X2),X1))
    | is_a_theorem(X0) ),
    inference(instantiation,[status(thm)],[c_209]) ).

cnf(c_431,plain,
    not(implies(X0,not(X1))) = and(X0,X1),
    inference(superposition,[status(thm)],[c_89,c_100]) ).

cnf(c_458,plain,
    ( ~ is_a_theorem(implies(implies(X0,and(X0,X0)),implies(not(and(and(X0,X0),X1)),not(and(X1,X0)))))
    | ~ is_a_theorem(implies(X0,and(X0,X0)))
    | is_a_theorem(implies(not(and(and(X0,X0),X1)),not(and(X1,X0)))) ),
    inference(instantiation,[status(thm)],[c_392]) ).

cnf(c_459,plain,
    is_a_theorem(implies(implies(X0,and(X0,X0)),implies(not(and(and(X0,X0),X1)),not(and(X1,X0))))),
    inference(instantiation,[status(thm)],[c_109]) ).

cnf(c_531,plain,
    implies(not(X0),X1) = or(X0,X1),
    inference(superposition,[status(thm)],[c_103,c_95]) ).

cnf(c_570,plain,
    ( not(and(and(X0,X1),not(X0))) != implies(and(X0,X1),X0)
    | ~ is_a_theorem(implies(and(X0,X1),X0))
    | is_a_theorem(not(and(and(X0,X1),not(X0)))) ),
    inference(instantiation,[status(thm)],[c_420]) ).

cnf(c_571,plain,
    not(and(and(X0,X1),not(X0))) = implies(and(X0,X1),X0),
    inference(instantiation,[status(thm)],[c_95]) ).

cnf(c_572,plain,
    ( not(and(and(sK0,sK0),not(sK0))) != implies(and(sK0,sK0),sK0)
    | ~ is_a_theorem(implies(and(sK0,sK0),sK0))
    | is_a_theorem(not(and(and(sK0,sK0),not(sK0)))) ),
    inference(instantiation,[status(thm)],[c_570]) ).

cnf(c_573,plain,
    not(and(and(sK0,sK0),not(sK0))) = implies(and(sK0,sK0),sK0),
    inference(instantiation,[status(thm)],[c_571]) ).

cnf(c_697,plain,
    ( ~ is_a_theorem(implies(X0,X0))
    | is_a_theorem(equiv(X0,X0)) ),
    inference(superposition,[status(thm)],[c_106,c_405]) ).

cnf(c_795,plain,
    not(or(X0,not(X1))) = and(not(X0),X1),
    inference(superposition,[status(thm)],[c_531,c_431]) ).

cnf(c_923,plain,
    ( ~ is_a_theorem(implies(not(and(and(X0,X1),not(X0))),X2))
    | ~ is_a_theorem(not(and(and(X0,X1),not(X0))))
    | is_a_theorem(X2) ),
    inference(instantiation,[status(thm)],[c_99]) ).

cnf(c_971,plain,
    and(not(not(X0)),X1) = and(X0,X1),
    inference(superposition,[status(thm)],[c_795,c_100]) ).

cnf(c_1128,plain,
    ( ~ is_a_theorem(or(X0,not(X0)))
    | is_a_theorem(equiv(not(X0),not(X0))) ),
    inference(superposition,[status(thm)],[c_531,c_697]) ).

cnf(c_1132,plain,
    ( ~ is_a_theorem(or(sK0,not(sK0)))
    | is_a_theorem(equiv(not(sK0),not(sK0))) ),
    inference(instantiation,[status(thm)],[c_1128]) ).

cnf(c_1358,plain,
    ( ~ is_a_theorem(not(not(X0)))
    | is_a_theorem(and(X0,not(not(X0)))) ),
    inference(superposition,[status(thm)],[c_971,c_405]) ).

cnf(c_1454,plain,
    ( X0 != implies(or(sK0,sK1),or(sK1,sK0))
    | ~ is_a_theorem(X0) ),
    inference(resolution,[status(thm)],[c_404,c_206]) ).

cnf(c_1476,plain,
    ( ~ is_a_theorem(implies(not(and(and(X0,X0),not(X0))),not(and(not(X0),X0))))
    | ~ is_a_theorem(not(and(and(X0,X0),not(X0))))
    | is_a_theorem(not(and(not(X0),X0))) ),
    inference(instantiation,[status(thm)],[c_923]) ).

cnf(c_1477,plain,
    ( ~ is_a_theorem(implies(implies(X0,and(X0,X0)),implies(not(and(and(X0,X0),not(X0))),not(and(not(X0),X0)))))
    | ~ is_a_theorem(implies(X0,and(X0,X0)))
    | is_a_theorem(implies(not(and(and(X0,X0),not(X0))),not(and(not(X0),X0)))) ),
    inference(instantiation,[status(thm)],[c_458]) ).

cnf(c_1478,plain,
    ( ~ is_a_theorem(implies(not(and(and(sK0,sK0),not(sK0))),not(and(not(sK0),sK0))))
    | ~ is_a_theorem(not(and(and(sK0,sK0),not(sK0))))
    | is_a_theorem(not(and(not(sK0),sK0))) ),
    inference(instantiation,[status(thm)],[c_1476]) ).

cnf(c_1479,plain,
    ( ~ is_a_theorem(implies(implies(sK0,and(sK0,sK0)),implies(not(and(and(sK0,sK0),not(sK0))),not(and(not(sK0),sK0)))))
    | ~ is_a_theorem(implies(sK0,and(sK0,sK0)))
    | is_a_theorem(implies(not(and(and(sK0,sK0),not(sK0))),not(and(not(sK0),sK0)))) ),
    inference(instantiation,[status(thm)],[c_1477]) ).

cnf(c_1517,plain,
    ( X0 != or(sK0,sK1)
    | X1 != or(sK1,sK0)
    | ~ is_a_theorem(implies(X0,X1)) ),
    inference(resolution,[status(thm)],[c_1454,c_210]) ).

cnf(c_4552,plain,
    is_a_theorem(implies(implies(X0,and(X0,X0)),implies(not(and(and(X0,X0),not(X0))),not(and(not(X0),X0))))),
    inference(instantiation,[status(thm)],[c_459]) ).

cnf(c_4553,plain,
    is_a_theorem(implies(implies(sK0,and(sK0,sK0)),implies(not(and(and(sK0,sK0),not(sK0))),not(and(not(sK0),sK0))))),
    inference(instantiation,[status(thm)],[c_4552]) ).

cnf(c_4725,plain,
    ( X0 != or(sK0,sK1)
    | ~ is_a_theorem(implies(X0,not(and(not(sK1),not(sK0))))) ),
    inference(resolution,[status(thm)],[c_1517,c_103]) ).

cnf(c_5393,plain,
    ~ is_a_theorem(implies(not(and(not(sK0),not(sK1))),not(and(not(sK1),not(sK0))))),
    inference(resolution,[status(thm)],[c_4725,c_103]) ).

cnf(c_5428,plain,
    ( ~ is_a_theorem(implies(X0,implies(not(and(not(sK0),not(sK1))),not(and(not(sK1),not(sK0))))))
    | ~ is_a_theorem(X0) ),
    inference(resolution,[status(thm)],[c_5393,c_99]) ).

cnf(c_6103,plain,
    ~ is_a_theorem(implies(not(sK0),not(sK0))),
    inference(resolution,[status(thm)],[c_5428,c_109]) ).

cnf(c_6159,plain,
    ( ~ is_a_theorem(implies(X0,implies(not(sK0),not(sK0))))
    | ~ is_a_theorem(X0) ),
    inference(resolution,[status(thm)],[c_6103,c_99]) ).

cnf(c_6484,plain,
    ~ is_a_theorem(and(implies(not(sK0),not(sK0)),X0)),
    inference(resolution,[status(thm)],[c_6159,c_81]) ).

cnf(c_6494,plain,
    ( and(implies(not(sK0),not(sK0)),X0) != X1
    | ~ is_a_theorem(X1) ),
    inference(resolution,[status(thm)],[c_6484,c_209]) ).

cnf(c_6739,plain,
    ~ is_a_theorem(equiv(not(sK0),not(sK0))),
    inference(resolution,[status(thm)],[c_6494,c_106]) ).

cnf(c_8968,plain,
    ( ~ is_a_theorem(not(not(X0)))
    | is_a_theorem(X0) ),
    inference(superposition,[status(thm)],[c_1358,c_406]) ).

cnf(c_9028,plain,
    ( ~ is_a_theorem(not(and(not(X0),X1)))
    | is_a_theorem(or(X0,not(X1))) ),
    inference(superposition,[status(thm)],[c_795,c_8968]) ).

cnf(c_9029,plain,
    ( ~ is_a_theorem(not(and(not(sK0),sK0)))
    | is_a_theorem(or(sK0,not(sK0))) ),
    inference(instantiation,[status(thm)],[c_9028]) ).

cnf(c_9030,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_9029,c_6739,c_4553,c_1479,c_1478,c_1132,c_573,c_572,c_73,c_72,c_64,c_65]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL520+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n008.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 06:08:02 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.71/1.67  % SZS status Started for theBenchmark.p
% 7.71/1.67  % SZS status Theorem for theBenchmark.p
% 7.71/1.67  
% 7.71/1.67  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.71/1.67  
% 7.71/1.67  ------  iProver source info
% 7.71/1.67  
% 7.71/1.67  git: date: 2023-05-31 18:12:56 +0000
% 7.71/1.67  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.71/1.67  git: non_committed_changes: false
% 7.71/1.67  git: last_make_outside_of_git: false
% 7.71/1.67  
% 7.71/1.67  ------ Parsing...
% 7.71/1.67  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.71/1.67  
% 7.71/1.67  ------ Preprocessing... sup_sim: 0  sf_s  rm: 12 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 7.71/1.67  
% 7.71/1.67  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.71/1.67  
% 7.71/1.67  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.71/1.67  ------ Proving...
% 7.71/1.67  ------ Problem Properties 
% 7.71/1.67  
% 7.71/1.67  
% 7.71/1.67  clauses                                 11
% 7.71/1.67  conjectures                             0
% 7.71/1.67  EPR                                     0
% 7.71/1.67  Horn                                    11
% 7.71/1.67  unary                                   9
% 7.71/1.67  binary                                  1
% 7.71/1.67  lits                                    14
% 7.71/1.67  lits eq                                 6
% 7.71/1.67  fd_pure                                 0
% 7.71/1.67  fd_pseudo                               0
% 7.71/1.67  fd_cond                                 0
% 7.71/1.67  fd_pseudo_cond                          1
% 7.71/1.67  AC symbols                              0
% 7.71/1.67  
% 7.71/1.67  ------ Input Options Time Limit: Unbounded
% 7.71/1.67  
% 7.71/1.67  
% 7.71/1.67  ------ 
% 7.71/1.67  Current options:
% 7.71/1.67  ------ 
% 7.71/1.67  
% 7.71/1.67  
% 7.71/1.67  
% 7.71/1.67  
% 7.71/1.67  ------ Proving...
% 7.71/1.67  
% 7.71/1.67  
% 7.71/1.67  % SZS status Theorem for theBenchmark.p
% 7.71/1.67  
% 7.71/1.67  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.71/1.67  
% 7.71/1.68  
%------------------------------------------------------------------------------