TSTP Solution File: LCL528+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : LCL528+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n011.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 02:38:07 EDT 2024

% Result   : Theorem 142.40s 19.85s
% Output   : CNFRefutation 142.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  116 (  44 unt;   0 def)
%            Number of atoms       :  216 (  13 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  184 (  84   ~;  76   |;   2   &)
%                                         (   8 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   12 (  10 usr;  10 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :  140 (   5 sgn  68   !;   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(f5,axiom,
    ( implies_2
  <=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).

fof(f6,axiom,
    ( implies_3
  <=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_3) ).

fof(f7,axiom,
    ( and_1
  <=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).

fof(f8,axiom,
    ( and_2
  <=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).

fof(f9,axiom,
    ( and_3
  <=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).

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

fof(f38,axiom,
    implies_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).

fof(f39,axiom,
    implies_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_3) ).

fof(f40,axiom,
    and_1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).

fof(f41,axiom,
    and_2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).

fof(f42,axiom,
    and_3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).

fof(f50,axiom,
    ( necessitation
  <=> ! [X0] :
        ( is_a_theorem(X0)
       => is_a_theorem(necessarily(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation) ).

fof(f63,axiom,
    ( axiom_m1
  <=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m1) ).

fof(f75,axiom,
    ( op_strict_implies
   => ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).

fof(f78,axiom,
    necessitation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_necessitation) ).

fof(f85,axiom,
    op_strict_implies,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).

fof(f88,conjecture,
    axiom_m1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m1) ).

fof(f89,negated_conjecture,
    ~ axiom_m1,
    inference(negated_conjecture,[],[f88]) ).

fof(f104,plain,
    ~ axiom_m1,
    inference(flattening,[],[f89]) ).

fof(f105,plain,
    ( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
   => axiom_m1 ),
    inference(unused_predicate_definition_removal,[],[f63]) ).

fof(f109,plain,
    ( necessitation
   => ! [X0] :
        ( is_a_theorem(X0)
       => is_a_theorem(necessarily(X0)) ) ),
    inference(unused_predicate_definition_removal,[],[f50]) ).

fof(f116,plain,
    ( and_3
   => ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
    inference(unused_predicate_definition_removal,[],[f9]) ).

fof(f117,plain,
    ( and_2
   => ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
    inference(unused_predicate_definition_removal,[],[f8]) ).

fof(f118,plain,
    ( and_1
   => ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(unused_predicate_definition_removal,[],[f7]) ).

fof(f119,plain,
    ( implies_3
   => ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
    inference(unused_predicate_definition_removal,[],[f6]) ).

fof(f120,plain,
    ( implies_2
   => ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
    inference(unused_predicate_definition_removal,[],[f5]) ).

fof(f124,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(f129,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(ennf_transformation,[],[f124]) ).

fof(f130,plain,
    ( ! [X0,X1] :
        ( is_a_theorem(X1)
        | ~ is_a_theorem(implies(X0,X1))
        | ~ is_a_theorem(X0) )
    | ~ modus_ponens ),
    inference(flattening,[],[f129]) ).

fof(f134,plain,
    ( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
    | ~ implies_2 ),
    inference(ennf_transformation,[],[f120]) ).

fof(f135,plain,
    ( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
    | ~ implies_3 ),
    inference(ennf_transformation,[],[f119]) ).

fof(f136,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
    | ~ and_1 ),
    inference(ennf_transformation,[],[f118]) ).

fof(f137,plain,
    ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
    | ~ and_2 ),
    inference(ennf_transformation,[],[f117]) ).

fof(f138,plain,
    ( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
    | ~ and_3 ),
    inference(ennf_transformation,[],[f116]) ).

fof(f148,plain,
    ( ! [X0] :
        ( is_a_theorem(necessarily(X0))
        | ~ is_a_theorem(X0) )
    | ~ necessitation ),
    inference(ennf_transformation,[],[f109]) ).

fof(f152,plain,
    ( axiom_m1
    | ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
    inference(ennf_transformation,[],[f105]) ).

fof(f154,plain,
    ( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
    | ~ op_strict_implies ),
    inference(ennf_transformation,[],[f75]) ).

fof(f156,plain,
    ( ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
   => ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
    introduced(choice_axiom,[]) ).

fof(f157,plain,
    ( axiom_m1
    | ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f152,f156]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( is_a_theorem(X1)
      | ~ is_a_theorem(implies(X0,X1))
      | ~ is_a_theorem(X0)
      | ~ modus_ponens ),
    inference(cnf_transformation,[],[f130]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
      | ~ implies_2 ),
    inference(cnf_transformation,[],[f134]) ).

fof(f163,plain,
    ! [X2,X0,X1] :
      ( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
      | ~ implies_3 ),
    inference(cnf_transformation,[],[f135]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(and(X0,X1),X0))
      | ~ and_1 ),
    inference(cnf_transformation,[],[f136]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(and(X0,X1),X1))
      | ~ and_2 ),
    inference(cnf_transformation,[],[f137]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
      | ~ and_3 ),
    inference(cnf_transformation,[],[f138]) ).

fof(f179,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f35]) ).

fof(f182,plain,
    implies_2,
    inference(cnf_transformation,[],[f38]) ).

fof(f183,plain,
    implies_3,
    inference(cnf_transformation,[],[f39]) ).

fof(f184,plain,
    and_1,
    inference(cnf_transformation,[],[f40]) ).

fof(f185,plain,
    and_2,
    inference(cnf_transformation,[],[f41]) ).

fof(f186,plain,
    and_3,
    inference(cnf_transformation,[],[f42]) ).

fof(f194,plain,
    ! [X0] :
      ( is_a_theorem(necessarily(X0))
      | ~ is_a_theorem(X0)
      | ~ necessitation ),
    inference(cnf_transformation,[],[f148]) ).

fof(f198,plain,
    ( axiom_m1
    | ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))) ),
    inference(cnf_transformation,[],[f157]) ).

fof(f200,plain,
    ! [X0,X1] :
      ( strict_implies(X0,X1) = necessarily(implies(X0,X1))
      | ~ op_strict_implies ),
    inference(cnf_transformation,[],[f154]) ).

fof(f203,plain,
    necessitation,
    inference(cnf_transformation,[],[f78]) ).

fof(f209,plain,
    op_strict_implies,
    inference(cnf_transformation,[],[f85]) ).

fof(f212,plain,
    ~ axiom_m1,
    inference(cnf_transformation,[],[f104]) ).

cnf(c_49,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | ~ modus_ponens
    | is_a_theorem(X1) ),
    inference(cnf_transformation,[],[f158]) ).

cnf(c_53,plain,
    ( ~ implies_2
    | is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_54,plain,
    ( ~ implies_3
    | is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
    inference(cnf_transformation,[],[f163]) ).

cnf(c_55,plain,
    ( ~ and_1
    | is_a_theorem(implies(and(X0,X1),X0)) ),
    inference(cnf_transformation,[],[f164]) ).

cnf(c_56,plain,
    ( ~ and_2
    | is_a_theorem(implies(and(X0,X1),X1)) ),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_57,plain,
    ( ~ and_3
    | is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
    inference(cnf_transformation,[],[f166]) ).

cnf(c_70,plain,
    modus_ponens,
    inference(cnf_transformation,[],[f179]) ).

cnf(c_73,plain,
    implies_2,
    inference(cnf_transformation,[],[f182]) ).

cnf(c_74,plain,
    implies_3,
    inference(cnf_transformation,[],[f183]) ).

cnf(c_75,plain,
    and_1,
    inference(cnf_transformation,[],[f184]) ).

cnf(c_76,plain,
    and_2,
    inference(cnf_transformation,[],[f185]) ).

cnf(c_77,plain,
    and_3,
    inference(cnf_transformation,[],[f186]) ).

cnf(c_85,plain,
    ( ~ is_a_theorem(X0)
    | ~ necessitation
    | is_a_theorem(necessarily(X0)) ),
    inference(cnf_transformation,[],[f194]) ).

cnf(c_89,plain,
    ( ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0)))
    | axiom_m1 ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_91,plain,
    ( ~ op_strict_implies
    | necessarily(implies(X0,X1)) = strict_implies(X0,X1) ),
    inference(cnf_transformation,[],[f200]) ).

cnf(c_94,plain,
    necessitation,
    inference(cnf_transformation,[],[f203]) ).

cnf(c_100,plain,
    op_strict_implies,
    inference(cnf_transformation,[],[f209]) ).

cnf(c_103,negated_conjecture,
    ~ axiom_m1,
    inference(cnf_transformation,[],[f212]) ).

cnf(c_131,plain,
    ( ~ is_a_theorem(X0)
    | is_a_theorem(necessarily(X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_85,c_94,c_85]) ).

cnf(c_139,plain,
    is_a_theorem(implies(and(X0,X1),X1)),
    inference(global_subsumption_just,[status(thm)],[c_56,c_76,c_56]) ).

cnf(c_142,plain,
    is_a_theorem(implies(and(X0,X1),X0)),
    inference(global_subsumption_just,[status(thm)],[c_55,c_75,c_55]) ).

cnf(c_153,plain,
    ~ is_a_theorem(strict_implies(and(sK0,sK1),and(sK1,sK0))),
    inference(global_subsumption_just,[status(thm)],[c_89,c_103,c_89]) ).

cnf(c_160,plain,
    is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
    inference(global_subsumption_just,[status(thm)],[c_57,c_77,c_57]) ).

cnf(c_163,plain,
    necessarily(implies(X0,X1)) = strict_implies(X0,X1),
    inference(global_subsumption_just,[status(thm)],[c_91,c_100,c_91]) ).

cnf(c_172,plain,
    is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
    inference(global_subsumption_just,[status(thm)],[c_53,c_73,c_53]) ).

cnf(c_178,plain,
    ( ~ is_a_theorem(X0)
    | ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_49,c_70,c_49]) ).

cnf(c_179,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | ~ is_a_theorem(X0)
    | is_a_theorem(X1) ),
    inference(renaming,[status(thm)],[c_178]) ).

cnf(c_195,plain,
    is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
    inference(global_subsumption_just,[status(thm)],[c_54,c_74,c_54]) ).

cnf(c_423,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_425,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_426,plain,
    ( X0 != X1
    | ~ is_a_theorem(X1)
    | is_a_theorem(X0) ),
    theory(equality) ).

cnf(c_1649,plain,
    ( X0 != X1
    | X1 = X0 ),
    inference(resolution,[status(thm)],[c_425,c_423]) ).

cnf(c_1660,plain,
    ( ~ is_a_theorem(implies(X0,implies(X0,X1)))
    | is_a_theorem(implies(X0,X1)) ),
    inference(superposition,[status(thm)],[c_172,c_179]) ).

cnf(c_1661,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(implies(implies(X1,X2),implies(X0,X2))) ),
    inference(superposition,[status(thm)],[c_195,c_179]) ).

cnf(c_1792,plain,
    strict_implies(X0,X1) = necessarily(implies(X0,X1)),
    inference(resolution,[status(thm)],[c_1649,c_163]) ).

cnf(c_2027,plain,
    ( ~ is_a_theorem(necessarily(implies(X0,X1)))
    | is_a_theorem(strict_implies(X0,X1)) ),
    inference(resolution,[status(thm)],[c_1792,c_426]) ).

cnf(c_2233,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(strict_implies(X0,X1)) ),
    inference(resolution,[status(thm)],[c_2027,c_131]) ).

cnf(c_2293,plain,
    ~ is_a_theorem(implies(and(sK0,sK1),and(sK1,sK0))),
    inference(resolution,[status(thm)],[c_153,c_2233]) ).

cnf(c_147205,plain,
    ( ~ is_a_theorem(implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0))))
    | is_a_theorem(implies(and(sK0,sK1),and(sK1,sK0))) ),
    inference(instantiation,[status(thm)],[c_1660]) ).

cnf(c_149517,plain,
    ( ~ is_a_theorem(implies(X0,implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0)))))
    | ~ is_a_theorem(X0)
    | is_a_theorem(implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0)))) ),
    inference(instantiation,[status(thm)],[c_179]) ).

cnf(c_149753,plain,
    ( ~ is_a_theorem(implies(X0,implies(X1,implies(and(sK0,sK1),and(sK1,sK0)))))
    | ~ is_a_theorem(X0)
    | is_a_theorem(implies(X1,implies(and(sK0,sK1),and(sK1,sK0)))) ),
    inference(instantiation,[status(thm)],[c_179]) ).

cnf(c_149803,plain,
    ( ~ is_a_theorem(implies(and(sK0,sK1),X0))
    | is_a_theorem(implies(implies(X0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0)))) ),
    inference(instantiation,[status(thm)],[c_1661]) ).

cnf(c_149805,plain,
    ( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
    | is_a_theorem(implies(implies(sK0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0)))) ),
    inference(instantiation,[status(thm)],[c_149803]) ).

cnf(c_153097,plain,
    ( ~ is_a_theorem(implies(implies(X0,implies(and(sK0,sK1),and(sK1,sK0))),implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0)))))
    | ~ is_a_theorem(implies(X0,implies(and(sK0,sK1),and(sK1,sK0))))
    | is_a_theorem(implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0)))) ),
    inference(instantiation,[status(thm)],[c_149517]) ).

cnf(c_153098,plain,
    ( ~ is_a_theorem(implies(and(sK0,sK1),X0))
    | is_a_theorem(implies(implies(X0,implies(and(sK0,sK1),and(sK1,sK0))),implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0))))) ),
    inference(instantiation,[status(thm)],[c_1661]) ).

cnf(c_153452,plain,
    is_a_theorem(implies(and(X0,sK1),sK1)),
    inference(instantiation,[status(thm)],[c_139]) ).

cnf(c_153454,plain,
    is_a_theorem(implies(and(sK0,sK1),sK1)),
    inference(instantiation,[status(thm)],[c_153452]) ).

cnf(c_153583,plain,
    is_a_theorem(implies(and(sK0,sK1),sK0)),
    inference(instantiation,[status(thm)],[c_142]) ).

cnf(c_154320,plain,
    is_a_theorem(implies(sK1,implies(sK0,and(sK1,sK0)))),
    inference(instantiation,[status(thm)],[c_160]) ).

cnf(c_154414,plain,
    ( ~ is_a_theorem(implies(implies(X0,implies(and(sK0,sK1),and(sK1,sK0))),implies(X1,implies(and(sK0,sK1),and(sK1,sK0)))))
    | ~ is_a_theorem(implies(X0,implies(and(sK0,sK1),and(sK1,sK0))))
    | is_a_theorem(implies(X1,implies(and(sK0,sK1),and(sK1,sK0)))) ),
    inference(instantiation,[status(thm)],[c_149753]) ).

cnf(c_154415,plain,
    ( ~ is_a_theorem(implies(X0,X1))
    | is_a_theorem(implies(implies(X1,implies(and(sK0,sK1),and(sK1,sK0))),implies(X0,implies(and(sK0,sK1),and(sK1,sK0))))) ),
    inference(instantiation,[status(thm)],[c_1661]) ).

cnf(c_158694,plain,
    ( ~ is_a_theorem(implies(implies(implies(X0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))),implies(X1,implies(and(sK0,sK1),and(sK1,sK0)))))
    | ~ is_a_theorem(implies(implies(X0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))))
    | is_a_theorem(implies(X1,implies(and(sK0,sK1),and(sK1,sK0)))) ),
    inference(instantiation,[status(thm)],[c_154414]) ).

cnf(c_166567,plain,
    ( ~ is_a_theorem(implies(X0,implies(X1,and(sK1,sK0))))
    | is_a_theorem(implies(implies(implies(X1,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))),implies(X0,implies(and(sK0,sK1),and(sK1,sK0))))) ),
    inference(instantiation,[status(thm)],[c_154415]) ).

cnf(c_183120,plain,
    ( ~ is_a_theorem(implies(sK1,implies(sK0,and(sK1,sK0))))
    | is_a_theorem(implies(implies(implies(sK0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))),implies(sK1,implies(and(sK0,sK1),and(sK1,sK0))))) ),
    inference(instantiation,[status(thm)],[c_166567]) ).

cnf(c_190032,plain,
    ( ~ is_a_theorem(implies(implies(implies(sK0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))),implies(sK1,implies(and(sK0,sK1),and(sK1,sK0)))))
    | ~ is_a_theorem(implies(implies(sK0,and(sK1,sK0)),implies(and(sK0,sK1),and(sK1,sK0))))
    | is_a_theorem(implies(sK1,implies(and(sK0,sK1),and(sK1,sK0)))) ),
    inference(instantiation,[status(thm)],[c_158694]) ).

cnf(c_207533,plain,
    ( ~ is_a_theorem(implies(implies(sK1,implies(and(sK0,sK1),and(sK1,sK0))),implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0)))))
    | ~ is_a_theorem(implies(sK1,implies(and(sK0,sK1),and(sK1,sK0))))
    | is_a_theorem(implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0)))) ),
    inference(instantiation,[status(thm)],[c_153097]) ).

cnf(c_242281,plain,
    ( ~ is_a_theorem(implies(and(sK0,sK1),sK1))
    | is_a_theorem(implies(implies(sK1,implies(and(sK0,sK1),and(sK1,sK0))),implies(and(sK0,sK1),implies(and(sK0,sK1),and(sK1,sK0))))) ),
    inference(instantiation,[status(thm)],[c_153098]) ).

cnf(c_242282,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_242281,c_207533,c_190032,c_183120,c_154320,c_153583,c_153454,c_149805,c_147205,c_2293]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : LCL528+1 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n011.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu May  2 19:03:33 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 142.40/19.85  % SZS status Started for theBenchmark.p
% 142.40/19.85  % SZS status Theorem for theBenchmark.p
% 142.40/19.85  
% 142.40/19.85  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 142.40/19.85  
% 142.40/19.85  ------  iProver source info
% 142.40/19.85  
% 142.40/19.85  git: date: 2024-05-02 19:28:25 +0000
% 142.40/19.85  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 142.40/19.85  git: non_committed_changes: false
% 142.40/19.85  
% 142.40/19.85  ------ Parsing...
% 142.40/19.85  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 142.40/19.85  
% 142.40/19.85  ------ Preprocessing... sup_sim: 3  sf_s  rm: 27 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 142.40/19.85  
% 142.40/19.85  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 142.40/19.85  
% 142.40/19.85  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 142.40/19.85  ------ Proving...
% 142.40/19.85  ------ Problem Properties 
% 142.40/19.85  
% 142.40/19.85  
% 142.40/19.85  clauses                                 26
% 142.40/19.85  conjectures                             0
% 142.40/19.85  EPR                                     0
% 142.40/19.85  Horn                                    26
% 142.40/19.85  unary                                   23
% 142.40/19.85  binary                                  2
% 142.40/19.85  lits                                    30
% 142.40/19.85  lits eq                                 7
% 142.40/19.85  fd_pure                                 0
% 142.40/19.85  fd_pseudo                               0
% 142.40/19.85  fd_cond                                 0
% 142.40/19.85  fd_pseudo_cond                          1
% 142.40/19.85  AC symbols                              0
% 142.40/19.85  
% 142.40/19.85  ------ Input Options Time Limit: Unbounded
% 142.40/19.85  
% 142.40/19.85  
% 142.40/19.85  ------ 
% 142.40/19.85  Current options:
% 142.40/19.85  ------ 
% 142.40/19.85  
% 142.40/19.85  
% 142.40/19.85  
% 142.40/19.85  
% 142.40/19.85  ------ Proving...
% 142.40/19.85  
% 142.40/19.85  
% 142.40/19.85  % SZS status Theorem for theBenchmark.p
% 142.40/19.85  
% 142.40/19.85  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 142.40/19.86  
% 142.40/19.87  
%------------------------------------------------------------------------------