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LisaST---0.9.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : LisaST---0.9
% Problem  : LCL533+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 07:54:48 AM UTC 2026

% Result   : Theorem 75.97s 16.95s
% Output   : CNFRefutation 75.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  135 (  67 unt;   0 def)
%            Number of atoms       :  220 (  23 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  151 (  66   ~;  61   |;   1   &)
%                                         (  15 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   23 (  21 usr;  21 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-2 aty)
%            Number of variables   :  155 (   4 sgn  35   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(s1_0_op_possibly,axiom,
    'op$upossibly' ).

fof(s1_0_op_or,axiom,
    'op$uor' ).

fof(s1_0_op_strict_implies,axiom,
    'op$ustrict$uimplies' ).

fof(s1_0_op_equiv,axiom,
    'op$uequiv' ).

fof(modus_ponens,axiom,
    ( 'modus$uponens'
  <=> ! [X0,X1] :
        ( ( 'is$ua$utheorem'(implies(X0,X1))
          & 'is$ua$utheorem'(X0) )
       => 'is$ua$utheorem'(X1) ) ) ).

fof(substitution_of_equivalents,axiom,
    ( 'substitution$uof$uequivalents'
  <=> ! [X0,X1] :
        ( 'is$ua$utheorem'(equiv(X0,X1))
       => X0 = X1 ) ) ).

fof(modus_tollens,axiom,
    ( 'modus$utollens'
  <=> ! [X0,X1] : 'is$ua$utheorem'(implies(implies(not(X1),not(X0)),implies(X0,X1))) ) ).

fof(implies_1,axiom,
    ( 'implies$u1'
  <=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,implies(X1,X0))) ) ).

fof(implies_2,axiom,
    ( 'implies$u2'
  <=> ! [X0,X1] : 'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ) ).

fof(implies_3,axiom,
    ( 'implies$u3'
  <=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ) ).

fof(and_1,axiom,
    ( 'and$u1'
  <=> ! [X0,X1] : 'is$ua$utheorem'(implies(and(X0,X1),X0)) ) ).

fof(and_3,axiom,
    ( 'and$u3'
  <=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1)))) ) ).

fof(or_3,axiom,
    ( 'or$u3'
  <=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ) ).

fof(cn3,axiom,
    ( cn3
  <=> ! [X0] : 'is$ua$utheorem'(implies(implies(not(X0),X0),X0)) ) ).

fof(op_or,axiom,
    ( 'op$uor'
   => ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ) ).

fof(op_implies_and,axiom,
    ( 'op$uimplies$uand'
   => ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ) ).

fof(op_equiv,axiom,
    ( 'op$uequiv'
   => ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ) ).

fof(hilbert_op_implies_and,axiom,
    'op$uimplies$uand' ).

fof(hilbert_modus_ponens,axiom,
    'modus$uponens' ).

fof(hilbert_modus_tollens,axiom,
    'modus$utollens' ).

fof(hilbert_implies_1,axiom,
    'implies$u1' ).

fof(hilbert_implies_2,axiom,
    'implies$u2' ).

fof(hilbert_implies_3,axiom,
    'implies$u3' ).

fof(hilbert_and_1,axiom,
    'and$u1' ).

fof(hilbert_and_3,axiom,
    'and$u3' ).

fof(hilbert_or_3,axiom,
    'or$u3' ).

fof(use_substitution_of_equivalents,axiom,
    'substitution$uof$uequivalents' ).

fof(necessitation,axiom,
    ( necessitation
  <=> ! [X0] :
        ( 'is$ua$utheorem'(X0)
       => 'is$ua$utheorem'(necessarily(X0)) ) ) ).

fof(axiom_M,axiom,
    ( 'axiom$uM'
  <=> ! [X0] : 'is$ua$utheorem'(implies(necessarily(X0),X0)) ) ).

fof(axiom_B,axiom,
    ( 'axiom$uB'
  <=> ! [X0] : 'is$ua$utheorem'(implies(X0,necessarily(possibly(X0)))) ) ).

fof(axiom_5,axiom,
    ( 'axiom$u5'
  <=> ! [X0] : 'is$ua$utheorem'(implies(possibly(X0),necessarily(possibly(X0)))) ) ).

fof(axiom_m6,axiom,
    ( 'axiom$um6'
  <=> ! [X0] : 'is$ua$utheorem'('strict$uimplies'(X0,possibly(X0))) ) ).

fof(op_possibly,axiom,
    ( 'op$upossibly'
   => ! [X0] : possibly(X0) = not(necessarily(not(X0))) ) ).

fof(op_strict_implies,axiom,
    ( 'op$ustrict$uimplies'
   => ! [X0,X1] : 'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1)) ) ).

fof(km5_necessitation,axiom,
    necessitation ).

fof(km5_axiom_M,axiom,
    'axiom$uM' ).

fof(km5_axiom_5,axiom,
    'axiom$u5' ).

fof(s1_0_m6s3m9b_axiom_m6,conjecture,
    'axiom$um6' ).

fof(negated_conjecture,negated_conjecture,
    ~ 'axiom$um6',
    inference(negate_conjecture,[status(cth)],[s1_0_m6s3m9b_axiom_m6]) ).

cnf(c0,plain,
    'op$upossibly',
    inference(clausification,[status(esa)],[s1_0_op_possibly]) ).

cnf(c1,plain,
    'op$uor',
    inference(clausification,[status(esa)],[s1_0_op_or]) ).

cnf(c3,plain,
    'op$ustrict$uimplies',
    inference(clausification,[status(esa)],[s1_0_op_strict_implies]) ).

cnf(c4,plain,
    'op$uequiv',
    inference(clausification,[status(esa)],[s1_0_op_equiv]) ).

cnf(c6,plain,
    ( 'is$ua$utheorem'(X1)
    | ~ 'is$ua$utheorem'(X0)
    | ~ 'is$ua$utheorem'(implies(X0,X1))
    | ~ 'modus$uponens' ),
    inference(clausification,[status(esa)],[modus_ponens]) ).

cnf(c10,plain,
    ( X1 = X0
    | ~ 'is$ua$utheorem'(equiv(X0,X1))
    | ~ 'substitution$uof$uequivalents' ),
    inference(clausification,[status(esa)],[substitution_of_equivalents]) ).

cnf(c13,plain,
    ( 'is$ua$utheorem'(implies(implies(not(X0),not(X1)),implies(X1,X0)))
    | ~ 'modus$utollens' ),
    inference(clausification,[status(esa)],[modus_tollens]) ).

cnf(c15,plain,
    ( 'is$ua$utheorem'(implies(X0,implies(X1,X0)))
    | ~ 'implies$u1' ),
    inference(clausification,[status(esa)],[implies_1]) ).

cnf(c17,plain,
    ( 'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
    | ~ 'implies$u2' ),
    inference(clausification,[status(esa)],[implies_2]) ).

cnf(c19,plain,
    ( 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
    | ~ 'implies$u3' ),
    inference(clausification,[status(esa)],[implies_3]) ).

cnf(c21,plain,
    ( 'is$ua$utheorem'(implies(and(X0,X1),X0))
    | ~ 'and$u1' ),
    inference(clausification,[status(esa)],[and_1]) ).

cnf(c25,plain,
    ( 'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1))))
    | ~ 'and$u3' ),
    inference(clausification,[status(esa)],[and_3]) ).

cnf(c31,plain,
    ( 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))
    | ~ 'or$u3' ),
    inference(clausification,[status(esa)],[or_3]) ).

cnf(c49,plain,
    ( 'is$ua$utheorem'(implies(implies(not(X0),X0),X0))
    | ~ cn3 ),
    inference(clausification,[status(esa)],[cn3]) ).

cnf(c50,plain,
    ( ~ 'is$ua$utheorem'(implies(implies(not(sK87),sK87),sK87))
    | cn3 ),
    inference(clausification,[status(esa)],[cn3]) ).

cnf(c61,plain,
    ( not(and(not(X0),not(X1))) = or(X0,X1)
    | ~ 'op$uor' ),
    inference(clausification,[status(esa)],[op_or]) ).

cnf(c63,plain,
    ( not(and(X0,not(X1))) = implies(X0,X1)
    | ~ 'op$uimplies$uand' ),
    inference(clausification,[status(esa)],[op_implies_and]) ).

cnf(c65,plain,
    ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1)
    | ~ 'op$uequiv' ),
    inference(clausification,[status(esa)],[op_equiv]) ).

cnf(c67,plain,
    'op$uimplies$uand',
    inference(clausification,[status(esa)],[hilbert_op_implies_and]) ).

cnf(c69,plain,
    'modus$uponens',
    inference(clausification,[status(esa)],[hilbert_modus_ponens]) ).

cnf(c70,plain,
    'modus$utollens',
    inference(clausification,[status(esa)],[hilbert_modus_tollens]) ).

cnf(c71,plain,
    'implies$u1',
    inference(clausification,[status(esa)],[hilbert_implies_1]) ).

cnf(c72,plain,
    'implies$u2',
    inference(clausification,[status(esa)],[hilbert_implies_2]) ).

cnf(c73,plain,
    'implies$u3',
    inference(clausification,[status(esa)],[hilbert_implies_3]) ).

cnf(c74,plain,
    'and$u1',
    inference(clausification,[status(esa)],[hilbert_and_1]) ).

cnf(c76,plain,
    'and$u3',
    inference(clausification,[status(esa)],[hilbert_and_3]) ).

cnf(c79,plain,
    'or$u3',
    inference(clausification,[status(esa)],[hilbert_or_3]) ).

cnf(c83,plain,
    'substitution$uof$uequivalents',
    inference(clausification,[status(esa)],[use_substitution_of_equivalents]) ).

cnf(c84,plain,
    ( 'is$ua$utheorem'(necessarily(X0))
    | ~ 'is$ua$utheorem'(X0)
    | ~ necessitation ),
    inference(clausification,[status(esa)],[necessitation]) ).

cnf(c100,plain,
    ( 'is$ua$utheorem'(implies(necessarily(X0),X0))
    | ~ 'axiom$uM' ),
    inference(clausification,[status(esa)],[axiom_M]) ).

cnf(c104,plain,
    ( 'is$ua$utheorem'(implies(X0,necessarily(possibly(X0))))
    | ~ 'axiom$uB' ),
    inference(clausification,[status(esa)],[axiom_B]) ).

cnf(c105,plain,
    ( ~ 'is$ua$utheorem'(implies(sK143,necessarily(possibly(sK143))))
    | 'axiom$uB' ),
    inference(clausification,[status(esa)],[axiom_B]) ).

cnf(c106,plain,
    ( 'is$ua$utheorem'(implies(possibly(X0),necessarily(possibly(X0))))
    | ~ 'axiom$u5' ),
    inference(clausification,[status(esa)],[axiom_5]) ).

cnf(c127,plain,
    ( ~ 'is$ua$utheorem'('strict$uimplies'(sK185,possibly(sK185)))
    | 'axiom$um6' ),
    inference(clausification,[status(esa)],[axiom_m6]) ).

cnf(c136,plain,
    ( not(necessarily(not(X0))) = possibly(X0)
    | ~ 'op$upossibly' ),
    inference(clausification,[status(esa)],[op_possibly]) ).

cnf(c138,plain,
    ( necessarily(implies(X0,X1)) = 'strict$uimplies'(X0,X1)
    | ~ 'op$ustrict$uimplies' ),
    inference(clausification,[status(esa)],[op_strict_implies]) ).

cnf(c141,plain,
    necessitation,
    inference(clausification,[status(esa)],[km5_necessitation]) ).

cnf(c143,plain,
    'axiom$uM',
    inference(clausification,[status(esa)],[km5_axiom_M]) ).

cnf(c144,plain,
    'axiom$u5',
    inference(clausification,[status(esa)],[km5_axiom_5]) ).

cnf(c145,plain,
    ~ 'axiom$um6',
    inference(clausification,[status(esa)],[negated_conjecture]) ).

cnf(d0,plain,
    ( ~ 'is$ua$utheorem'(equiv(X1,X0))
    | X0 = X1 ),
    inference(resolution,[status(thm)],[c83,c10]) ).

cnf(d1,plain,
    'is$ua$utheorem'(implies(possibly(X0),necessarily(possibly(X0)))),
    inference(resolution,[status(thm)],[c144,c106]) ).

cnf(d2,plain,
    ( ~ 'is$ua$utheorem'(implies(X1,X0))
    | ~ 'is$ua$utheorem'(X1)
    | 'is$ua$utheorem'(X0) ),
    inference(resolution,[status(thm)],[c69,c6]) ).

cnf(d3,plain,
    'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1)))),
    inference(resolution,[status(thm)],[c76,c25]) ).

cnf(d4,plain,
    ( 'is$ua$utheorem'(implies(X1,and(X0,X1)))
    | ~ 'is$ua$utheorem'(X0) ),
    inference(resolution,[status(thm)],[d3,d2]) ).

cnf(d5,plain,
    ( 'is$ua$utheorem'(and(X0,X1))
    | ~ 'is$ua$utheorem'(X1)
    | ~ 'is$ua$utheorem'(X0) ),
    inference(resolution,[status(thm)],[d4,d2]) ).

cnf(d6,plain,
    and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
    inference(resolution,[status(thm)],[c4,c65]) ).

cnf(d7,plain,
    ( ~ 'is$ua$utheorem'(implies(X0,X1))
    | ~ 'is$ua$utheorem'(implies(X1,X0))
    | 'is$ua$utheorem'(equiv(X0,X1)) ),
    inference(superposition,[status(thm)],[d6,d5]) ).

cnf(d8,plain,
    ( 'is$ua$utheorem'(equiv(possibly(X0),necessarily(possibly(X0))))
    | ~ 'is$ua$utheorem'(implies(necessarily(possibly(X0)),possibly(X0))) ),
    inference(resolution,[status(thm)],[d7,d1]) ).

cnf(d9,plain,
    'is$ua$utheorem'(implies(necessarily(X0),X0)),
    inference(resolution,[status(thm)],[c143,c100]) ).

cnf(d10,plain,
    'is$ua$utheorem'(equiv(possibly(X0),necessarily(possibly(X0)))),
    inference(resolution,[status(thm)],[d9,d8]) ).

cnf(d11,plain,
    necessarily(possibly(X0)) = possibly(X0),
    inference(resolution,[status(thm)],[d10,d0]) ).

cnf(d12,plain,
    ( 'axiom$uB'
    | ~ 'is$ua$utheorem'(implies(sK143,possibly(sK143))) ),
    inference(demodulation,[status(thm)],[c105,d11]) ).

cnf(d13,plain,
    ~ 'is$ua$utheorem'('strict$uimplies'(sK185,possibly(sK185))),
    inference(resolution,[status(thm)],[c145,c127]) ).

cnf(d14,plain,
    ( 'is$ua$utheorem'(necessarily(X0))
    | ~ 'is$ua$utheorem'(X0) ),
    inference(resolution,[status(thm)],[c141,c84]) ).

cnf(d15,plain,
    necessarily(implies(X0,X1)) = 'strict$uimplies'(X0,X1),
    inference(resolution,[status(thm)],[c3,c138]) ).

cnf(d16,plain,
    ( ~ 'is$ua$utheorem'(implies(X0,X1))
    | 'is$ua$utheorem'('strict$uimplies'(X0,X1)) ),
    inference(superposition,[status(thm)],[d15,d14]) ).

cnf(d17,plain,
    ( ~ 'axiom$uB'
    | 'is$ua$utheorem'('strict$uimplies'(X0,necessarily(possibly(X0)))) ),
    inference(resolution,[status(thm)],[d16,c104]) ).

cnf(d18,plain,
    ( ~ 'axiom$uB'
    | 'is$ua$utheorem'('strict$uimplies'(X0,possibly(X0))) ),
    inference(demodulation,[status(thm)],[d17,d11]) ).

cnf(d19,plain,
    ~ 'axiom$uB',
    inference(resolution,[status(thm)],[d18,d13]) ).

cnf(d20,plain,
    ~ 'is$ua$utheorem'(implies(sK143,possibly(sK143))),
    inference(resolution,[status(thm)],[d19,d12]) ).

cnf(d21,plain,
    not(and(X0,not(X1))) = implies(X0,X1),
    inference(resolution,[status(thm)],[c67,c63]) ).

cnf(d22,plain,
    not(and(not(X0),not(X1))) = or(X0,X1),
    inference(resolution,[status(thm)],[c1,c61]) ).

cnf(d23,plain,
    implies(not(X0),X1) = or(X0,X1),
    inference(demodulation,[status(thm)],[d22,d21]) ).

cnf(d24,plain,
    'is$ua$utheorem'(implies(implies(not(X0),not(X1)),implies(X1,X0))),
    inference(resolution,[status(thm)],[c70,c13]) ).

cnf(d25,plain,
    ( 'is$ua$utheorem'(implies(X1,X0))
    | ~ 'is$ua$utheorem'(implies(not(X0),not(X1))) ),
    inference(resolution,[status(thm)],[d24,d2]) ).

cnf(d26,plain,
    ( ~ 'is$ua$utheorem'(or(X0,not(X1)))
    | 'is$ua$utheorem'(implies(X1,X0)) ),
    inference(demodulation,[status(thm)],[d25,d23]) ).

cnf(d27,plain,
    'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
    inference(resolution,[status(thm)],[c72,c17]) ).

cnf(d28,plain,
    ( 'is$ua$utheorem'(implies(X0,X1))
    | ~ 'is$ua$utheorem'(implies(X0,implies(X0,X1))) ),
    inference(resolution,[status(thm)],[d27,d2]) ).

cnf(d29,plain,
    'is$ua$utheorem'(implies(X0,and(X0,X0))),
    inference(resolution,[status(thm)],[d28,d3]) ).

cnf(d30,plain,
    ( 'is$ua$utheorem'(equiv(X0,and(X0,X0)))
    | ~ 'is$ua$utheorem'(implies(and(X0,X0),X0)) ),
    inference(resolution,[status(thm)],[d7,d29]) ).

cnf(d31,plain,
    'is$ua$utheorem'(implies(and(X0,X1),X0)),
    inference(resolution,[status(thm)],[c74,c21]) ).

cnf(d32,plain,
    'is$ua$utheorem'(equiv(X0,and(X0,X0))),
    inference(resolution,[status(thm)],[d31,d30]) ).

cnf(d33,plain,
    and(X0,X0) = X0,
    inference(resolution,[status(thm)],[d32,d0]) ).

cnf(d34,plain,
    not(necessarily(not(X0))) = possibly(X0),
    inference(resolution,[status(thm)],[c0,c136]) ).

cnf(d35,plain,
    not(and(X1,possibly(X0))) = implies(X1,necessarily(not(X0))),
    inference(superposition,[status(thm)],[d34,d21]) ).

cnf(d36,plain,
    implies(implies(X0,necessarily(not(X1))),X2) = or(and(X0,possibly(X1)),X2),
    inference(superposition,[status(thm)],[d35,d23]) ).

cnf(d37,plain,
    ( ~ cn3
    | 'is$ua$utheorem'(implies(implies(possibly(X0),necessarily(not(X0))),necessarily(not(X0)))) ),
    inference(superposition,[status(thm)],[d34,c49]) ).

cnf(d38,plain,
    'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
    inference(resolution,[status(thm)],[c73,c19]) ).

cnf(d39,plain,
    ( 'is$ua$utheorem'(implies(implies(X1,X2),implies(X0,X2)))
    | ~ 'is$ua$utheorem'(implies(X0,X1)) ),
    inference(resolution,[status(thm)],[d38,d2]) ).

cnf(d40,plain,
    ( 'is$ua$utheorem'(implies(X0,X2))
    | ~ 'is$ua$utheorem'(implies(X1,X2))
    | ~ 'is$ua$utheorem'(implies(X0,X1)) ),
    inference(resolution,[status(thm)],[d39,d2]) ).

cnf(d41,plain,
    ( ~ cn3
    | 'is$ua$utheorem'(implies(implies(possibly(X0),necessarily(not(X0))),X1))
    | ~ 'is$ua$utheorem'(implies(necessarily(not(X0)),X1)) ),
    inference(resolution,[status(thm)],[d40,d37]) ).

cnf(d42,plain,
    ( ~ cn3
    | ~ 'is$ua$utheorem'(implies(necessarily(not(X0)),X1))
    | 'is$ua$utheorem'(or(and(possibly(X0),possibly(X0)),X1)) ),
    inference(demodulation,[status(thm)],[d41,d36]) ).

cnf(d43,plain,
    ( ~ cn3
    | ~ 'is$ua$utheorem'(implies(necessarily(not(X0)),X1))
    | 'is$ua$utheorem'(or(possibly(X0),X1)) ),
    inference(demodulation,[status(thm)],[d42,d33]) ).

cnf(d44,plain,
    ( cn3
    | ~ 'is$ua$utheorem'(implies(or(sK87,sK87),sK87)) ),
    inference(demodulation,[status(thm)],[c50,d23]) ).

cnf(d45,plain,
    'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),
    inference(resolution,[status(thm)],[c79,c31]) ).

cnf(d46,plain,
    ( 'is$ua$utheorem'(implies(implies(X2,X1),implies(or(X0,X2),X1)))
    | ~ 'is$ua$utheorem'(implies(X0,X1)) ),
    inference(resolution,[status(thm)],[d45,d2]) ).

cnf(d47,plain,
    ( 'is$ua$utheorem'(implies(or(X0,X2),X1))
    | ~ 'is$ua$utheorem'(implies(X2,X1))
    | ~ 'is$ua$utheorem'(implies(X0,X1)) ),
    inference(resolution,[status(thm)],[d46,d2]) ).

cnf(d48,plain,
    ( cn3
    | ~ 'is$ua$utheorem'(implies(sK87,sK87))
    | ~ 'is$ua$utheorem'(implies(sK87,sK87)) ),
    inference(resolution,[status(thm)],[d47,d44]) ).

cnf(d49,plain,
    'is$ua$utheorem'(implies(X0,implies(X1,X0))),
    inference(resolution,[status(thm)],[c71,c15]) ).

cnf(d50,plain,
    'is$ua$utheorem'(implies(X0,X0)),
    inference(resolution,[status(thm)],[d28,d49]) ).

cnf(d51,plain,
    cn3,
    inference(resolution,[status(thm)],[d50,d48]) ).

cnf(d52,plain,
    ( ~ 'is$ua$utheorem'(implies(necessarily(not(X0)),X1))
    | 'is$ua$utheorem'(or(possibly(X0),X1)) ),
    inference(resolution,[status(thm)],[d51,d43]) ).

cnf(d53,plain,
    'is$ua$utheorem'(or(possibly(X0),not(X0))),
    inference(resolution,[status(thm)],[d52,d9]) ).

cnf(d54,plain,
    'is$ua$utheorem'(implies(X0,possibly(X0))),
    inference(resolution,[status(thm)],[d53,d26]) ).

cnf(d55,plain,
    $false,
    inference(resolution,[status(thm)],[d54,d20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : LCL533+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04  % Command  : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.37  % Computer : n026.cluster.edu
% 0.11/5.37  % Model    : x86_64 x86_64
% 0.11/5.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37  % Memory   : 8046.5625MB
% 0.11/5.37  % OS       : Linux 6.8.0-71-generic
% 0.11/5.37  % CPULimit : 300
% 0.11/5.37  % WCLimit  : 300
% 0.11/5.37  % DateTime : Fri Sep 25 22:45:46 UTC 2026
% 0.11/5.37  % CPUTime  : 
% 0.11/5.37  Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 75.97/16.95  % SZS status Theorem for theBenchmark.p
% 75.97/16.95  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------