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LisaST---0.9.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : LisaST---0.9
% Problem  : LCL493+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 : n013.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 07:54:44 AM UTC 2026

% Result   : Theorem 89.76s 14.36s
% Output   : CNFRefutation 89.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   28
% Syntax   : Number of formulae    :  141 (  85 unt;   0 def)
%            Number of atoms       :  207 (  30 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  120 (  54   ~;  48   |;   1   &)
%                                         (  10 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   18 (  16 usr;  16 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :  220 (  28 sgn  31   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(hilbert_op_or,axiom,
    'op$uor' ).

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

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

fof(or_1,axiom,
    ( 'or$u1'
  <=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,or(X0,X1))) ) ).

fof(equivalence_1,axiom,
    ( 'equivalence$u1'
  <=> ! [X0,X1] : 'is$ua$utheorem'(implies(equiv(X0,X1),implies(X0,X1))) ) ).

fof(r1,axiom,
    ( r1
  <=> ! [X0] : 'is$ua$utheorem'(implies(or(X0,X0),X0)) ) ).

fof(r2,axiom,
    ( r2
  <=> ! [X0,X1] : 'is$ua$utheorem'(implies(X1,or(X0,X1))) ) ).

fof(r3,axiom,
    ( r3
  <=> ! [X0,X1] : 'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0))) ) ).

fof(r4,axiom,
    ( r4
  <=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ) ).

fof(r5,axiom,
    ( r5
  <=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ) ).

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

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

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

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

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

fof(principia_op_implies_or,axiom,
    'op$uimplies$uor' ).

fof(principia_op_and,axiom,
    'op$uand' ).

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

fof(principia_r1,axiom,
    r1 ).

fof(principia_r2,axiom,
    r2 ).

fof(principia_r3,axiom,
    r3 ).

fof(principia_r4,axiom,
    r4 ).

fof(principia_r5,axiom,
    r5 ).

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

fof(hilbert_equivalence_1,conjecture,
    'equivalence$u1' ).

fof(negated_conjecture,negated_conjecture,
    ~ 'equivalence$u1',
    inference(negate_conjecture,[status(cth)],[hilbert_equivalence_1]) ).

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

cnf(c1,plain,
    'op$uimplies$uand',
    inference(clausification,[status(esa)],[hilbert_op_implies_and]) ).

cnf(c2,plain,
    'op$uequiv',
    inference(clausification,[status(esa)],[hilbert_op_equiv]) ).

cnf(c3,plain,
    ( 'is$ua$utheorem'(X1)
    | ~ 'is$ua$utheorem'(X0)
    | ~ 'is$ua$utheorem'(implies(X0,X1))
    | ~ 'modus$uponens' ),
    inference(clausification,[status(esa)],[modus_ponens]) ).

cnf(c7,plain,
    ( X1 = X0
    | ~ 'is$ua$utheorem'(equiv(X0,X1))
    | ~ 'substitution$uof$uequivalents' ),
    inference(clausification,[status(esa)],[substitution_of_equivalents]) ).

cnf(c18,plain,
    ( 'is$ua$utheorem'(implies(and(X0,X1),X0))
    | ~ 'and$u1' ),
    inference(clausification,[status(esa)],[and_1]) ).

cnf(c19,plain,
    ( ~ 'is$ua$utheorem'(implies(and(sK28,sK29),sK28))
    | 'and$u1' ),
    inference(clausification,[status(esa)],[and_1]) ).

cnf(c24,plain,
    ( 'is$ua$utheorem'(implies(X0,or(X0,X1)))
    | ~ 'or$u1' ),
    inference(clausification,[status(esa)],[or_1]) ).

cnf(c25,plain,
    ( ~ 'is$ua$utheorem'(implies(sK40,or(sK40,sK41)))
    | 'or$u1' ),
    inference(clausification,[status(esa)],[or_1]) ).

cnf(c31,plain,
    ( ~ 'is$ua$utheorem'(implies(equiv(sK54,sK55),implies(sK54,sK55)))
    | 'equivalence$u1' ),
    inference(clausification,[status(esa)],[equivalence_1]) ).

cnf(c48,plain,
    ( 'is$ua$utheorem'(implies(or(X0,X0),X0))
    | ~ r1 ),
    inference(clausification,[status(esa)],[r1]) ).

cnf(c50,plain,
    ( 'is$ua$utheorem'(implies(X0,or(X1,X0)))
    | ~ r2 ),
    inference(clausification,[status(esa)],[r2]) ).

cnf(c52,plain,
    ( 'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0)))
    | ~ r3 ),
    inference(clausification,[status(esa)],[r3]) ).

cnf(c54,plain,
    ( 'is$ua$utheorem'(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
    | ~ r4 ),
    inference(clausification,[status(esa)],[r4]) ).

cnf(c56,plain,
    ( 'is$ua$utheorem'(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))
    | ~ r5 ),
    inference(clausification,[status(esa)],[r5]) ).

cnf(c58,plain,
    ( not(and(not(X0),not(X1))) = or(X0,X1)
    | ~ 'op$uor' ),
    inference(clausification,[status(esa)],[op_or]) ).

cnf(c59,plain,
    ( not(or(not(X0),not(X1))) = and(X0,X1)
    | ~ 'op$uand' ),
    inference(clausification,[status(esa)],[op_and]) ).

cnf(c60,plain,
    ( not(and(X0,not(X1))) = implies(X0,X1)
    | ~ 'op$uimplies$uand' ),
    inference(clausification,[status(esa)],[op_implies_and]) ).

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

cnf(c62,plain,
    ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1)
    | ~ 'op$uequiv' ),
    inference(clausification,[status(esa)],[op_equiv]) ).

cnf(c63,plain,
    'op$uimplies$uor',
    inference(clausification,[status(esa)],[principia_op_implies_or]) ).

cnf(c64,plain,
    'op$uand',
    inference(clausification,[status(esa)],[principia_op_and]) ).

cnf(c66,plain,
    'modus$uponens',
    inference(clausification,[status(esa)],[principia_modus_ponens]) ).

cnf(c67,plain,
    r1,
    inference(clausification,[status(esa)],[principia_r1]) ).

cnf(c68,plain,
    r2,
    inference(clausification,[status(esa)],[principia_r2]) ).

cnf(c69,plain,
    r3,
    inference(clausification,[status(esa)],[principia_r3]) ).

cnf(c70,plain,
    r4,
    inference(clausification,[status(esa)],[principia_r4]) ).

cnf(c71,plain,
    r5,
    inference(clausification,[status(esa)],[principia_r5]) ).

cnf(c72,plain,
    'substitution$uof$uequivalents',
    inference(clausification,[status(esa)],[use_substitution_of_equivalents]) ).

cnf(c73,plain,
    ~ 'equivalence$u1',
    inference(clausification,[status(esa)],[negated_conjecture]) ).

cnf(d0,plain,
    ( ~ 'is$ua$utheorem'(implies(X1,X0))
    | ~ 'is$ua$utheorem'(X1)
    | 'is$ua$utheorem'(X0) ),
    inference(resolution,[status(thm)],[c66,c3]) ).

cnf(d1,plain,
    'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0))),
    inference(resolution,[status(thm)],[c69,c52]) ).

cnf(d2,plain,
    ( 'is$ua$utheorem'(or(X1,X0))
    | ~ 'is$ua$utheorem'(or(X0,X1)) ),
    inference(resolution,[status(thm)],[d1,d0]) ).

cnf(d3,plain,
    not(and(X0,not(X1))) = implies(X0,X1),
    inference(resolution,[status(thm)],[c1,c60]) ).

cnf(d4,plain,
    not(and(not(X0),not(X1))) = or(X0,X1),
    inference(resolution,[status(thm)],[c0,c58]) ).

cnf(d5,plain,
    implies(not(X0),X1) = or(X0,X1),
    inference(demodulation,[status(thm)],[d4,d3]) ).

cnf(d6,plain,
    or(not(X0),X1) = implies(X0,X1),
    inference(resolution,[status(thm)],[c63,c61]) ).

cnf(d7,plain,
    ( ~ 'or$u1'
    | 'is$ua$utheorem'(implies(not(X0),implies(X0,X1))) ),
    inference(superposition,[status(thm)],[d6,c24]) ).

cnf(d8,plain,
    ( ~ 'or$u1'
    | 'is$ua$utheorem'(or(X0,implies(X0,X1))) ),
    inference(demodulation,[status(thm)],[d7,d5]) ).

cnf(d9,plain,
    ( 'is$ua$utheorem'(or(implies(X0,X1),X0))
    | ~ 'or$u1' ),
    inference(resolution,[status(thm)],[d8,d2]) ).

cnf(d10,plain,
    ( ~ 'op$uand'
    | not(implies(X0,not(X1))) = and(X0,X1) ),
    inference(demodulation,[status(thm)],[c59,d6]) ).

cnf(d11,plain,
    not(implies(X0,not(X1))) = and(X0,X1),
    inference(resolution,[status(thm)],[c64,d10]) ).

cnf(d12,plain,
    not(and(and(X0,X1),not(X2))) = or(implies(X0,not(X1)),X2),
    inference(superposition,[status(thm)],[d11,d4]) ).

cnf(d13,plain,
    implies(and(X0,X1),X2) = or(implies(X0,not(X1)),X2),
    inference(demodulation,[status(thm)],[d12,d3]) ).

cnf(d14,plain,
    ( ~ 'or$u1'
    | 'is$ua$utheorem'(implies(and(X0,X1),X0)) ),
    inference(superposition,[status(thm)],[d13,d9]) ).

cnf(d15,plain,
    ( 'and$u1'
    | ~ 'or$u1' ),
    inference(resolution,[status(thm)],[d14,c19]) ).

cnf(d16,plain,
    ~ 'is$ua$utheorem'(implies(equiv(sK54,sK55),implies(sK54,sK55))),
    inference(resolution,[status(thm)],[c73,c31]) ).

cnf(d17,plain,
    and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
    inference(resolution,[status(thm)],[c2,c62]) ).

cnf(d18,plain,
    ( ~ 'and$u1'
    | 'is$ua$utheorem'(implies(equiv(X0,X1),implies(X0,X1))) ),
    inference(superposition,[status(thm)],[d17,c18]) ).

cnf(d19,plain,
    ~ 'and$u1',
    inference(resolution,[status(thm)],[d18,d16]) ).

cnf(d20,plain,
    ~ 'or$u1',
    inference(resolution,[status(thm)],[d19,d15]) ).

cnf(d21,plain,
    ~ 'is$ua$utheorem'(implies(sK40,or(sK40,sK41))),
    inference(resolution,[status(thm)],[d20,c25]) ).

cnf(d22,plain,
    'is$ua$utheorem'(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
    inference(resolution,[status(thm)],[c70,c54]) ).

cnf(d23,plain,
    ( 'is$ua$utheorem'(or(X1,or(X0,X2)))
    | ~ 'is$ua$utheorem'(or(X0,or(X1,X2))) ),
    inference(resolution,[status(thm)],[d22,d0]) ).

cnf(d24,plain,
    ( 'is$ua$utheorem'(or(not(X0),or(X2,X1)))
    | ~ 'is$ua$utheorem'(or(X2,implies(X0,X1))) ),
    inference(superposition,[status(thm)],[d6,d23]) ).

cnf(d25,plain,
    ( 'is$ua$utheorem'(implies(X0,or(X1,X2)))
    | ~ 'is$ua$utheorem'(or(X1,implies(X0,X2))) ),
    inference(demodulation,[status(thm)],[d24,d6]) ).

cnf(d26,plain,
    or(and(X0,X1),X2) = implies(implies(X0,not(X1)),X2),
    inference(superposition,[status(thm)],[d11,d6]) ).

cnf(d27,plain,
    'is$ua$utheorem'(implies(or(X1,not(X0)),implies(X0,X1))),
    inference(superposition,[status(thm)],[d6,d1]) ).

cnf(d28,plain,
    'is$ua$utheorem'(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
    inference(superposition,[status(thm)],[d6,d27]) ).

cnf(d29,plain,
    'is$ua$utheorem'(or(and(X0,X1),implies(X1,not(X0)))),
    inference(demodulation,[status(thm)],[d28,d26]) ).

cnf(d30,plain,
    'is$ua$utheorem'(implies(X0,or(X1,X0))),
    inference(resolution,[status(thm)],[c68,c50]) ).

cnf(d31,plain,
    'is$ua$utheorem'(implies(X1,implies(X0,X1))),
    inference(superposition,[status(thm)],[d6,d30]) ).

cnf(d32,plain,
    'is$ua$utheorem'(or(X0,implies(X1,not(X0)))),
    inference(superposition,[status(thm)],[d5,d31]) ).

cnf(d33,plain,
    'is$ua$utheorem'(or(implies(X0,not(X1)),X1)),
    inference(resolution,[status(thm)],[d32,d2]) ).

cnf(d34,plain,
    'is$ua$utheorem'(implies(and(X0,X1),X1)),
    inference(demodulation,[status(thm)],[d33,d13]) ).

cnf(d35,plain,
    or(or(X0,X1),X2) = implies(and(not(X0),not(X1)),X2),
    inference(superposition,[status(thm)],[d4,d6]) ).

cnf(d36,plain,
    'is$ua$utheorem'(or(or(X0,X1),not(X1))),
    inference(superposition,[status(thm)],[d35,d34]) ).

cnf(d37,plain,
    'is$ua$utheorem'(or(implies(X0,X1),not(X1))),
    inference(superposition,[status(thm)],[d6,d36]) ).

cnf(d38,plain,
    'is$ua$utheorem'(implies(and(X0,X1),not(not(X1)))),
    inference(superposition,[status(thm)],[d13,d37]) ).

cnf(d39,plain,
    ( 'is$ua$utheorem'(or(X1,not(X0)))
    | ~ 'is$ua$utheorem'(implies(X0,X1)) ),
    inference(superposition,[status(thm)],[d6,d2]) ).

cnf(d40,plain,
    ( ~ 'is$ua$utheorem'(implies(X1,not(X0)))
    | 'is$ua$utheorem'(implies(X0,not(X1))) ),
    inference(superposition,[status(thm)],[d6,d39]) ).

cnf(d41,plain,
    'is$ua$utheorem'(implies(not(X0),not(and(X1,X0)))),
    inference(resolution,[status(thm)],[d40,d38]) ).

cnf(d42,plain,
    'is$ua$utheorem'(or(X0,not(and(X1,X0)))),
    inference(demodulation,[status(thm)],[d41,d5]) ).

cnf(d43,plain,
    'is$ua$utheorem'(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
    inference(resolution,[status(thm)],[c71,c56]) ).

cnf(d44,plain,
    ( 'is$ua$utheorem'(implies(or(X2,X0),or(X2,X1)))
    | ~ 'is$ua$utheorem'(implies(X0,X1)) ),
    inference(resolution,[status(thm)],[d43,d0]) ).

cnf(d45,plain,
    ( 'is$ua$utheorem'(or(X2,X1))
    | ~ 'is$ua$utheorem'(or(X2,X0))
    | ~ 'is$ua$utheorem'(implies(X0,X1)) ),
    inference(resolution,[status(thm)],[d44,d0]) ).

cnf(d46,plain,
    ( 'is$ua$utheorem'(or(X1,X2))
    | ~ 'is$ua$utheorem'(implies(not(and(X0,X1)),X2)) ),
    inference(resolution,[status(thm)],[d45,d42]) ).

cnf(d47,plain,
    ( 'is$ua$utheorem'(or(X1,X2))
    | ~ 'is$ua$utheorem'(or(and(X0,X1),X2)) ),
    inference(demodulation,[status(thm)],[d46,d5]) ).

cnf(d48,plain,
    'is$ua$utheorem'(or(X0,implies(X0,not(X1)))),
    inference(resolution,[status(thm)],[d47,d29]) ).

cnf(d49,plain,
    ( ~ 'is$ua$utheorem'(equiv(X1,X0))
    | X0 = X1 ),
    inference(resolution,[status(thm)],[c72,c7]) ).

cnf(d50,plain,
    'is$ua$utheorem'(implies(or(X0,X0),X0)),
    inference(resolution,[status(thm)],[c67,c48]) ).

cnf(d51,plain,
    'is$ua$utheorem'(implies(implies(X0,not(X0)),not(X0))),
    inference(superposition,[status(thm)],[d6,d50]) ).

cnf(d52,plain,
    'is$ua$utheorem'(or(and(X0,X0),not(X0))),
    inference(demodulation,[status(thm)],[d51,d26]) ).

cnf(d53,plain,
    not(and(or(X0,X1),not(X2))) = or(and(not(X0),not(X1)),X2),
    inference(superposition,[status(thm)],[d4,d4]) ).

cnf(d54,plain,
    implies(or(X0,X1),X2) = or(and(not(X0),not(X1)),X2),
    inference(demodulation,[status(thm)],[d53,d3]) ).

cnf(d55,plain,
    'is$ua$utheorem'(implies(or(X0,X0),not(not(X0)))),
    inference(superposition,[status(thm)],[d54,d52]) ).

cnf(d56,plain,
    ( 'is$ua$utheorem'(not(not(X0)))
    | ~ 'is$ua$utheorem'(or(X0,X0)) ),
    inference(resolution,[status(thm)],[d55,d0]) ).

cnf(d57,plain,
    or(implies(X0,X1),X2) = implies(and(X0,not(X1)),X2),
    inference(superposition,[status(thm)],[d3,d6]) ).

cnf(d58,plain,
    'is$ua$utheorem'(or(X0,or(X1,not(X0)))),
    inference(superposition,[status(thm)],[d5,d30]) ).

cnf(d59,plain,
    'is$ua$utheorem'(or(X0,or(X1,not(X1)))),
    inference(resolution,[status(thm)],[d23,d58]) ).

cnf(d60,plain,
    'is$ua$utheorem'(or(or(X0,not(X0)),X1)),
    inference(resolution,[status(thm)],[d59,d2]) ).

cnf(d61,plain,
    'is$ua$utheorem'(or(implies(X0,not(not(X0))),X1)),
    inference(superposition,[status(thm)],[d6,d60]) ).

cnf(d62,plain,
    'is$ua$utheorem'(implies(and(X0,not(X0)),X1)),
    inference(demodulation,[status(thm)],[d61,d13]) ).

cnf(d63,plain,
    'is$ua$utheorem'(or(implies(X0,X0),X1)),
    inference(demodulation,[status(thm)],[d62,d57]) ).

cnf(d64,plain,
    'is$ua$utheorem'(not(not(implies(X0,X0)))),
    inference(resolution,[status(thm)],[d63,d56]) ).

cnf(d65,plain,
    ( 'is$ua$utheorem'(X1)
    | ~ 'is$ua$utheorem'(not(X0))
    | ~ 'is$ua$utheorem'(or(X0,X1)) ),
    inference(superposition,[status(thm)],[d5,d0]) ).

cnf(d66,plain,
    ( ~ 'is$ua$utheorem'(not(not(X0)))
    | 'is$ua$utheorem'(X1)
    | ~ 'is$ua$utheorem'(implies(X0,X1)) ),
    inference(superposition,[status(thm)],[d6,d65]) ).

cnf(d67,plain,
    ( ~ 'is$ua$utheorem'(implies(implies(X1,X1),X0))
    | 'is$ua$utheorem'(X0) ),
    inference(resolution,[status(thm)],[d66,d64]) ).

cnf(d68,plain,
    ( 'is$ua$utheorem'(implies(X1,X0))
    | ~ 'is$ua$utheorem'(or(X0,not(X1))) ),
    inference(resolution,[status(thm)],[d27,d0]) ).

cnf(d69,plain,
    'is$ua$utheorem'(implies(X0,or(and(X1,X0),not(X1)))),
    inference(resolution,[status(thm)],[d25,d29]) ).

cnf(d70,plain,
    'is$ua$utheorem'(or(and(X0,implies(X1,X1)),not(X0))),
    inference(resolution,[status(thm)],[d67,d69]) ).

cnf(d71,plain,
    'is$ua$utheorem'(implies(X0,and(X0,implies(X1,X1)))),
    inference(resolution,[status(thm)],[d70,d68]) ).

cnf(d72,plain,
    'is$ua$utheorem'(and(implies(X0,X0),implies(X1,X1))),
    inference(resolution,[status(thm)],[d71,d67]) ).

cnf(d73,plain,
    'is$ua$utheorem'(and(or(X0,not(X0)),implies(X1,X1))),
    inference(superposition,[status(thm)],[d5,d72]) ).

cnf(d74,plain,
    'is$ua$utheorem'(and(implies(X0,not(not(X0))),implies(X1,X1))),
    inference(superposition,[status(thm)],[d6,d73]) ).

cnf(d75,plain,
    and(implies(X1,not(X0)),or(X0,X1)) = equiv(X1,not(X0)),
    inference(superposition,[status(thm)],[d5,d17]) ).

cnf(d76,plain,
    and(implies(X1,not(not(X0))),implies(X0,X1)) = equiv(X1,not(not(X0))),
    inference(superposition,[status(thm)],[d6,d75]) ).

cnf(d77,plain,
    'is$ua$utheorem'(equiv(X0,not(not(X0)))),
    inference(superposition,[status(thm)],[d76,d74]) ).

cnf(d78,plain,
    not(not(X0)) = X0,
    inference(resolution,[status(thm)],[d77,d49]) ).

cnf(d79,plain,
    'is$ua$utheorem'(or(X1,implies(X1,X0))),
    inference(superposition,[status(thm)],[d78,d48]) ).

cnf(d80,plain,
    'is$ua$utheorem'(implies(X0,or(X0,X1))),
    inference(resolution,[status(thm)],[d79,d25]) ).

cnf(d81,plain,
    $false,
    inference(resolution,[status(thm)],[d80,d21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL493+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03  % Command  : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36  % Computer : n013.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Fri Sep 25 22:39:21 UTC 2026
% 0.09/0.36  % CPUTime  : 
% 0.09/0.36  Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 89.76/14.36  % SZS status Theorem for theBenchmark.p
% 89.76/14.36  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------