%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL535+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 : n001.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 79.46s 28.85s
% Output : CNFRefutation 79.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 44
% Syntax : Number of formulae : 201 ( 96 unt; 0 def)
% Number of atoms : 336 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 246 ( 111 ~; 107 |; 1 &)
% ( 19 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 27 ( 25 usr; 25 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 225 ( 8 sgn 42 !; 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_1,axiom,
( 'or$u1'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,or(X0,X1))) ) ).
fof(or_2,axiom,
( 'or$u2'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X1,or(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$utheorem'(implies(implies(not(X0),X0),X0)) ) ).
fof(r3,axiom,
( r3
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0))) ) ).
fof(op_or,axiom,
( 'op$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_1,axiom,
'or$u1' ).
fof(hilbert_or_2,axiom,
'or$u2' ).
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(axiom_m9,axiom,
( 'axiom$um9'
<=> ! [X0] : 'is$ua$utheorem'('strict$uimplies'(possibly(possibly(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_m9,conjecture,
'axiom$um9' ).
fof(negated_conjecture,negated_conjecture,
~ 'axiom$um9',
inference(negate_conjecture,[status(cth)],[s1_0_m6s3m9b_axiom_m9]) ).
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(c27,plain,
( 'is$ua$utheorem'(implies(X0,or(X0,X1)))
| ~ 'or$u1' ),
inference(clausification,[status(esa)],[or_1]) ).
cnf(c29,plain,
( 'is$ua$utheorem'(implies(X0,or(X1,X0)))
| ~ 'or$u2' ),
inference(clausification,[status(esa)],[or_2]) ).
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$utheorem'(implies(implies(not(sK87),sK87),sK87))
| cn3 ),
inference(clausification,[status(esa)],[cn3]) ).
cnf(c55,plain,
( 'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(clausification,[status(esa)],[r3]) ).
cnf(c56,plain,
( ~ 'is$ua$utheorem'(implies(or(sK96,sK97),or(sK97,sK96)))
| r3 ),
inference(clausification,[status(esa)],[r3]) ).
cnf(c61,plain,
( not(and(not(X0),not(X1))) = or(X0,X1)
| ~ 'op$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(c77,plain,
'or$u1',
inference(clausification,[status(esa)],[hilbert_or_1]) ).
cnf(c78,plain,
'or$u2',
inference(clausification,[status(esa)],[hilbert_or_2]) ).
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$u5' ),
inference(clausification,[status(esa)],[axiom_5]) ).
cnf(c126,plain,
( 'is$ua$utheorem'('strict$uimplies'(X0,possibly(X0)))
| ~ 'axiom$um6' ),
inference(clausification,[status(esa)],[axiom_m6]) ).
cnf(c127,plain,
( ~ 'is$ua$utheorem'('strict$uimplies'(sK185,possibly(sK185)))
| 'axiom$um6' ),
inference(clausification,[status(esa)],[axiom_m6]) ).
cnf(c133,plain,
( ~ 'is$ua$utheorem'('strict$uimplies'(possibly(possibly(sK195)),possibly(sK195)))
| 'axiom$um9' ),
inference(clausification,[status(esa)],[axiom_m9]) ).
cnf(c136,plain,
( not(necessarily(not(X0))) = possibly(X0)
| ~ 'op$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$u5',
inference(clausification,[status(esa)],[km5_axiom_5]) ).
cnf(c145,plain,
~ 'axiom$um9',
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,
not(and(X0,not(X1))) = implies(X0,X1),
inference(resolution,[status(thm)],[c67,c63]) ).
cnf(d2,plain,
not(and(not(X0),not(X1))) = or(X0,X1),
inference(resolution,[status(thm)],[c1,c61]) ).
cnf(d3,plain,
implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c69,c6]) ).
cnf(d5,plain,
'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1)))),
inference(resolution,[status(thm)],[c76,c25]) ).
cnf(d6,plain,
( 'is$ua$utheorem'(implies(X1,and(X0,X1)))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( 'is$ua$utheorem'(and(X0,X1))
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(resolution,[status(thm)],[c4,c65]) ).
cnf(d9,plain,
( ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(implies(X1,X0))
| 'is$ua$utheorem'(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( 'is$ua$utheorem'(or(X1,X0))
| ~ 'is$ua$utheorem'(or(X0,X1))
| ~ r3 ),
inference(resolution,[status(thm)],[c55,d4]) ).
cnf(d11,plain,
'is$ua$utheorem'(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[c71,c15]) ).
cnf(d12,plain,
'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[c72,c17]) ).
cnf(d13,plain,
( 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
'is$ua$utheorem'(implies(X0,X0)),
inference(resolution,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
'is$ua$utheorem'(or(X0,not(X0))),
inference(superposition,[status(thm)],[d3,d14]) ).
cnf(d16,plain,
( ~ r3
| 'is$ua$utheorem'(or(not(X0),X0)) ),
inference(resolution,[status(thm)],[d15,d10]) ).
cnf(d17,plain,
'is$ua$utheorem'(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(resolution,[status(thm)],[c70,c13]) ).
cnf(d18,plain,
( 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(implies(not(X0),not(X1))) ),
inference(resolution,[status(thm)],[d17,d4]) ).
cnf(d19,plain,
( ~ 'is$ua$utheorem'(or(X0,not(X1)))
| 'is$ua$utheorem'(implies(X1,X0)) ),
inference(demodulation,[status(thm)],[d18,d3]) ).
cnf(d20,plain,
( ~ r3
| 'is$ua$utheorem'(implies(X0,not(not(X0)))) ),
inference(resolution,[status(thm)],[d19,d16]) ).
cnf(d21,plain,
( 'is$ua$utheorem'(equiv(X0,not(not(X0))))
| ~ 'is$ua$utheorem'(implies(not(not(X0)),X0))
| ~ r3 ),
inference(resolution,[status(thm)],[d20,d9]) ).
cnf(d22,plain,
( ~ r3
| 'is$ua$utheorem'(equiv(X0,not(not(X0))))
| ~ 'is$ua$utheorem'(or(not(X0),X0)) ),
inference(demodulation,[status(thm)],[d21,d3]) ).
cnf(d23,plain,
( ~ cn3
| 'is$ua$utheorem'(implies(or(X0,X0),X0)) ),
inference(demodulation,[status(thm)],[c49,d3]) ).
cnf(d24,plain,
( cn3
| ~ 'is$ua$utheorem'(implies(or(sK87,sK87),sK87)) ),
inference(demodulation,[status(thm)],[c50,d3]) ).
cnf(d25,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),
inference(resolution,[status(thm)],[c79,c31]) ).
cnf(d26,plain,
( 'is$ua$utheorem'(implies(implies(X2,X1),implies(or(X0,X2),X1)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d25,d4]) ).
cnf(d27,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)],[d26,d4]) ).
cnf(d28,plain,
( cn3
| ~ 'is$ua$utheorem'(implies(sK87,sK87))
| ~ 'is$ua$utheorem'(implies(sK87,sK87)) ),
inference(resolution,[status(thm)],[d27,d24]) ).
cnf(d29,plain,
cn3,
inference(resolution,[status(thm)],[d14,d28]) ).
cnf(d30,plain,
'is$ua$utheorem'(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[d29,d23]) ).
cnf(d31,plain,
'is$ua$utheorem'(implies(X0,or(X0,X1))),
inference(resolution,[status(thm)],[c77,c27]) ).
cnf(d32,plain,
( 'is$ua$utheorem'(equiv(X0,or(X0,X1)))
| ~ 'is$ua$utheorem'(implies(or(X0,X1),X0)) ),
inference(resolution,[status(thm)],[d9,d31]) ).
cnf(d33,plain,
'is$ua$utheorem'(equiv(X0,or(X0,X0))),
inference(resolution,[status(thm)],[d32,d30]) ).
cnf(d34,plain,
or(X0,X0) = X0,
inference(resolution,[status(thm)],[d33,d0]) ).
cnf(d35,plain,
not(and(not(X2),or(X0,X1))) = or(X2,and(not(X0),not(X1))),
inference(superposition,[status(thm)],[d2,d2]) ).
cnf(d36,plain,
'is$ua$utheorem'(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[d13,d5]) ).
cnf(d37,plain,
'is$ua$utheorem'(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[d3,d36]) ).
cnf(d38,plain,
'is$ua$utheorem'(not(and(not(X0),or(X0,X0)))),
inference(demodulation,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
'is$ua$utheorem'(not(and(not(X0),X0))),
inference(demodulation,[status(thm)],[d38,d34]) ).
cnf(d40,plain,
'is$ua$utheorem'(implies(not(not(X0)),X0)),
inference(superposition,[status(thm)],[d1,d39]) ).
cnf(d41,plain,
'is$ua$utheorem'(or(not(X0),X0)),
inference(demodulation,[status(thm)],[d40,d3]) ).
cnf(d42,plain,
( ~ r3
| 'is$ua$utheorem'(equiv(X0,not(not(X0)))) ),
inference(resolution,[status(thm)],[d41,d22]) ).
cnf(d43,plain,
( not(not(X0)) = X0
| ~ r3 ),
inference(resolution,[status(thm)],[d42,d0]) ).
cnf(d44,plain,
( r3
| ~ 'is$ua$utheorem'(implies(sK96,or(sK97,sK96)))
| ~ 'is$ua$utheorem'(implies(sK97,or(sK97,sK96))) ),
inference(resolution,[status(thm)],[d27,c56]) ).
cnf(d45,plain,
( r3
| ~ 'is$ua$utheorem'(implies(sK96,or(sK97,sK96))) ),
inference(resolution,[status(thm)],[d31,d44]) ).
cnf(d46,plain,
'is$ua$utheorem'(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[c78,c29]) ).
cnf(d47,plain,
r3,
inference(resolution,[status(thm)],[d46,d45]) ).
cnf(d48,plain,
not(not(X0)) = X0,
inference(resolution,[status(thm)],[d47,d43]) ).
cnf(d49,plain,
'is$ua$utheorem'(implies(necessarily(X0),X0)),
inference(resolution,[status(thm)],[c143,c100]) ).
cnf(d50,plain,
( 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(necessarily(X0)) ),
inference(resolution,[status(thm)],[d49,d4]) ).
cnf(d51,plain,
necessarily(implies(X0,X1)) = 'strict$uimplies'(X0,X1),
inference(resolution,[status(thm)],[c3,c138]) ).
cnf(d52,plain,
( 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'('strict$uimplies'(X0,X1)) ),
inference(superposition,[status(thm)],[d51,d50]) ).
cnf(d53,plain,
( ~ 'axiom$um6'
| 'is$ua$utheorem'(implies(X0,possibly(X0))) ),
inference(resolution,[status(thm)],[d52,c126]) ).
cnf(d54,plain,
( ~ 'axiom$um6'
| 'is$ua$utheorem'(or(X0,possibly(not(X0)))) ),
inference(superposition,[status(thm)],[d3,d53]) ).
cnf(d55,plain,
( ~ r3
| 'is$ua$utheorem'(or(possibly(not(X0)),X0))
| ~ 'axiom$um6' ),
inference(resolution,[status(thm)],[d54,d10]) ).
cnf(d56,plain,
( ~ 'axiom$um6'
| ~ r3
| 'is$ua$utheorem'(implies(X0,possibly(not(not(X0))))) ),
inference(resolution,[status(thm)],[d19,d55]) ).
cnf(d57,plain,
( 'is$ua$utheorem'(equiv(X0,possibly(not(not(X0)))))
| ~ 'is$ua$utheorem'(implies(possibly(not(not(X0))),X0))
| ~ 'axiom$um6'
| ~ r3 ),
inference(resolution,[status(thm)],[d56,d9]) ).
cnf(d58,plain,
( ~ 'axiom$um6'
| ~ r3
| 'is$ua$utheorem'(equiv(X0,possibly(not(not(X0)))))
| ~ 'is$ua$utheorem'(implies(possibly(X0),X0)) ),
inference(demodulation,[status(thm)],[d57,d48]) ).
cnf(d59,plain,
( ~ 'axiom$um6'
| ~ r3
| 'is$ua$utheorem'(equiv(X0,possibly(X0)))
| ~ 'is$ua$utheorem'(implies(possibly(X0),X0)) ),
inference(demodulation,[status(thm)],[d58,d48]) ).
cnf(d60,plain,
( ~ 'axiom$um6'
| 'is$ua$utheorem'(equiv(X0,possibly(X0)))
| ~ 'is$ua$utheorem'(implies(possibly(X0),X0)) ),
inference(resolution,[status(thm)],[d47,d59]) ).
cnf(d61,plain,
'is$ua$utheorem'(implies(possibly(X0),necessarily(possibly(X0)))),
inference(resolution,[status(thm)],[c144,c106]) ).
cnf(d62,plain,
( 'is$ua$utheorem'(equiv(possibly(X0),necessarily(possibly(X0))))
| ~ 'is$ua$utheorem'(implies(necessarily(possibly(X0)),possibly(X0))) ),
inference(resolution,[status(thm)],[d9,d61]) ).
cnf(d63,plain,
'is$ua$utheorem'(equiv(possibly(X0),necessarily(possibly(X0)))),
inference(resolution,[status(thm)],[d49,d62]) ).
cnf(d64,plain,
necessarily(possibly(X0)) = possibly(X0),
inference(resolution,[status(thm)],[d63,d0]) ).
cnf(d65,plain,
( 'is$ua$utheorem'(necessarily(X0))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c141,c84]) ).
cnf(d66,plain,
( ~ 'is$ua$utheorem'(implies(X0,X1))
| 'is$ua$utheorem'('strict$uimplies'(X0,X1)) ),
inference(superposition,[status(thm)],[d51,d65]) ).
cnf(d67,plain,
( ~ 'axiom$uB'
| 'is$ua$utheorem'('strict$uimplies'(X0,necessarily(possibly(X0)))) ),
inference(resolution,[status(thm)],[d66,c104]) ).
cnf(d68,plain,
( ~ 'axiom$uB'
| 'is$ua$utheorem'('strict$uimplies'(X0,possibly(X0))) ),
inference(demodulation,[status(thm)],[d67,d64]) ).
cnf(d69,plain,
( 'axiom$um6'
| ~ 'axiom$uB' ),
inference(resolution,[status(thm)],[d68,c127]) ).
cnf(d70,plain,
( 'axiom$uB'
| ~ 'is$ua$utheorem'(implies(sK143,possibly(sK143))) ),
inference(demodulation,[status(thm)],[c105,d64]) ).
cnf(d71,plain,
( 'is$ua$utheorem'(equiv(X0,and(X0,X0)))
| ~ 'is$ua$utheorem'(implies(and(X0,X0),X0)) ),
inference(resolution,[status(thm)],[d9,d36]) ).
cnf(d72,plain,
'is$ua$utheorem'(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c74,c21]) ).
cnf(d73,plain,
'is$ua$utheorem'(equiv(X0,and(X0,X0))),
inference(resolution,[status(thm)],[d72,d71]) ).
cnf(d74,plain,
and(X0,X0) = X0,
inference(resolution,[status(thm)],[d73,d0]) ).
cnf(d75,plain,
not(necessarily(not(X0))) = possibly(X0),
inference(resolution,[status(thm)],[c0,c136]) ).
cnf(d76,plain,
not(and(X1,possibly(X0))) = implies(X1,necessarily(not(X0))),
inference(superposition,[status(thm)],[d75,d1]) ).
cnf(d77,plain,
implies(implies(X0,necessarily(not(X1))),X2) = or(and(X0,possibly(X1)),X2),
inference(superposition,[status(thm)],[d76,d3]) ).
cnf(d78,plain,
( ~ cn3
| 'is$ua$utheorem'(implies(implies(possibly(X0),necessarily(not(X0))),necessarily(not(X0)))) ),
inference(superposition,[status(thm)],[d75,c49]) ).
cnf(d79,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(resolution,[status(thm)],[c73,c19]) ).
cnf(d80,plain,
( 'is$ua$utheorem'(implies(implies(X1,X2),implies(X0,X2)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d79,d4]) ).
cnf(d81,plain,
( 'is$ua$utheorem'(implies(X0,X2))
| ~ 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d80,d4]) ).
cnf(d82,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)],[d81,d78]) ).
cnf(d83,plain,
( ~ cn3
| ~ 'is$ua$utheorem'(implies(necessarily(not(X0)),X1))
| 'is$ua$utheorem'(or(and(possibly(X0),possibly(X0)),X1)) ),
inference(demodulation,[status(thm)],[d82,d77]) ).
cnf(d84,plain,
( ~ cn3
| ~ 'is$ua$utheorem'(implies(necessarily(not(X0)),X1))
| 'is$ua$utheorem'(or(possibly(X0),X1)) ),
inference(demodulation,[status(thm)],[d83,d74]) ).
cnf(d85,plain,
( ~ 'is$ua$utheorem'(implies(necessarily(not(X0)),X1))
| 'is$ua$utheorem'(or(possibly(X0),X1)) ),
inference(resolution,[status(thm)],[d29,d84]) ).
cnf(d86,plain,
'is$ua$utheorem'(or(possibly(X0),not(X0))),
inference(resolution,[status(thm)],[d85,d49]) ).
cnf(d87,plain,
'is$ua$utheorem'(implies(X0,possibly(X0))),
inference(resolution,[status(thm)],[d86,d19]) ).
cnf(d88,plain,
'axiom$uB',
inference(resolution,[status(thm)],[d87,d70]) ).
cnf(d89,plain,
'axiom$um6',
inference(resolution,[status(thm)],[d88,d69]) ).
cnf(d90,plain,
( 'is$ua$utheorem'(equiv(X0,possibly(X0)))
| ~ 'is$ua$utheorem'(implies(possibly(X0),X0)) ),
inference(resolution,[status(thm)],[d89,d60]) ).
cnf(d91,plain,
not(and(possibly(X0),not(X1))) = or(necessarily(not(X0)),X1),
inference(superposition,[status(thm)],[d75,d2]) ).
cnf(d92,plain,
implies(possibly(X0),X1) = or(necessarily(not(X0)),X1),
inference(demodulation,[status(thm)],[d91,d1]) ).
cnf(d93,plain,
not(necessarily(possibly(X0))) = possibly(necessarily(not(X0))),
inference(superposition,[status(thm)],[d75,d75]) ).
cnf(d94,plain,
'is$ua$utheorem'(implies(not(necessarily(possibly(X0))),necessarily(possibly(necessarily(not(X0)))))),
inference(superposition,[status(thm)],[d93,d61]) ).
cnf(d95,plain,
'is$ua$utheorem'(or(necessarily(possibly(X0)),necessarily(possibly(necessarily(not(X0)))))),
inference(demodulation,[status(thm)],[d94,d3]) ).
cnf(d96,plain,
'is$ua$utheorem'(or(necessarily(possibly(X0)),necessarily(not(necessarily(possibly(X0)))))),
inference(demodulation,[status(thm)],[d95,d93]) ).
cnf(d97,plain,
( ~ r3
| 'is$ua$utheorem'(or(necessarily(not(necessarily(possibly(X0)))),necessarily(possibly(X0)))) ),
inference(resolution,[status(thm)],[d96,d10]) ).
cnf(d98,plain,
( ~ r3
| 'is$ua$utheorem'(implies(possibly(necessarily(possibly(X0))),necessarily(possibly(X0)))) ),
inference(demodulation,[status(thm)],[d97,d92]) ).
cnf(d99,plain,
( ~ r3
| 'is$ua$utheorem'(implies(possibly(possibly(X0)),necessarily(possibly(X0)))) ),
inference(demodulation,[status(thm)],[d98,d64]) ).
cnf(d100,plain,
( ~ r3
| 'is$ua$utheorem'(implies(possibly(possibly(X0)),possibly(X0))) ),
inference(demodulation,[status(thm)],[d99,d64]) ).
cnf(d101,plain,
'is$ua$utheorem'(implies(possibly(possibly(X0)),possibly(X0))),
inference(resolution,[status(thm)],[d47,d100]) ).
cnf(d102,plain,
'is$ua$utheorem'(equiv(possibly(X0),possibly(possibly(X0)))),
inference(resolution,[status(thm)],[d101,d90]) ).
cnf(d103,plain,
possibly(possibly(X0)) = possibly(X0),
inference(resolution,[status(thm)],[d102,d0]) ).
cnf(d104,plain,
~ 'is$ua$utheorem'('strict$uimplies'(possibly(possibly(sK195)),possibly(sK195))),
inference(resolution,[status(thm)],[c145,c133]) ).
cnf(d105,plain,
~ 'is$ua$utheorem'('strict$uimplies'(possibly(sK195),possibly(sK195))),
inference(demodulation,[status(thm)],[d104,d103]) ).
cnf(d106,plain,
'is$ua$utheorem'('strict$uimplies'(X0,X0)),
inference(resolution,[status(thm)],[d14,d66]) ).
cnf(d107,plain,
$false,
inference(resolution,[status(thm)],[d106,d105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL535+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.44 % Computer : n001.cluster.edu
% 0.15/5.44 % Model : x86_64 x86_64
% 0.15/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.44 % Memory : 8046.5625MB
% 0.15/5.44 % OS : Linux 6.8.0-71-generic
% 0.15/5.45 % CPULimit : 300
% 0.15/5.45 % WCLimit : 300
% 0.15/5.45 % DateTime : Fri Sep 25 22:48:46 UTC 2026
% 0.15/5.45 % CPUTime :
% 0.15/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 79.46/28.85 % SZS status Theorem for theBenchmark.p
% 79.46/28.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------