%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL549+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 : n004.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 07:54:50 AM UTC 2026
% Result : Theorem 49.87s 28.53s
% Output : CNFRefutation 49.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 40
% Syntax : Number of formulae : 154 ( 78 unt; 0 def)
% Number of atoms : 257 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 179 ( 76 ~; 75 |; 2 &)
% ( 17 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 25 ( 23 usr; 23 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 151 ( 6 sgn 36 !; 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(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(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$utheorem'(implies(X0,or(X0,X1))) ) ).
fof(or_3,axiom,
( 'or$u3'
<=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ) ).
fof(kn1,axiom,
( kn1
<=> ! [X0] : 'is$ua$utheorem'(implies(X0,and(X0,X0))) ) ).
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$uponens' ).
fof(hilbert_implies_1,axiom,
'implies$u1' ).
fof(hilbert_implies_2,axiom,
'implies$u2' ).
fof(hilbert_and_1,axiom,
'and$u1' ).
fof(hilbert_and_3,axiom,
'and$u3' ).
fof(hilbert_or_1,axiom,
'or$u1' ).
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$utheorem'(necessarily(X0)) ) ) ).
fof(adjunction,axiom,
( adjunction
<=> ! [X0,X1] :
( ( 'is$ua$utheorem'(X1)
& 'is$ua$utheorem'(X0) )
=> 'is$ua$utheorem'(and(X0,X1)) ) ) ).
fof(axiom_M,axiom,
( 'axiom$uM'
<=> ! [X0] : 'is$ua$utheorem'(implies(necessarily(X0),X0)) ) ).
fof(axiom_4,axiom,
( 'axiom$u4'
<=> ! [X0] : 'is$ua$utheorem'(implies(necessarily(X0),necessarily(necessarily(X0)))) ) ).
fof(axiom_B,axiom,
( 'axiom$uB'
<=> ! [X0] : 'is$ua$utheorem'(implies(X0,necessarily(possibly(X0)))) ) ).
fof(axiom_5,axiom,
( 'axiom$u5'
<=> ! [X0] : 'is$ua$utheorem'(implies(possibly(X0),necessarily(possibly(X0)))) ) ).
fof(axiom_m10,axiom,
( 'axiom$um10'
<=> ! [X0] : 'is$ua$utheorem'('strict$uimplies'(possibly(X0),necessarily(possibly(X0)))) ) ).
fof(op_possibly,axiom,
( 'op$upossibly'
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ) ).
fof(op_strict_implies,axiom,
( 'op$ustrict$uimplies'
=> ! [X0,X1] : 'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1)) ) ).
fof(km4b_necessitation,axiom,
necessitation ).
fof(km4b_axiom_M,axiom,
'axiom$uM' ).
fof(km4b_axiom_4,axiom,
'axiom$u4' ).
fof(km4b_axiom_B,axiom,
'axiom$uB' ).
fof(s1_0_m10_axiom_m10,conjecture,
'axiom$um10' ).
fof(negated_conjecture,negated_conjecture,
~ 'axiom$um10',
inference(negate_conjecture,[status(cth)],[s1_0_m10_axiom_m10]) ).
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$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0)
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(c10,plain,
( X0 = X1
| ~ 'is$ua$utheorem'(equiv(X0,X1))
| ~ 'substitution$uof$uequivalents' ),
inference(clausification,[status(esa)],[substitution_of_equivalents]) ).
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(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$u1' ),
inference(clausification,[status(esa)],[or_1]) ).
cnf(c31,plain,
( 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))
| ~ 'or$u3' ),
inference(clausification,[status(esa)],[or_3]) ).
cnf(c39,plain,
( 'is$ua$utheorem'(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(clausification,[status(esa)],[kn1]) ).
cnf(c40,plain,
( ~ 'is$ua$utheorem'(implies(sK65,and(sK65,sK65)))
| kn1 ),
inference(clausification,[status(esa)],[kn1]) ).
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,
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ 'op$uor' ),
inference(clausification,[status(esa)],[op_or]) ).
cnf(c63,plain,
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ 'op$uimplies$uand' ),
inference(clausification,[status(esa)],[op_implies_and]) ).
cnf(c65,plain,
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ 'op$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$uponens',
inference(clausification,[status(esa)],[hilbert_modus_ponens]) ).
cnf(c71,plain,
'implies$u1',
inference(clausification,[status(esa)],[hilbert_implies_1]) ).
cnf(c72,plain,
'implies$u2',
inference(clausification,[status(esa)],[hilbert_implies_2]) ).
cnf(c74,plain,
'and$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(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$utheorem'(X0)
| ~ necessitation ),
inference(clausification,[status(esa)],[necessitation]) ).
cnf(c91,plain,
( 'is$ua$utheorem'(and(X0,X1))
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0)
| ~ adjunction ),
inference(clausification,[status(esa)],[adjunction]) ).
cnf(c92,plain,
( 'is$ua$utheorem'(sK128)
| adjunction ),
inference(clausification,[status(esa)],[adjunction]) ).
cnf(c93,plain,
( 'is$ua$utheorem'(sK129)
| adjunction ),
inference(clausification,[status(esa)],[adjunction]) ).
cnf(c94,plain,
( ~ 'is$ua$utheorem'(and(sK128,sK129))
| adjunction ),
inference(clausification,[status(esa)],[adjunction]) ).
cnf(c100,plain,
( 'is$ua$utheorem'(implies(necessarily(X0),X0))
| ~ 'axiom$uM' ),
inference(clausification,[status(esa)],[axiom_M]) ).
cnf(c102,plain,
( 'is$ua$utheorem'(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ 'axiom$u4' ),
inference(clausification,[status(esa)],[axiom_4]) ).
cnf(c104,plain,
( 'is$ua$utheorem'(implies(X0,necessarily(possibly(X0))))
| ~ 'axiom$uB' ),
inference(clausification,[status(esa)],[axiom_B]) ).
cnf(c106,plain,
( 'is$ua$utheorem'(implies(possibly(X0),necessarily(possibly(X0))))
| ~ 'axiom$u5' ),
inference(clausification,[status(esa)],[axiom_5]) ).
cnf(c107,plain,
( ~ 'is$ua$utheorem'(implies(possibly(sK145),necessarily(possibly(sK145))))
| 'axiom$u5' ),
inference(clausification,[status(esa)],[axiom_5]) ).
cnf(c135,plain,
( ~ 'is$ua$utheorem'('strict$uimplies'(possibly(sK197),necessarily(possibly(sK197))))
| 'axiom$um10' ),
inference(clausification,[status(esa)],[axiom_m10]) ).
cnf(c136,plain,
( possibly(X0) = not(necessarily(not(X0)))
| ~ 'op$upossibly' ),
inference(clausification,[status(esa)],[op_possibly]) ).
cnf(c138,plain,
( 'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1))
| ~ 'op$ustrict$uimplies' ),
inference(clausification,[status(esa)],[op_strict_implies]) ).
cnf(c141,plain,
necessitation,
inference(clausification,[status(esa)],[km4b_necessitation]) ).
cnf(c143,plain,
'axiom$uM',
inference(clausification,[status(esa)],[km4b_axiom_M]) ).
cnf(c144,plain,
'axiom$u4',
inference(clausification,[status(esa)],[km4b_axiom_4]) ).
cnf(c145,plain,
'axiom$uB',
inference(clausification,[status(esa)],[km4b_axiom_B]) ).
cnf(c146,plain,
~ 'axiom$um10',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'('strict$uimplies'(possibly(sK197),necessarily(possibly(sK197)))),
inference(resolution,[status(thm)],[c146,c135]) ).
cnf(d1,plain,
( 'is$ua$utheorem'(necessarily(X0))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c141,c84]) ).
cnf(d2,plain,
'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1)),
inference(resolution,[status(thm)],[c3,c138]) ).
cnf(d3,plain,
( ~ 'is$ua$utheorem'(implies(X0,X1))
| 'is$ua$utheorem'('strict$uimplies'(X0,X1)) ),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ 'axiom$u5'
| 'is$ua$utheorem'('strict$uimplies'(possibly(X0),necessarily(possibly(X0)))) ),
inference(resolution,[status(thm)],[d3,c106]) ).
cnf(d5,plain,
~ 'axiom$u5',
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
~ 'is$ua$utheorem'(implies(possibly(sK145),necessarily(possibly(sK145)))),
inference(resolution,[status(thm)],[d5,c107]) ).
cnf(d7,plain,
( ~ 'is$ua$utheorem'(equiv(X0,X1))
| X0 = X1 ),
inference(resolution,[status(thm)],[c83,c10]) ).
cnf(d8,plain,
implies(X0,X1) = not(and(X0,not(X1))),
inference(resolution,[status(thm)],[c67,c63]) ).
cnf(d9,plain,
or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c1,c61]) ).
cnf(d10,plain,
or(X0,X1) = implies(not(X0),X1),
inference(demodulation,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( ~ cn3
| 'is$ua$utheorem'(implies(or(X0,X0),X0)) ),
inference(demodulation,[status(thm)],[c49,d10]) ).
cnf(d12,plain,
equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(resolution,[status(thm)],[c4,c65]) ).
cnf(d13,plain,
( ~ adjunction
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(implies(X1,X0))
| 'is$ua$utheorem'(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[d12,c91]) ).
cnf(d14,plain,
( ~ cn3
| ~ adjunction
| 'is$ua$utheorem'(equiv(or(X0,X0),X0))
| ~ 'is$ua$utheorem'(implies(X0,or(X0,X0))) ),
inference(resolution,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
'is$ua$utheorem'(implies(X0,or(X0,X1))),
inference(resolution,[status(thm)],[c77,c27]) ).
cnf(d16,plain,
( ~ adjunction
| ~ cn3
| 'is$ua$utheorem'(equiv(or(X0,X0),X0)) ),
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c69,c6]) ).
cnf(d18,plain,
'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1)))),
inference(resolution,[status(thm)],[c76,c25]) ).
cnf(d19,plain,
( 'is$ua$utheorem'(implies(X1,and(X0,X1)))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d17,d18]) ).
cnf(d20,plain,
( 'is$ua$utheorem'(and(X0,X1))
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
( adjunction
| ~ 'is$ua$utheorem'(sK128)
| ~ 'is$ua$utheorem'(sK129) ),
inference(resolution,[status(thm)],[d20,c94]) ).
cnf(d22,plain,
( adjunction
| adjunction
| ~ 'is$ua$utheorem'(sK128) ),
inference(resolution,[status(thm)],[d21,c93]) ).
cnf(d23,plain,
( adjunction
| adjunction ),
inference(resolution,[status(thm)],[d22,c92]) ).
cnf(d24,plain,
( ~ cn3
| 'is$ua$utheorem'(equiv(or(X0,X0),X0)) ),
inference(resolution,[status(thm)],[d23,d16]) ).
cnf(d25,plain,
( or(X0,X0) = X0
| ~ cn3 ),
inference(resolution,[status(thm)],[d24,d7]) ).
cnf(d26,plain,
( cn3
| ~ 'is$ua$utheorem'(implies(or(sK87,sK87),sK87)) ),
inference(demodulation,[status(thm)],[c50,d10]) ).
cnf(d27,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),
inference(resolution,[status(thm)],[c79,c31]) ).
cnf(d28,plain,
( 'is$ua$utheorem'(implies(implies(X2,X1),implies(or(X0,X2),X1)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d17,d27]) ).
cnf(d29,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)],[d28,d17]) ).
cnf(d30,plain,
( cn3
| ~ 'is$ua$utheorem'(implies(sK87,sK87))
| ~ 'is$ua$utheorem'(implies(sK87,sK87)) ),
inference(resolution,[status(thm)],[d29,d26]) ).
cnf(d31,plain,
'is$ua$utheorem'(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[c71,c15]) ).
cnf(d32,plain,
'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[c72,c17]) ).
cnf(d33,plain,
( 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[d17,d32]) ).
cnf(d34,plain,
'is$ua$utheorem'(implies(X0,X0)),
inference(resolution,[status(thm)],[d33,d31]) ).
cnf(d35,plain,
cn3,
inference(resolution,[status(thm)],[d34,d30]) ).
cnf(d36,plain,
or(X0,X0) = X0,
inference(resolution,[status(thm)],[d35,d25]) ).
cnf(d37,plain,
( ~ kn1
| ~ adjunction
| 'is$ua$utheorem'(equiv(X0,and(X0,X0)))
| ~ 'is$ua$utheorem'(implies(and(X0,X0),X0)) ),
inference(resolution,[status(thm)],[d13,c39]) ).
cnf(d38,plain,
'is$ua$utheorem'(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c74,c21]) ).
cnf(d39,plain,
( ~ adjunction
| ~ kn1
| 'is$ua$utheorem'(equiv(X0,and(X0,X0))) ),
inference(resolution,[status(thm)],[d38,d37]) ).
cnf(d40,plain,
'is$ua$utheorem'(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[d33,d18]) ).
cnf(d41,plain,
kn1,
inference(resolution,[status(thm)],[d40,c40]) ).
cnf(d42,plain,
( ~ adjunction
| 'is$ua$utheorem'(equiv(X0,and(X0,X0))) ),
inference(resolution,[status(thm)],[d41,d39]) ).
cnf(d43,plain,
'is$ua$utheorem'(equiv(X0,and(X0,X0))),
inference(resolution,[status(thm)],[d23,d42]) ).
cnf(d44,plain,
X0 = and(X0,X0),
inference(resolution,[status(thm)],[d43,d7]) ).
cnf(d45,plain,
implies(not(X0),X0) = not(not(X0)),
inference(superposition,[status(thm)],[d44,d8]) ).
cnf(d46,plain,
or(X0,X0) = not(not(X0)),
inference(demodulation,[status(thm)],[d45,d10]) ).
cnf(d47,plain,
X0 = not(not(X0)),
inference(demodulation,[status(thm)],[d46,d36]) ).
cnf(d48,plain,
possibly(X0) = not(necessarily(not(X0))),
inference(resolution,[status(thm)],[c0,c136]) ).
cnf(d49,plain,
possibly(not(X0)) = not(necessarily(X0)),
inference(superposition,[status(thm)],[d47,d48]) ).
cnf(d50,plain,
'is$ua$utheorem'(implies(necessarily(X0),necessarily(necessarily(X0)))),
inference(resolution,[status(thm)],[c144,c102]) ).
cnf(d51,plain,
( ~ adjunction
| 'is$ua$utheorem'(equiv(necessarily(X0),necessarily(necessarily(X0))))
| ~ 'is$ua$utheorem'(implies(necessarily(necessarily(X0)),necessarily(X0))) ),
inference(resolution,[status(thm)],[d13,d50]) ).
cnf(d52,plain,
'is$ua$utheorem'(implies(necessarily(X0),X0)),
inference(resolution,[status(thm)],[c143,c100]) ).
cnf(d53,plain,
( ~ adjunction
| 'is$ua$utheorem'(equiv(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(resolution,[status(thm)],[d52,d51]) ).
cnf(d54,plain,
'is$ua$utheorem'(equiv(necessarily(X0),necessarily(necessarily(X0)))),
inference(resolution,[status(thm)],[d23,d53]) ).
cnf(d55,plain,
necessarily(X0) = necessarily(necessarily(X0)),
inference(resolution,[status(thm)],[d54,d7]) ).
cnf(d56,plain,
possibly(not(necessarily(X0))) = not(necessarily(X0)),
inference(superposition,[status(thm)],[d55,d49]) ).
cnf(d57,plain,
possibly(possibly(not(X0))) = not(necessarily(X0)),
inference(demodulation,[status(thm)],[d56,d49]) ).
cnf(d58,plain,
possibly(possibly(not(X0))) = possibly(not(X0)),
inference(demodulation,[status(thm)],[d57,d49]) ).
cnf(d59,plain,
'is$ua$utheorem'(implies(X0,necessarily(possibly(X0)))),
inference(resolution,[status(thm)],[c145,c104]) ).
cnf(d60,plain,
'is$ua$utheorem'(or(X0,necessarily(possibly(not(X0))))),
inference(superposition,[status(thm)],[d10,d59]) ).
cnf(d61,plain,
or(necessarily(not(X0)),X1) = implies(possibly(X0),X1),
inference(superposition,[status(thm)],[d48,d10]) ).
cnf(d62,plain,
'is$ua$utheorem'(implies(possibly(X0),necessarily(possibly(not(necessarily(not(X0))))))),
inference(superposition,[status(thm)],[d61,d60]) ).
cnf(d63,plain,
'is$ua$utheorem'(implies(possibly(X0),necessarily(possibly(possibly(not(not(X0))))))),
inference(demodulation,[status(thm)],[d62,d49]) ).
cnf(d64,plain,
'is$ua$utheorem'(implies(possibly(X0),necessarily(possibly(not(not(X0)))))),
inference(demodulation,[status(thm)],[d63,d58]) ).
cnf(d65,plain,
'is$ua$utheorem'(implies(possibly(X0),necessarily(possibly(X0)))),
inference(demodulation,[status(thm)],[d64,d47]) ).
cnf(d66,plain,
$false,
inference(resolution,[status(thm)],[d65,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL549+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 22:43:37 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.87/28.53 % SZS status Theorem for theBenchmark.p
% 49.87/28.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------