%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL517+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 : n003.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 07:54:46 AM UTC 2026
% Result : Theorem 173.86s 37.04s
% Output : CNFRefutation 173.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 19
% Syntax : Number of formulae : 157 ( 68 unt; 0 def)
% Number of atoms : 276 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 232 ( 113 ~; 106 |; 1 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 274 ( 41 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(luka_op_or,axiom,
'op$uor' ).
fof(luka_op_equiv,axiom,
'op$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$utheorem'(equiv(X0,X1))
=> X0 = X1 ) ) ).
fof(kn1,axiom,
( kn1
<=> ! [X0] : 'is$ua$utheorem'(implies(X0,and(X0,X0))) ) ).
fof(kn2,axiom,
( kn2
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(and(X0,X1),X0)) ) ).
fof(kn3,axiom,
( kn3
<=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ) ).
fof(cn3,axiom,
( cn3
<=> ! [X0] : 'is$ua$utheorem'(implies(implies(not(X0),X0),X0)) ) ).
fof(r1,axiom,
( r1
<=> ! [X0] : 'is$ua$utheorem'(implies(or(X0,X0),X0)) ) ).
fof(op_or,axiom,
( 'op$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$uequiv'
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ) ).
fof(rosser_op_implies_and,axiom,
'op$uimplies$uand' ).
fof(rosser_modus_ponens,axiom,
'modus$uponens' ).
fof(rosser_kn1,axiom,
kn1 ).
fof(rosser_kn2,axiom,
kn2 ).
fof(rosser_kn3,axiom,
kn3 ).
fof(use_substitution_of_equivalents,axiom,
'substitution$uof$uequivalents' ).
fof(luka_cn3,conjecture,
cn3 ).
fof(negated_conjecture,negated_conjecture,
~ cn3,
inference(negate_conjecture,[status(cth)],[luka_cn3]) ).
cnf(c0,plain,
'op$uor',
inference(clausification,[status(esa)],[luka_op_or]) ).
cnf(c2,plain,
'op$uequiv',
inference(clausification,[status(esa)],[luka_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$uequivalents' ),
inference(clausification,[status(esa)],[substitution_of_equivalents]) ).
cnf(c36,plain,
( 'is$ua$utheorem'(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(clausification,[status(esa)],[kn1]) ).
cnf(c38,plain,
( 'is$ua$utheorem'(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(clausification,[status(esa)],[kn2]) ).
cnf(c40,plain,
( 'is$ua$utheorem'(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(clausification,[status(esa)],[kn3]) ).
cnf(c47,plain,
( ~ 'is$ua$utheorem'(implies(implies(not(sK87),sK87),sK87))
| cn3 ),
inference(clausification,[status(esa)],[cn3]) ).
cnf(c48,plain,
( 'is$ua$utheorem'(implies(or(X0,X0),X0))
| ~ r1 ),
inference(clausification,[status(esa)],[r1]) ).
cnf(c49,plain,
( ~ 'is$ua$utheorem'(implies(or(sK89,sK89),sK89))
| r1 ),
inference(clausification,[status(esa)],[r1]) ).
cnf(c58,plain,
( not(and(not(X0),not(X1))) = or(X0,X1)
| ~ 'op$uor' ),
inference(clausification,[status(esa)],[op_or]) ).
cnf(c60,plain,
( not(and(X0,not(X1))) = implies(X0,X1)
| ~ 'op$uimplies$uand' ),
inference(clausification,[status(esa)],[op_implies_and]) ).
cnf(c62,plain,
( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1)
| ~ 'op$uequiv' ),
inference(clausification,[status(esa)],[op_equiv]) ).
cnf(c64,plain,
'op$uimplies$uand',
inference(clausification,[status(esa)],[rosser_op_implies_and]) ).
cnf(c66,plain,
'modus$uponens',
inference(clausification,[status(esa)],[rosser_modus_ponens]) ).
cnf(c67,plain,
kn1,
inference(clausification,[status(esa)],[rosser_kn1]) ).
cnf(c68,plain,
kn2,
inference(clausification,[status(esa)],[rosser_kn2]) ).
cnf(c69,plain,
kn3,
inference(clausification,[status(esa)],[rosser_kn3]) ).
cnf(c70,plain,
'substitution$uof$uequivalents',
inference(clausification,[status(esa)],[use_substitution_of_equivalents]) ).
cnf(c71,plain,
~ cn3,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(resolution,[status(thm)],[c64,c60]) ).
cnf(d1,plain,
not(and(not(X0),not(X1))) = or(X0,X1),
inference(resolution,[status(thm)],[c0,c58]) ).
cnf(d2,plain,
implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
~ 'is$ua$utheorem'(implies(implies(not(sK87),sK87),sK87)),
inference(resolution,[status(thm)],[c71,c47]) ).
cnf(d4,plain,
~ 'is$ua$utheorem'(implies(or(sK87,sK87),sK87)),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
~ r1,
inference(resolution,[status(thm)],[d4,c48]) ).
cnf(d6,plain,
~ 'is$ua$utheorem'(implies(or(sK89,sK89),sK89)),
inference(resolution,[status(thm)],[d5,c49]) ).
cnf(d7,plain,
not(and(not(X2),or(X0,X1))) = or(X2,and(not(X0),not(X1))),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d8,plain,
'is$ua$utheorem'(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[c67,c36]) ).
cnf(d9,plain,
'is$ua$utheorem'(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[d2,d8]) ).
cnf(d10,plain,
'is$ua$utheorem'(not(and(not(X0),or(X0,X0)))),
inference(demodulation,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c66,c3]) ).
cnf(d12,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(not(X0))
| ~ 'is$ua$utheorem'(or(X0,X1)) ),
inference(superposition,[status(thm)],[d2,d11]) ).
cnf(d13,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(resolution,[status(thm)],[c69,c40]) ).
cnf(d14,plain,
( 'is$ua$utheorem'(implies(not(and(X1,X2)),not(and(X2,X0))))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
( 'is$ua$utheorem'(or(and(X0,X1),not(and(X1,X2))))
| ~ 'is$ua$utheorem'(implies(X2,X0)) ),
inference(demodulation,[status(thm)],[d14,d2]) ).
cnf(d16,plain,
( ~ 'is$ua$utheorem'(implies(not(X1),X2))
| 'is$ua$utheorem'(or(and(X2,X0),implies(X0,X1))) ),
inference(superposition,[status(thm)],[d0,d15]) ).
cnf(d17,plain,
( 'is$ua$utheorem'(or(and(X1,X2),implies(X2,X0)))
| ~ 'is$ua$utheorem'(or(X0,X1)) ),
inference(demodulation,[status(thm)],[d16,d2]) ).
cnf(d18,plain,
( ~ 'is$ua$utheorem'(not(and(X1,X2)))
| 'is$ua$utheorem'(implies(X2,X0))
| ~ 'is$ua$utheorem'(or(X0,X1)) ),
inference(resolution,[status(thm)],[d17,d12]) ).
cnf(d19,plain,
( ~ 'is$ua$utheorem'(or(X1,not(X0)))
| 'is$ua$utheorem'(implies(or(X0,X0),X1)) ),
inference(resolution,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
~ 'is$ua$utheorem'(or(sK89,not(sK89))),
inference(resolution,[status(thm)],[d19,d6]) ).
cnf(d21,plain,
'is$ua$utheorem'(implies(implies(X2,X0),implies(implies(X0,X1),not(and(not(X1),X2))))),
inference(superposition,[status(thm)],[d0,d13]) ).
cnf(d22,plain,
'is$ua$utheorem'(implies(or(X0,X1),implies(implies(X1,X2),not(and(not(X2),not(X0)))))),
inference(superposition,[status(thm)],[d2,d21]) ).
cnf(d23,plain,
'is$ua$utheorem'(implies(or(X1,X2),implies(implies(X2,X0),implies(not(X0),X1)))),
inference(demodulation,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
'is$ua$utheorem'(implies(or(X1,X2),implies(implies(X2,X0),or(X0,X1)))),
inference(demodulation,[status(thm)],[d23,d2]) ).
cnf(d25,plain,
( 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(or(X1,X1))
| ~ 'is$ua$utheorem'(or(X0,not(X1))) ),
inference(resolution,[status(thm)],[d19,d11]) ).
cnf(d26,plain,
implies(implies(X0,X1),X2) = or(and(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d0,d2]) ).
cnf(d27,plain,
'is$ua$utheorem'(implies(implies(not(X1),X2),implies(not(and(X2,not(X0))),or(X0,X1)))),
inference(superposition,[status(thm)],[d1,d13]) ).
cnf(d28,plain,
'is$ua$utheorem'(implies(or(X0,X1),implies(not(and(X1,not(X2))),or(X2,X0)))),
inference(demodulation,[status(thm)],[d27,d2]) ).
cnf(d29,plain,
'is$ua$utheorem'(implies(or(X2,X0),or(and(X0,not(X1)),or(X1,X2)))),
inference(demodulation,[status(thm)],[d28,d2]) ).
cnf(d30,plain,
( 'is$ua$utheorem'(or(and(X1,not(X2)),or(X2,X0)))
| ~ 'is$ua$utheorem'(or(X0,X1)) ),
inference(resolution,[status(thm)],[d29,d11]) ).
cnf(d31,plain,
( 'is$ua$utheorem'(implies(implies(X0,X1),or(X1,X2)))
| ~ 'is$ua$utheorem'(or(X2,X0)) ),
inference(demodulation,[status(thm)],[d30,d26]) ).
cnf(d32,plain,
( 'is$ua$utheorem'(or(X2,X0))
| ~ 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(or(X0,X1)) ),
inference(resolution,[status(thm)],[d31,d11]) ).
cnf(d33,plain,
'is$ua$utheorem'(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c68,c38]) ).
cnf(d34,plain,
( 'is$ua$utheorem'(implies(implies(X1,X2),not(and(not(X2),X0))))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d21,d11]) ).
cnf(d35,plain,
( 'is$ua$utheorem'(not(and(not(X2),X0)))
| ~ 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d34,d11]) ).
cnf(d36,plain,
( 'is$ua$utheorem'(not(and(not(X1),X0)))
| ~ 'is$ua$utheorem'(implies(and(X0,X0),X1)) ),
inference(resolution,[status(thm)],[d35,d8]) ).
cnf(d37,plain,
'is$ua$utheorem'(not(and(not(X0),X0))),
inference(resolution,[status(thm)],[d36,d33]) ).
cnf(d38,plain,
'is$ua$utheorem'(implies(not(not(X0)),X0)),
inference(superposition,[status(thm)],[d0,d37]) ).
cnf(d39,plain,
'is$ua$utheorem'(or(not(X0),X0)),
inference(demodulation,[status(thm)],[d38,d2]) ).
cnf(d40,plain,
( 'is$ua$utheorem'(or(X1,not(X0)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d39,d32]) ).
cnf(d41,plain,
( ~ 'is$ua$utheorem'(or(X0,X0))
| 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d40,d25]) ).
cnf(d42,plain,
( ~ 'is$ua$utheorem'(or(X1,not(X0)))
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d37,d18]) ).
cnf(d43,plain,
'is$ua$utheorem'(implies(X0,not(not(X0)))),
inference(resolution,[status(thm)],[d42,d39]) ).
cnf(d44,plain,
'is$ua$utheorem'(or(X0,not(not(not(X0))))),
inference(superposition,[status(thm)],[d2,d43]) ).
cnf(d45,plain,
( 'is$ua$utheorem'(or(X1,X0))
| ~ 'is$ua$utheorem'(implies(not(not(not(X0))),X1)) ),
inference(resolution,[status(thm)],[d44,d32]) ).
cnf(d46,plain,
( 'is$ua$utheorem'(or(X1,X0))
| ~ 'is$ua$utheorem'(or(not(not(X0)),X1)) ),
inference(demodulation,[status(thm)],[d45,d2]) ).
cnf(d47,plain,
( ~ 'is$ua$utheorem'(implies(X0,not(not(X1))))
| 'is$ua$utheorem'(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[d46,d40]) ).
cnf(d48,plain,
'is$ua$utheorem'(or(not(and(not(not(X0)),X1)),X0)),
inference(resolution,[status(thm)],[d47,d33]) ).
cnf(d49,plain,
'is$ua$utheorem'(implies(X0,not(and(not(not(not(X0))),X1)))),
inference(resolution,[status(thm)],[d48,d42]) ).
cnf(d50,plain,
( ~ 'is$ua$utheorem'(equiv(X1,X0))
| X0 = X1 ),
inference(resolution,[status(thm)],[c70,c7]) ).
cnf(d51,plain,
( ~ 'is$ua$utheorem'(not(X1))
| 'is$ua$utheorem'(not(X0))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d40,d12]) ).
cnf(d52,plain,
( 'is$ua$utheorem'(not(and(X0,X1)))
| ~ 'is$ua$utheorem'(not(X0)) ),
inference(resolution,[status(thm)],[d51,d33]) ).
cnf(d53,plain,
( ~ 'is$ua$utheorem'(not(X0))
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(superposition,[status(thm)],[d0,d52]) ).
cnf(d54,plain,
( 'is$ua$utheorem'(not(not(X0)))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d43,d11]) ).
cnf(d55,plain,
( ~ 'is$ua$utheorem'(not(not(X0)))
| 'is$ua$utheorem'(or(X0,X1)) ),
inference(superposition,[status(thm)],[d2,d53]) ).
cnf(d56,plain,
( ~ 'is$ua$utheorem'(X0)
| 'is$ua$utheorem'(or(X0,X1)) ),
inference(resolution,[status(thm)],[d55,d54]) ).
cnf(d57,plain,
( 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d56,d42]) ).
cnf(d58,plain,
( ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(or(X0,X1)) ),
inference(superposition,[status(thm)],[d2,d57]) ).
cnf(d59,plain,
( 'is$ua$utheorem'(or(X1,X2))
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d58,d32]) ).
cnf(d60,plain,
( 'is$ua$utheorem'(or(and(X0,X0),X1))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d59,d8]) ).
cnf(d61,plain,
( ~ 'is$ua$utheorem'(implies(and(X0,X0),X1))
| 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d60,d41]) ).
cnf(d62,plain,
( ~ 'is$ua$utheorem'(implies(X1,X2))
| 'is$ua$utheorem'(implies(and(X0,X1),and(X2,X0))) ),
inference(resolution,[status(thm)],[d42,d15]) ).
cnf(d63,plain,
( ~ 'is$ua$utheorem'(X0)
| 'is$ua$utheorem'(and(X1,X0))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d62,d61]) ).
cnf(d64,plain,
'is$ua$utheorem'(not(and(not(not(not(and(X0,X0)))),X0))),
inference(resolution,[status(thm)],[d43,d36]) ).
cnf(d65,plain,
'is$ua$utheorem'(implies(not(not(not(and(not(X0),not(X0))))),X0)),
inference(superposition,[status(thm)],[d0,d64]) ).
cnf(d66,plain,
'is$ua$utheorem'(or(not(not(and(not(X0),not(X0)))),X0)),
inference(demodulation,[status(thm)],[d65,d2]) ).
cnf(d67,plain,
'is$ua$utheorem'(or(not(implies(not(X0),X0)),X0)),
inference(demodulation,[status(thm)],[d66,d0]) ).
cnf(d68,plain,
'is$ua$utheorem'(or(not(or(X0,X0)),X0)),
inference(demodulation,[status(thm)],[d67,d2]) ).
cnf(d69,plain,
( 'is$ua$utheorem'(not(and(not(X0),X1)))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d57,d36]) ).
cnf(d70,plain,
( ~ 'is$ua$utheorem'(or(X2,not(X0)))
| 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d69,d18]) ).
cnf(d71,plain,
( ~ 'is$ua$utheorem'(implies(X0,X2))
| 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d70,d40]) ).
cnf(d72,plain,
( 'is$ua$utheorem'(implies(X2,X1))
| ~ 'is$ua$utheorem'(not(X0))
| ~ 'is$ua$utheorem'(or(X0,X1)) ),
inference(superposition,[status(thm)],[d2,d71]) ).
cnf(d73,plain,
( ~ 'is$ua$utheorem'(not(not(or(X1,X1))))
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d72,d68]) ).
cnf(d74,plain,
( ~ 'is$ua$utheorem'(or(X1,X1))
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d73,d54]) ).
cnf(d75,plain,
( 'is$ua$utheorem'(or(X1,X2))
| ~ 'is$ua$utheorem'(not(X0))
| ~ 'is$ua$utheorem'(or(X0,X1)) ),
inference(superposition,[status(thm)],[d2,d59]) ).
cnf(d76,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| 'is$ua$utheorem'(or(not(X1),X2))
| ~ 'is$ua$utheorem'(not(X0)) ),
inference(resolution,[status(thm)],[d75,d40]) ).
cnf(d77,plain,
( 'is$ua$utheorem'(or(not(and(X0,X1)),X2))
| ~ 'is$ua$utheorem'(not(X0)) ),
inference(resolution,[status(thm)],[d76,d33]) ).
cnf(d78,plain,
( ~ 'is$ua$utheorem'(not(X0))
| 'is$ua$utheorem'(or(implies(X0,X1),X2)) ),
inference(superposition,[status(thm)],[d0,d77]) ).
cnf(d79,plain,
( 'is$ua$utheorem'(implies(X1,implies(X0,X2)))
| ~ 'is$ua$utheorem'(not(X0)) ),
inference(resolution,[status(thm)],[d78,d74]) ).
cnf(d80,plain,
( 'is$ua$utheorem'(and(implies(X0,X2),X1))
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(not(X0)) ),
inference(resolution,[status(thm)],[d79,d63]) ).
cnf(d81,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(resolution,[status(thm)],[c2,c62]) ).
cnf(d82,plain,
( ~ 'is$ua$utheorem'(not(X0))
| ~ 'is$ua$utheorem'(implies(X1,X0))
| 'is$ua$utheorem'(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[d81,d80]) ).
cnf(d83,plain,
( ~ 'is$ua$utheorem'(not(X1))
| ~ 'is$ua$utheorem'(not(X0))
| 'is$ua$utheorem'(equiv(X0,X1)) ),
inference(resolution,[status(thm)],[d82,d53]) ).
cnf(d84,plain,
( X0 = X1
| ~ 'is$ua$utheorem'(not(X1))
| ~ 'is$ua$utheorem'(not(X0)) ),
inference(resolution,[status(thm)],[d83,d50]) ).
cnf(d85,plain,
( ~ 'is$ua$utheorem'(not(X1))
| and(not(X0),X0) = X1 ),
inference(resolution,[status(thm)],[d84,d37]) ).
cnf(d86,plain,
and(not(X0),X0) = and(not(X1),X1),
inference(resolution,[status(thm)],[d85,d37]) ).
cnf(d87,plain,
'is$ua$utheorem'(implies(X0,not(and(not(X1),X1)))),
inference(superposition,[status(thm)],[d86,d49]) ).
cnf(d88,plain,
'is$ua$utheorem'(implies(X1,implies(not(not(X0)),X0))),
inference(superposition,[status(thm)],[d0,d87]) ).
cnf(d89,plain,
'is$ua$utheorem'(implies(X1,or(not(X0),X0))),
inference(demodulation,[status(thm)],[d88,d2]) ).
cnf(d90,plain,
'is$ua$utheorem'(or(X0,or(not(X1),X1))),
inference(superposition,[status(thm)],[d2,d89]) ).
cnf(d91,plain,
( ~ 'is$ua$utheorem'(implies(or(not(X1),X1),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d90,d41]) ).
cnf(d92,plain,
'is$ua$utheorem'(implies(implies(X0,X1),or(X1,not(X0)))),
inference(resolution,[status(thm)],[d91,d24]) ).
cnf(d93,plain,
( ~ 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(not(and(X2,X0)))
| 'is$ua$utheorem'(not(and(X0,X1))) ),
inference(resolution,[status(thm)],[d12,d15]) ).
cnf(d94,plain,
( 'is$ua$utheorem'(not(and(X1,X0)))
| ~ 'is$ua$utheorem'(implies(X0,not(X1))) ),
inference(resolution,[status(thm)],[d37,d93]) ).
cnf(d95,plain,
'is$ua$utheorem'(not(and(X0,and(not(X0),X1)))),
inference(resolution,[status(thm)],[d94,d33]) ).
cnf(d96,plain,
( ~ 'is$ua$utheorem'(or(X2,X0))
| 'is$ua$utheorem'(implies(and(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[d95,d18]) ).
cnf(d97,plain,
( ~ 'is$ua$utheorem'(not(X1))
| 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(or(X0,X1)) ),
inference(resolution,[status(thm)],[d96,d61]) ).
cnf(d98,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(not(not(X1)))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d97,d40]) ).
cnf(d99,plain,
( ~ 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(not(X1))
| not(X0) = X1 ),
inference(resolution,[status(thm)],[d84,d54]) ).
cnf(d100,plain,
( ~ 'is$ua$utheorem'(X0)
| not(X0) = and(not(X1),X1) ),
inference(resolution,[status(thm)],[d99,d37]) ).
cnf(d101,plain,
not(implies(and(X0,X1),X0)) = and(not(X2),X2),
inference(resolution,[status(thm)],[d100,d33]) ).
cnf(d102,plain,
'is$ua$utheorem'(not(not(implies(and(X1,X2),X1)))),
inference(superposition,[status(thm)],[d101,d37]) ).
cnf(d103,plain,
( ~ 'is$ua$utheorem'(implies(implies(and(X1,X2),X1),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d102,d98]) ).
cnf(d104,plain,
'is$ua$utheorem'(or(X0,not(and(X0,X1)))),
inference(resolution,[status(thm)],[d103,d92]) ).
cnf(d105,plain,
'is$ua$utheorem'(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[d0,d104]) ).
cnf(d106,plain,
'is$ua$utheorem'(or(not(X0),or(X0,X1))),
inference(superposition,[status(thm)],[d2,d105]) ).
cnf(d107,plain,
( ~ 'is$ua$utheorem'(or(not(not(X0)),not(not(X0))))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d44,d25]) ).
cnf(d108,plain,
( ~ 'is$ua$utheorem'(implies(not(X0),not(not(X0))))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d107,d40]) ).
cnf(d109,plain,
( ~ 'is$ua$utheorem'(or(X0,not(not(X0))))
| 'is$ua$utheorem'(X0) ),
inference(demodulation,[status(thm)],[d108,d2]) ).
cnf(d110,plain,
( ~ 'is$ua$utheorem'(implies(not(X0),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d109,d40]) ).
cnf(d111,plain,
( ~ 'is$ua$utheorem'(or(X0,X0))
| 'is$ua$utheorem'(X0) ),
inference(demodulation,[status(thm)],[d110,d2]) ).
cnf(d112,plain,
( 'is$ua$utheorem'(or(X2,X0))
| ~ 'is$ua$utheorem'(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d105,d32]) ).
cnf(d113,plain,
( ~ 'is$ua$utheorem'(or(X1,X2))
| 'is$ua$utheorem'(or(or(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d112,d31]) ).
cnf(d114,plain,
( 'is$ua$utheorem'(or(X1,X0))
| ~ 'is$ua$utheorem'(or(X0,or(X1,X0))) ),
inference(resolution,[status(thm)],[d113,d111]) ).
cnf(d115,plain,
'is$ua$utheorem'(or(X0,not(X0))),
inference(resolution,[status(thm)],[d114,d106]) ).
cnf(d116,plain,
$false,
inference(resolution,[status(thm)],[d115,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL517+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
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 22:43:08 UTC 2026
% 0.01/0.36 % CPUTime :
% 0.01/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 173.86/37.04 % SZS status Theorem for theBenchmark.p
% 173.86/37.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------