%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL519+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 : n002.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 247.55s 40.80s
% Output : CNFRefutation 247.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 22
% Syntax : Number of formulae : 113 ( 79 unt; 0 def)
% Number of atoms : 154 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 30 ~; 27 |; 1 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 193 ( 14 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(principia_op_implies_or,axiom,
'op$uimplies$uor' ).
fof(principia_op_and,axiom,
'op$uand' ).
fof(principia_op_equiv,axiom,
'op$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$utheorem'(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ) ).
fof(r2,axiom,
( r2
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X1,or(X0,X1))) ) ).
fof(op_or,axiom,
( 'op$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(rosser_op_or,axiom,
'op$uor' ).
fof(rosser_op_implies_and,axiom,
'op$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(principia_r2,conjecture,
r2 ).
fof(negated_conjecture,negated_conjecture,
~ r2,
inference(negate_conjecture,[status(cth)],[principia_r2]) ).
cnf(c0,plain,
'op$uimplies$uor',
inference(clausification,[status(esa)],[principia_op_implies_or]) ).
cnf(c1,plain,
'op$uand',
inference(clausification,[status(esa)],[principia_op_and]) ).
cnf(c2,plain,
'op$uequiv',
inference(clausification,[status(esa)],[principia_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$utheorem'(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(clausification,[status(esa)],[kn3]) ).
cnf(c51,plain,
( ~ 'is$ua$utheorem'(implies(sK93,or(sK92,sK93)))
| r2 ),
inference(clausification,[status(esa)],[r2]) ).
cnf(c58,plain,
( not(and(not(X0),not(X1))) = or(X0,X1)
| ~ 'op$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$uor',
inference(clausification,[status(esa)],[rosser_op_or]) ).
cnf(c64,plain,
'op$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,
~ r2,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'(implies(sK93,or(sK92,sK93))),
inference(resolution,[status(thm)],[c71,c51]) ).
cnf(d1,plain,
or(not(X0),X1) = implies(X0,X1),
inference(resolution,[status(thm)],[c0,c61]) ).
cnf(d2,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(resolution,[status(thm)],[c64,c60]) ).
cnf(d3,plain,
( ~ 'op$uor'
| implies(not(X0),X1) = or(X0,X1) ),
inference(demodulation,[status(thm)],[c58,d2]) ).
cnf(d4,plain,
implies(not(X0),X1) = or(X0,X1),
inference(resolution,[status(thm)],[c63,d3]) ).
cnf(d5,plain,
implies(implies(X0,X1),X2) = or(and(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(resolution,[status(thm)],[c69,c40]) ).
cnf(d7,plain,
'is$ua$utheorem'(implies(implies(not(X1),X2),implies(not(and(X2,X0)),implies(X0,X1)))),
inference(superposition,[status(thm)],[d2,d6]) ).
cnf(d8,plain,
'is$ua$utheorem'(implies(or(X0,X1),implies(not(and(X1,X2)),implies(X2,X0)))),
inference(demodulation,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
'is$ua$utheorem'(implies(or(X2,X0),or(and(X0,X1),implies(X1,X2)))),
inference(demodulation,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
'is$ua$utheorem'(implies(or(X1,X2),or(and(X2,not(X0)),or(X0,X1)))),
inference(superposition,[status(thm)],[d4,d9]) ).
cnf(d11,plain,
'is$ua$utheorem'(implies(or(X2,X0),implies(implies(X0,X1),or(X1,X2)))),
inference(demodulation,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c66,c3]) ).
cnf(d13,plain,
'is$ua$utheorem'(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c68,c38]) ).
cnf(d14,plain,
( ~ 'is$ua$utheorem'(implies(implies(and(X1,X2),X1),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d12,d13]) ).
cnf(d15,plain,
'is$ua$utheorem'(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[c67,c36]) ).
cnf(d16,plain,
( ~ 'is$ua$utheorem'(implies(implies(X1,and(X1,X1)),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d12,d15]) ).
cnf(d17,plain,
'is$ua$utheorem'(implies(implies(X2,X0),implies(implies(X0,X1),not(and(not(X1),X2))))),
inference(superposition,[status(thm)],[d2,d6]) ).
cnf(d18,plain,
'is$ua$utheorem'(implies(implies(and(X0,X0),X1),not(and(not(X1),X0)))),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
'is$ua$utheorem'(not(and(not(X0),X0))),
inference(resolution,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
'is$ua$utheorem'(implies(not(not(X0)),X0)),
inference(superposition,[status(thm)],[d2,d19]) ).
cnf(d21,plain,
'is$ua$utheorem'(or(not(X0),X0)),
inference(demodulation,[status(thm)],[d20,d4]) ).
cnf(d22,plain,
'is$ua$utheorem'(implies(X0,X0)),
inference(demodulation,[status(thm)],[d21,d1]) ).
cnf(d23,plain,
'is$ua$utheorem'(or(X0,not(X0))),
inference(superposition,[status(thm)],[d4,d22]) ).
cnf(d24,plain,
( ~ 'is$ua$utheorem'(implies(or(X1,not(X1)),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d23,d12]) ).
cnf(d25,plain,
'is$ua$utheorem'(implies(implies(not(X0),X1),or(X1,X0))),
inference(resolution,[status(thm)],[d24,d11]) ).
cnf(d26,plain,
'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0))),
inference(demodulation,[status(thm)],[d25,d4]) ).
cnf(d27,plain,
( ~ 'op$uand'
| not(implies(X0,not(X1))) = and(X0,X1) ),
inference(demodulation,[status(thm)],[c59,d1]) ).
cnf(d28,plain,
not(implies(X0,not(X1))) = and(X0,X1),
inference(resolution,[status(thm)],[c1,d27]) ).
cnf(d29,plain,
not(or(X0,not(X1))) = and(not(X0),X1),
inference(superposition,[status(thm)],[d4,d28]) ).
cnf(d30,plain,
implies(and(not(X0),X1),X2) = or(or(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d29,d4]) ).
cnf(d31,plain,
'is$ua$utheorem'(implies(implies(and(not(X0),X1),X2),or(X2,or(X0,not(X1))))),
inference(superposition,[status(thm)],[d30,d26]) ).
cnf(d32,plain,
implies(and(X0,X1),X2) = or(implies(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d28,d4]) ).
cnf(d33,plain,
'is$ua$utheorem'(implies(implies(X0,X1),or(and(X1,X2),implies(X2,not(X0))))),
inference(superposition,[status(thm)],[d1,d9]) ).
cnf(d34,plain,
( ~ 'is$ua$utheorem'(implies(implies(X1,X1),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d22,d12]) ).
cnf(d35,plain,
'is$ua$utheorem'(or(and(X0,X1),implies(X1,not(X0)))),
inference(resolution,[status(thm)],[d34,d33]) ).
cnf(d36,plain,
( ~ 'is$ua$utheorem'(implies(or(and(X1,X2),implies(X2,not(X1))),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d35,d12]) ).
cnf(d37,plain,
or(implies(X0,X1),X2) = implies(and(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d38,plain,
( 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(implies(or(implies(X0,X1),X0),X2)) ),
inference(superposition,[status(thm)],[d37,d14]) ).
cnf(d39,plain,
'is$ua$utheorem'(implies(implies(X0,X1),or(X1,implies(X0,X2)))),
inference(resolution,[status(thm)],[d11,d38]) ).
cnf(d40,plain,
'is$ua$utheorem'(or(X0,implies(X0,X1))),
inference(resolution,[status(thm)],[d34,d39]) ).
cnf(d41,plain,
( ~ 'is$ua$utheorem'(implies(or(X1,implies(X1,X2)),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d40,d12]) ).
cnf(d42,plain,
or(and(X0,X1),X2) = implies(implies(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d28,d1]) ).
cnf(d43,plain,
'is$ua$utheorem'(implies(or(X3,implies(X0,not(X1))),implies(or(and(X0,X1),X2),or(X2,X3)))),
inference(superposition,[status(thm)],[d42,d11]) ).
cnf(d44,plain,
'is$ua$utheorem'(implies(or(and(X0,X1),X2),or(X2,X0))),
inference(resolution,[status(thm)],[d43,d41]) ).
cnf(d45,plain,
'is$ua$utheorem'(or(implies(X0,not(X1)),X1)),
inference(resolution,[status(thm)],[d44,d36]) ).
cnf(d46,plain,
'is$ua$utheorem'(implies(and(X0,X1),X1)),
inference(demodulation,[status(thm)],[d45,d32]) ).
cnf(d47,plain,
( ~ 'is$ua$utheorem'(implies(implies(and(X1,X2),X2),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d46,d12]) ).
cnf(d48,plain,
'is$ua$utheorem'(or(X0,or(X1,not(X0)))),
inference(resolution,[status(thm)],[d47,d31]) ).
cnf(d49,plain,
( ~ 'is$ua$utheorem'(equiv(X1,X0))
| X0 = X1 ),
inference(resolution,[status(thm)],[c70,c7]) ).
cnf(d50,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(resolution,[status(thm)],[c2,c62]) ).
cnf(d51,plain,
and(implies(X1,not(X0)),or(X0,X1)) = equiv(X1,not(X0)),
inference(superposition,[status(thm)],[d4,d50]) ).
cnf(d52,plain,
and(implies(X1,not(not(X0))),implies(X0,X1)) = equiv(X1,not(not(X0))),
inference(superposition,[status(thm)],[d1,d51]) ).
cnf(d53,plain,
not(or(and(X0,X1),not(X2))) = and(implies(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d42,d28]) ).
cnf(d54,plain,
and(not(and(X0,X1)),X2) = and(implies(X0,not(X1)),X2),
inference(demodulation,[status(thm)],[d53,d29]) ).
cnf(d55,plain,
not(and(X2,implies(X0,X1))) = implies(X2,and(X0,not(X1))),
inference(superposition,[status(thm)],[d2,d2]) ).
cnf(d56,plain,
not(and(X2,or(X0,X1))) = implies(X2,and(not(X0),not(X1))),
inference(superposition,[status(thm)],[d4,d55]) ).
cnf(d57,plain,
not(and(X2,or(X3,and(X0,not(X1))))) = implies(X2,and(not(X3),implies(X0,X1))),
inference(superposition,[status(thm)],[d2,d56]) ).
cnf(d58,plain,
'is$ua$utheorem'(not(and(not(X0),or(X0,X0)))),
inference(superposition,[status(thm)],[d56,d15]) ).
cnf(d59,plain,
'is$ua$utheorem'(not(and(implies(X0,X1),or(and(X0,not(X1)),and(X0,not(X1)))))),
inference(superposition,[status(thm)],[d2,d58]) ).
cnf(d60,plain,
'is$ua$utheorem'(implies(implies(X0,X1),and(not(and(X0,not(X1))),implies(X0,X1)))),
inference(demodulation,[status(thm)],[d59,d57]) ).
cnf(d61,plain,
'is$ua$utheorem'(implies(implies(X0,X1),and(implies(X0,not(not(X1))),implies(X0,X1)))),
inference(demodulation,[status(thm)],[d60,d54]) ).
cnf(d62,plain,
'is$ua$utheorem'(and(implies(X0,not(not(X0))),implies(X0,X0))),
inference(resolution,[status(thm)],[d61,d34]) ).
cnf(d63,plain,
'is$ua$utheorem'(equiv(X0,not(not(X0)))),
inference(demodulation,[status(thm)],[d62,d52]) ).
cnf(d64,plain,
not(not(X0)) = X0,
inference(resolution,[status(thm)],[d63,d49]) ).
cnf(d65,plain,
'is$ua$utheorem'(or(not(X0),or(X1,X0))),
inference(superposition,[status(thm)],[d64,d48]) ).
cnf(d66,plain,
'is$ua$utheorem'(implies(X0,or(X1,X0))),
inference(demodulation,[status(thm)],[d65,d1]) ).
cnf(d67,plain,
$false,
inference(resolution,[status(thm)],[d66,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL519+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
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 22:44:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 247.55/40.80 % SZS status Theorem for theBenchmark.p
% 247.55/40.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------