%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL489+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 07:54:43 AM UTC 2026
% Result : Theorem 59.53s 14.54s
% Output : CNFRefutation 59.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 26
% Syntax : Number of formulae : 122 ( 81 unt; 0 def)
% Number of atoms : 171 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 85 ( 36 ~; 33 |; 1 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 195 ( 11 sgn 27 !; 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$utheorem'(equiv(X0,X1))
=> X0 = X1 ) ) ).
fof(and_3,axiom,
( 'and$u3'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,implies(X1,and(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$uequivalents' ).
fof(hilbert_and_3,conjecture,
'and$u3' ).
fof(negated_conjecture,negated_conjecture,
~ 'and$u3',
inference(negate_conjecture,[status(cth)],[hilbert_and_3]) ).
cnf(c0,plain,
'op$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(c23,plain,
( ~ 'is$ua$utheorem'(implies(sK36,implies(sK37,and(sK36,sK37))))
| 'and$u3' ),
inference(clausification,[status(esa)],[and_3]) ).
cnf(c48,plain,
( 'is$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,
~ 'and$u3',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'(implies(sK36,implies(sK37,and(sK36,sK37)))),
inference(resolution,[status(thm)],[c73,c23]) ).
cnf(d1,plain,
or(not(X0),X1) = implies(X0,X1),
inference(resolution,[status(thm)],[c63,c61]) ).
cnf(d2,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c66,c3]) ).
cnf(d3,plain,
'is$ua$utheorem'(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[c70,c54]) ).
cnf(d4,plain,
( 'is$ua$utheorem'(or(X1,or(X0,X2)))
| ~ 'is$ua$utheorem'(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( 'is$ua$utheorem'(or(X1,or(not(X0),X2)))
| ~ 'is$ua$utheorem'(implies(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[d1,d4]) ).
cnf(d6,plain,
( 'is$ua$utheorem'(or(X2,implies(X0,X1)))
| ~ 'is$ua$utheorem'(implies(X0,or(X2,X1))) ),
inference(demodulation,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( 'is$ua$utheorem'(or(not(X0),implies(X2,X1)))
| ~ 'is$ua$utheorem'(implies(X2,implies(X0,X1))) ),
inference(superposition,[status(thm)],[d1,d6]) ).
cnf(d8,plain,
( 'is$ua$utheorem'(implies(X0,implies(X1,X2)))
| ~ 'is$ua$utheorem'(implies(X1,implies(X0,X2))) ),
inference(demodulation,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
( ~ 'op$uand'
| not(implies(X0,not(X1))) = and(X0,X1) ),
inference(demodulation,[status(thm)],[c59,d1]) ).
cnf(d10,plain,
not(implies(X0,not(X1))) = and(X0,X1),
inference(resolution,[status(thm)],[c64,d9]) ).
cnf(d11,plain,
or(and(X0,X1),X2) = implies(implies(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[c69,c52]) ).
cnf(d13,plain,
'is$ua$utheorem'(implies(or(X1,not(X0)),implies(X0,X1))),
inference(superposition,[status(thm)],[d1,d12]) ).
cnf(d14,plain,
'is$ua$utheorem'(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
inference(superposition,[status(thm)],[d1,d13]) ).
cnf(d15,plain,
'is$ua$utheorem'(or(and(X0,X1),implies(X1,not(X0)))),
inference(demodulation,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[c71,c56]) ).
cnf(d17,plain,
( 'is$ua$utheorem'(implies(or(X2,X0),or(X2,X1)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d16,d2]) ).
cnf(d18,plain,
( 'is$ua$utheorem'(or(X2,X1))
| ~ 'is$ua$utheorem'(or(X2,X0))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d17,d2]) ).
cnf(d19,plain,
'is$ua$utheorem'(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[status(thm)],[d1,d12]) ).
cnf(d20,plain,
'is$ua$utheorem'(or(X0,implies(implies(X1,X0),not(X1)))),
inference(resolution,[status(thm)],[d6,d19]) ).
cnf(d21,plain,
( 'is$ua$utheorem'(or(X1,X2))
| ~ 'is$ua$utheorem'(implies(implies(implies(X0,X1),not(X0)),X2)) ),
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
( 'is$ua$utheorem'(or(X1,X2))
| ~ 'is$ua$utheorem'(or(and(implies(X0,X1),X0),X2)) ),
inference(demodulation,[status(thm)],[d21,d11]) ).
cnf(d23,plain,
'is$ua$utheorem'(or(X0,implies(X1,not(implies(X1,X0))))),
inference(resolution,[status(thm)],[d22,d15]) ).
cnf(d24,plain,
( ~ 'is$ua$utheorem'(equiv(X1,X0))
| X0 = X1 ),
inference(resolution,[status(thm)],[c72,c7]) ).
cnf(d25,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(resolution,[status(thm)],[c1,c60]) ).
cnf(d26,plain,
not(and(X2,implies(X0,X1))) = implies(X2,and(X0,not(X1))),
inference(superposition,[status(thm)],[d25,d25]) ).
cnf(d27,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(resolution,[status(thm)],[c2,c62]) ).
cnf(d28,plain,
not(equiv(X0,X1)) = implies(implies(X0,X1),and(X1,not(X0))),
inference(superposition,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
not(implies(X2,and(X0,X1))) = and(X2,implies(X0,not(X1))),
inference(superposition,[status(thm)],[d10,d10]) ).
cnf(d30,plain,
not(and(not(X0),not(X1))) = or(X0,X1),
inference(resolution,[status(thm)],[c0,c58]) ).
cnf(d31,plain,
implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[d30,d25]) ).
cnf(d32,plain,
and(or(X0,X1),implies(X1,not(X0))) = equiv(not(X0),X1),
inference(superposition,[status(thm)],[d31,d27]) ).
cnf(d33,plain,
not(implies(or(X0,X1),and(X1,X0))) = equiv(not(X0),X1),
inference(demodulation,[status(thm)],[d32,d29]) ).
cnf(d34,plain,
not(implies(implies(X0,X1),and(X1,not(X0)))) = equiv(not(not(X0)),X1),
inference(superposition,[status(thm)],[d1,d33]) ).
cnf(d35,plain,
not(not(equiv(X0,X1))) = equiv(not(not(X0)),X1),
inference(demodulation,[status(thm)],[d34,d28]) ).
cnf(d36,plain,
'is$ua$utheorem'(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[c67,c48]) ).
cnf(d37,plain,
'is$ua$utheorem'(implies(implies(X0,not(X0)),not(X0))),
inference(superposition,[status(thm)],[d1,d36]) ).
cnf(d38,plain,
'is$ua$utheorem'(or(and(X0,X0),not(X0))),
inference(demodulation,[status(thm)],[d37,d11]) ).
cnf(d39,plain,
not(and(or(X0,X1),not(X2))) = or(and(not(X0),not(X1)),X2),
inference(superposition,[status(thm)],[d30,d30]) ).
cnf(d40,plain,
implies(or(X0,X1),X2) = or(and(not(X0),not(X1)),X2),
inference(demodulation,[status(thm)],[d39,d25]) ).
cnf(d41,plain,
'is$ua$utheorem'(implies(or(X0,X0),not(not(X0)))),
inference(superposition,[status(thm)],[d40,d38]) ).
cnf(d42,plain,
( 'is$ua$utheorem'(not(not(X0)))
| ~ 'is$ua$utheorem'(or(X0,X0)) ),
inference(resolution,[status(thm)],[d41,d2]) ).
cnf(d43,plain,
( 'is$ua$utheorem'(or(X1,X0))
| ~ 'is$ua$utheorem'(or(X0,X1)) ),
inference(resolution,[status(thm)],[d12,d2]) ).
cnf(d44,plain,
'is$ua$utheorem'(or(not(X0),and(X0,X0))),
inference(resolution,[status(thm)],[d38,d43]) ).
cnf(d45,plain,
'is$ua$utheorem'(implies(X0,and(X0,X0))),
inference(demodulation,[status(thm)],[d44,d1]) ).
cnf(d46,plain,
'is$ua$utheorem'(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[d27,d45]) ).
cnf(d47,plain,
or(implies(X0,X1),X2) = implies(and(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d25,d1]) ).
cnf(d48,plain,
not(and(and(X0,X1),not(X2))) = or(implies(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d10,d30]) ).
cnf(d49,plain,
implies(and(X0,X1),X2) = or(implies(X0,not(X1)),X2),
inference(demodulation,[status(thm)],[d48,d25]) ).
cnf(d50,plain,
'is$ua$utheorem'(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[c68,c50]) ).
cnf(d51,plain,
'is$ua$utheorem'(or(X0,or(X1,not(X0)))),
inference(superposition,[status(thm)],[d31,d50]) ).
cnf(d52,plain,
'is$ua$utheorem'(or(X0,or(X1,not(X1)))),
inference(resolution,[status(thm)],[d4,d51]) ).
cnf(d53,plain,
'is$ua$utheorem'(or(or(X0,not(X0)),X1)),
inference(resolution,[status(thm)],[d52,d43]) ).
cnf(d54,plain,
'is$ua$utheorem'(or(implies(X0,not(not(X0))),X1)),
inference(superposition,[status(thm)],[d1,d53]) ).
cnf(d55,plain,
'is$ua$utheorem'(implies(and(X0,not(X0)),X1)),
inference(demodulation,[status(thm)],[d54,d49]) ).
cnf(d56,plain,
'is$ua$utheorem'(or(implies(X0,X0),X1)),
inference(demodulation,[status(thm)],[d55,d47]) ).
cnf(d57,plain,
'is$ua$utheorem'(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[d56,d43]) ).
cnf(d58,plain,
( 'is$ua$utheorem'(or(X2,X1))
| ~ 'is$ua$utheorem'(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[d18,d57]) ).
cnf(d59,plain,
'is$ua$utheorem'(or(X0,equiv(X1,X1))),
inference(resolution,[status(thm)],[d58,d46]) ).
cnf(d60,plain,
'is$ua$utheorem'(not(not(equiv(X0,X0)))),
inference(resolution,[status(thm)],[d59,d42]) ).
cnf(d61,plain,
'is$ua$utheorem'(equiv(not(not(X0)),X0)),
inference(demodulation,[status(thm)],[d60,d35]) ).
cnf(d62,plain,
X0 = not(not(X0)),
inference(resolution,[status(thm)],[d61,d24]) ).
cnf(d63,plain,
not(and(X1,X0)) = implies(X1,not(X0)),
inference(superposition,[status(thm)],[d62,d25]) ).
cnf(d64,plain,
and(X0,X1) = not(implies(X0,not(X1))),
inference(superposition,[status(thm)],[d63,d62]) ).
cnf(d65,plain,
'is$ua$utheorem'(or(not(X1),implies(X0,and(X0,X1)))),
inference(superposition,[status(thm)],[d64,d23]) ).
cnf(d66,plain,
'is$ua$utheorem'(implies(X0,implies(X1,and(X1,X0)))),
inference(demodulation,[status(thm)],[d65,d1]) ).
cnf(d67,plain,
'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1)))),
inference(resolution,[status(thm)],[d66,d8]) ).
cnf(d68,plain,
$false,
inference(resolution,[status(thm)],[d67,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL489+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
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 22:41:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 59.53/14.54 % SZS status Theorem for theBenchmark.p
% 59.53/14.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------