%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL518+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 : n014.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 32.64s 7.55s
% Output : CNFRefutation 32.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 70 ( 45 unt; 0 def)
% Number of atoms : 100 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 22 ~; 19 |; 1 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 96 ( 3 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(principia_op_implies_or,axiom,
'op$uimplies$uor' ).
fof(principia_op_and,axiom,
'op$uand' ).
fof(modus_ponens,axiom,
( 'modus$uponens'
<=> ! [X0,X1] :
( ( 'is$ua$utheorem'(implies(X0,X1))
& 'is$ua$utheorem'(X0) )
=> 'is$ua$utheorem'(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(r1,axiom,
( r1
<=> ! [X0] : 'is$ua$utheorem'(implies(or(X0,X0),X0)) ) ).
fof(op_or,axiom,
( 'op$uor'
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ) ).
fof(op_and,axiom,
( 'op$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(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(principia_r1,conjecture,
r1 ).
fof(negated_conjecture,negated_conjecture,
~ r1,
inference(negate_conjecture,[status(cth)],[principia_r1]) ).
cnf(c0,plain,
'op$uimplies$uor',
inference(clausification,[status(esa)],[principia_op_implies_or]) ).
cnf(c1,plain,
'op$uand',
inference(clausification,[status(esa)],[principia_op_and]) ).
cnf(c3,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(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(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$uor' ),
inference(clausification,[status(esa)],[op_or]) ).
cnf(c59,plain,
( not(or(not(X0),not(X1))) = and(X0,X1)
| ~ 'op$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(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(c71,plain,
~ r1,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'(implies(or(sK89,sK89),sK89)),
inference(resolution,[status(thm)],[c71,c49]) ).
cnf(d1,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(resolution,[status(thm)],[c64,c60]) ).
cnf(d2,plain,
( ~ 'op$uor'
| implies(not(X0),X1) = or(X0,X1) ),
inference(demodulation,[status(thm)],[c58,d1]) ).
cnf(d3,plain,
implies(not(X0),X1) = or(X0,X1),
inference(resolution,[status(thm)],[c63,d2]) ).
cnf(d4,plain,
or(not(X0),X1) = implies(X0,X1),
inference(resolution,[status(thm)],[c0,c61]) ).
cnf(d5,plain,
( ~ 'op$uand'
| not(implies(X0,not(X1))) = and(X0,X1) ),
inference(demodulation,[status(thm)],[c59,d4]) ).
cnf(d6,plain,
not(implies(X0,not(X1))) = and(X0,X1),
inference(resolution,[status(thm)],[c1,d5]) ).
cnf(d7,plain,
not(or(X0,not(X1))) = and(not(X0),X1),
inference(superposition,[status(thm)],[d3,d6]) ).
cnf(d8,plain,
or(implies(X0,X1),X2) = implies(and(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d1,d4]) ).
cnf(d9,plain,
not(or(implies(X0,X1),not(X2))) = and(and(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
and(not(implies(X0,X1)),X2) = and(and(X0,not(X1)),X2),
inference(demodulation,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(resolution,[status(thm)],[c69,c40]) ).
cnf(d12,plain,
'is$ua$utheorem'(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[c67,c36]) ).
cnf(d13,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c66,c3]) ).
cnf(d14,plain,
( ~ 'is$ua$utheorem'(implies(implies(X1,and(X1,X1)),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
'is$ua$utheorem'(implies(not(and(and(X0,X0),X1)),not(and(X1,X0)))),
inference(resolution,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
'is$ua$utheorem'(or(and(and(X0,X0),X1),not(and(X1,X0)))),
inference(demodulation,[status(thm)],[d15,d3]) ).
cnf(d17,plain,
'is$ua$utheorem'(or(and(and(not(X1),not(X1)),X0),implies(X0,X1))),
inference(superposition,[status(thm)],[d1,d16]) ).
cnf(d18,plain,
'is$ua$utheorem'(or(and(not(implies(not(X0),X0)),X1),implies(X1,X0))),
inference(demodulation,[status(thm)],[d17,d10]) ).
cnf(d19,plain,
'is$ua$utheorem'(or(and(not(or(X0,X0)),X1),implies(X1,X0))),
inference(demodulation,[status(thm)],[d18,d3]) ).
cnf(d20,plain,
'is$ua$utheorem'(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c68,c38]) ).
cnf(d21,plain,
( ~ 'is$ua$utheorem'(implies(implies(and(X1,X2),X1),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d13,d20]) ).
cnf(d22,plain,
'is$ua$utheorem'(implies(implies(X2,X0),implies(implies(X0,X1),not(and(not(X1),X2))))),
inference(superposition,[status(thm)],[d1,d11]) ).
cnf(d23,plain,
'is$ua$utheorem'(implies(implies(and(X0,X0),X1),not(and(not(X1),X0)))),
inference(resolution,[status(thm)],[d22,d14]) ).
cnf(d24,plain,
'is$ua$utheorem'(not(and(not(X0),X0))),
inference(resolution,[status(thm)],[d23,d21]) ).
cnf(d25,plain,
'is$ua$utheorem'(implies(not(not(X0)),X0)),
inference(superposition,[status(thm)],[d1,d24]) ).
cnf(d26,plain,
'is$ua$utheorem'(or(not(X0),X0)),
inference(demodulation,[status(thm)],[d25,d3]) ).
cnf(d27,plain,
'is$ua$utheorem'(implies(X0,X0)),
inference(demodulation,[status(thm)],[d26,d4]) ).
cnf(d28,plain,
( ~ 'is$ua$utheorem'(implies(implies(X1,X1),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d27,d13]) ).
cnf(d29,plain,
or(and(X0,X1),X2) = implies(implies(X0,not(X1)),X2),
inference(superposition,[status(thm)],[d6,d4]) ).
cnf(d30,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(or(and(not(X0),X0),X1)) ),
inference(superposition,[status(thm)],[d29,d28]) ).
cnf(d31,plain,
'is$ua$utheorem'(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[d30,d19]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[d31,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL518+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
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 22:41:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.64/7.55 % SZS status Theorem for theBenchmark.p
% 32.64/7.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------