%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL499+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 07:54:45 AM UTC 2026
% Result : Theorem 21.62s 5.23s
% Output : CNFRefutation 21.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 22 unt; 0 def)
% Number of atoms : 61 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 17 ~; 14 |; 1 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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$utheorem'(implies(X0,and(X0,X0))) ) ).
fof(r1,axiom,
( r1
<=> ! [X0] : 'is$ua$utheorem'(implies(or(X0,X0),X0)) ) ).
fof(r3,axiom,
( r3
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0))) ) ).
fof(op_and,axiom,
( 'op$uand'
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ) ).
fof(op_implies_or,axiom,
( 'op$uimplies$uor'
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ) ).
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_r3,axiom,
r3 ).
fof(rosser_kn1,conjecture,
kn1 ).
fof(negated_conjecture,negated_conjecture,
~ kn1,
inference(negate_conjecture,[status(cth)],[rosser_kn1]) ).
cnf(c3,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0)
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(c37,plain,
( ~ 'is$ua$utheorem'(implies(sK65,and(sK65,sK65)))
| kn1 ),
inference(clausification,[status(esa)],[kn1]) ).
cnf(c48,plain,
( 'is$ua$utheorem'(implies(or(X0,X0),X0))
| ~ r1 ),
inference(clausification,[status(esa)],[r1]) ).
cnf(c52,plain,
( 'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(clausification,[status(esa)],[r3]) ).
cnf(c59,plain,
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ 'op$uand' ),
inference(clausification,[status(esa)],[op_and]) ).
cnf(c61,plain,
( implies(X0,X1) = or(not(X0),X1)
| ~ 'op$uimplies$uor' ),
inference(clausification,[status(esa)],[op_implies_or]) ).
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(c69,plain,
r3,
inference(clausification,[status(esa)],[principia_r3]) ).
cnf(c73,plain,
~ kn1,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'(implies(sK65,and(sK65,sK65))),
inference(resolution,[status(thm)],[c73,c37]) ).
cnf(d1,plain,
implies(X0,X1) = or(not(X0),X1),
inference(resolution,[status(thm)],[c63,c61]) ).
cnf(d2,plain,
( ~ 'op$uand'
| and(X0,X1) = not(implies(X0,not(X1))) ),
inference(demodulation,[status(thm)],[c59,d1]) ).
cnf(d3,plain,
and(X0,X1) = not(implies(X0,not(X1))),
inference(resolution,[status(thm)],[c64,d2]) ).
cnf(d4,plain,
'is$ua$utheorem'(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[c67,c48]) ).
cnf(d5,plain,
'is$ua$utheorem'(implies(implies(X0,not(X0)),not(X0))),
inference(superposition,[status(thm)],[d1,d4]) ).
cnf(d6,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c66,c3]) ).
cnf(d7,plain,
'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[c69,c52]) ).
cnf(d8,plain,
( 'is$ua$utheorem'(or(X1,X0))
| ~ 'is$ua$utheorem'(or(X0,X1)) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( 'is$ua$utheorem'(or(X1,not(X0)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(superposition,[status(thm)],[d1,d8]) ).
cnf(d10,plain,
( ~ 'is$ua$utheorem'(implies(X1,not(X0)))
| 'is$ua$utheorem'(implies(X0,not(X1))) ),
inference(superposition,[status(thm)],[d1,d9]) ).
cnf(d11,plain,
'is$ua$utheorem'(implies(X0,not(implies(X0,not(X0))))),
inference(resolution,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
'is$ua$utheorem'(implies(X0,and(X0,X0))),
inference(demodulation,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL499+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 : n002.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 22:42:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.62/5.23 % SZS status Theorem for theBenchmark.p
% 21.62/5.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------