%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL520+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 : n005.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 34.67s 5.81s
% Output : CNFRefutation 34.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 58 ( 37 unt; 0 def)
% Number of atoms : 84 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 19 ~; 16 |; 1 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 76 ( 3 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(principia_op_implies_or,axiom,
'op$uimplies$uor' ).
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$utheorem'(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ) ).
fof(r3,axiom,
( r3
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0))) ) ).
fof(op_or,axiom,
( 'op$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_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_r3,conjecture,
r3 ).
fof(negated_conjecture,negated_conjecture,
~ r3,
inference(negate_conjecture,[status(cth)],[principia_r3]) ).
cnf(c0,plain,
'op$uimplies$uor',
inference(clausification,[status(esa)],[principia_op_implies_or]) ).
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$utheorem'(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(clausification,[status(esa)],[kn3]) ).
cnf(c53,plain,
( ~ 'is$ua$utheorem'(implies(or(sK96,sK97),or(sK97,sK96)))
| r3 ),
inference(clausification,[status(esa)],[r3]) ).
cnf(c58,plain,
( not(and(not(X0),not(X1))) = or(X0,X1)
| ~ 'op$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(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,
~ r3,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'(implies(or(sK96,sK97),or(sK97,sK96))),
inference(resolution,[status(thm)],[c71,c53]) ).
cnf(d1,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(resolution,[status(thm)],[c64,c60]) ).
cnf(d2,plain,
( ~ 'op$uor'
| implies(not(X0),X1) = or(X0,X1) ),
inference(demodulation,[status(thm)],[c58,d1]) ).
cnf(d3,plain,
implies(not(X0),X1) = or(X0,X1),
inference(resolution,[status(thm)],[c63,d2]) ).
cnf(d4,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(resolution,[status(thm)],[c69,c40]) ).
cnf(d5,plain,
'is$ua$utheorem'(implies(implies(X2,X0),implies(implies(X0,X1),not(and(not(X1),X2))))),
inference(superposition,[status(thm)],[d1,d4]) ).
cnf(d6,plain,
'is$ua$utheorem'(implies(or(X0,X1),implies(implies(X1,X2),not(and(not(X2),not(X0)))))),
inference(superposition,[status(thm)],[d3,d5]) ).
cnf(d7,plain,
'is$ua$utheorem'(implies(or(X1,X2),implies(implies(X2,X0),implies(not(X0),X1)))),
inference(demodulation,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
'is$ua$utheorem'(implies(or(X1,X2),implies(implies(X2,X0),or(X0,X1)))),
inference(demodulation,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c66,c3]) ).
cnf(d10,plain,
or(not(X0),X1) = implies(X0,X1),
inference(resolution,[status(thm)],[c0,c61]) ).
cnf(d11,plain,
'is$ua$utheorem'(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c68,c38]) ).
cnf(d12,plain,
( ~ 'is$ua$utheorem'(implies(implies(and(X1,X2),X1),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d9,d11]) ).
cnf(d13,plain,
'is$ua$utheorem'(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[c67,c36]) ).
cnf(d14,plain,
( ~ 'is$ua$utheorem'(implies(implies(X1,and(X1,X1)),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d9,d13]) ).
cnf(d15,plain,
'is$ua$utheorem'(implies(implies(and(X0,X0),X1),not(and(not(X1),X0)))),
inference(resolution,[status(thm)],[d5,d14]) ).
cnf(d16,plain,
'is$ua$utheorem'(not(and(not(X0),X0))),
inference(resolution,[status(thm)],[d15,d12]) ).
cnf(d17,plain,
'is$ua$utheorem'(implies(not(not(X0)),X0)),
inference(superposition,[status(thm)],[d1,d16]) ).
cnf(d18,plain,
'is$ua$utheorem'(or(not(X0),X0)),
inference(demodulation,[status(thm)],[d17,d3]) ).
cnf(d19,plain,
'is$ua$utheorem'(implies(X0,X0)),
inference(demodulation,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
'is$ua$utheorem'(or(X0,not(X0))),
inference(superposition,[status(thm)],[d3,d19]) ).
cnf(d21,plain,
( ~ 'is$ua$utheorem'(implies(or(X1,not(X1)),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d20,d9]) ).
cnf(d22,plain,
'is$ua$utheorem'(implies(implies(not(X0),X1),or(X1,X0))),
inference(resolution,[status(thm)],[d21,d8]) ).
cnf(d23,plain,
'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0))),
inference(demodulation,[status(thm)],[d22,d3]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[d23,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL520+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
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 22:41:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.67/5.81 % SZS status Theorem for theBenchmark.p
% 34.67/5.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------