%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL239-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 07:54:11 AM UTC 2026
% Result : Unsatisfiable 13.58s 2.22s
% Output : CNFRefutation 13.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 37 ( 24 unt; 0 nHn; 16 RR)
% Number of literals : 52 ( 5 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 64 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this,negated_conjecture,
~ theorem(not(and(p,not(p)))) ).
cnf(axiom_1_2,axiom,
axiom(implies(or(X0,X0),X0)) ).
cnf(axiom_1_3,axiom,
axiom(implies(X0,or(X1,X0))) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(X0,X1),or(X1,X0))) ).
cnf(axiom_1_5,axiom,
axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ).
cnf(implies_definition,axiom,
implies(X0,X1) = or(not(X0),X1) ).
cnf(rule_1,axiom,
( ~ axiom(X0)
| theorem(X0) ) ).
cnf(rule_2,axiom,
( ~ theorem(X1)
| ~ theorem(implies(X1,X0))
| theorem(X0) ) ).
cnf(and_defn,axiom,
and(X0,X1) = not(or(not(X0),not(X1))) ).
cnf(c0,plain,
~ theorem(not(and(p,not(p)))),
inference(clausification,[status(esa)],[prove_this]) ).
cnf(c1,plain,
axiom(implies(or(X0,X0),X0)),
inference(clausification,[status(esa)],[axiom_1_2]) ).
cnf(c2,plain,
axiom(implies(X0,or(X1,X0))),
inference(clausification,[status(esa)],[axiom_1_3]) ).
cnf(c3,plain,
axiom(implies(or(X0,X1),or(X1,X0))),
inference(clausification,[status(esa)],[axiom_1_4]) ).
cnf(c4,plain,
axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(clausification,[status(esa)],[axiom_1_5]) ).
cnf(c6,plain,
implies(X0,X1) = or(not(X0),X1),
inference(clausification,[status(esa)],[implies_definition]) ).
cnf(c7,plain,
( ~ axiom(X0)
| theorem(X0) ),
inference(clausification,[status(esa)],[rule_1]) ).
cnf(c8,plain,
( ~ theorem(X1)
| ~ theorem(implies(X1,X0))
| theorem(X0) ),
inference(clausification,[status(esa)],[rule_2]) ).
cnf(c9,plain,
and(X0,X1) = not(or(not(X0),not(X1))),
inference(clausification,[status(esa)],[and_defn]) ).
cnf(d0,plain,
theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[c3,c7]) ).
cnf(d1,plain,
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[d0,c8]) ).
cnf(d2,plain,
( theorem(or(X1,not(X0)))
| ~ theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c6,d1]) ).
cnf(d3,plain,
( ~ theorem(implies(X1,not(X0)))
| theorem(implies(X0,not(X1))) ),
inference(superposition,[status(thm)],[c6,d2]) ).
cnf(d4,plain,
theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[c1,c7]) ).
cnf(d5,plain,
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[c8,d4]) ).
cnf(d6,plain,
theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[c2,c7]) ).
cnf(d7,plain,
theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[c4,c7]) ).
cnf(d8,plain,
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
( theorem(or(X1,or(not(X0),X2)))
| ~ theorem(implies(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[c6,d8]) ).
cnf(d10,plain,
( theorem(or(X2,implies(X0,X1)))
| ~ theorem(implies(X0,or(X2,X1))) ),
inference(demodulation,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[d11,d5]) ).
cnf(d13,plain,
theorem(implies(X0,not(not(X0)))),
inference(resolution,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
( ~ theorem(X0)
| theorem(not(not(X0))) ),
inference(resolution,[status(thm)],[d13,c8]) ).
cnf(d15,plain,
and(X0,X1) = not(implies(X0,not(X1))),
inference(demodulation,[status(thm)],[c9,c6]) ).
cnf(d16,plain,
( ~ theorem(implies(X0,not(X1)))
| theorem(not(and(X0,X1))) ),
inference(superposition,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
theorem(not(and(X0,not(X0)))),
inference(resolution,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL239-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.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 22:05:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.58/2.22 % SZS status Unsatisfiable for theBenchmark.p
% 13.58/2.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------