%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL298-3 : 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 : n012.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 07:54:17 AM UTC 2026
% Result : Unsatisfiable 3.27s 40.67s
% Output : CNFRefutation 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 11
% Syntax : Number of clauses : 96 ( 48 unt; 0 nHn; 31 RR)
% Number of literals : 151 ( 9 equ; 58 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 197 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this,negated_conjecture,
~ theorem(equivalent(not(and(p,q)),or(not(p),not(q)))) ).
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(axiom_1_6,axiom,
axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ).
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(equivalent_defn,axiom,
equivalent(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ).
cnf(c0,plain,
~ theorem(equivalent(not(and(p,q)),or(not(p),not(q)))),
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(c5,plain,
axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(clausification,[status(esa)],[axiom_1_6]) ).
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(c10,plain,
equivalent(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(clausification,[status(esa)],[equivalent_defn]) ).
cnf(d0,plain,
~ theorem(equivalent(not(and(p,q)),implies(p,not(q)))),
inference(demodulation,[status(thm)],[c0,c6]) ).
cnf(d1,plain,
theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[c4,c7]) ).
cnf(d2,plain,
theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))),
inference(superposition,[status(thm)],[c6,d1]) ).
cnf(d3,plain,
theorem(implies(implies(X0,or(X2,X1)),or(X2,implies(X0,X1)))),
inference(demodulation,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
( ~ theorem(implies(X1,or(X0,X2)))
| theorem(or(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[c1,c7]) ).
cnf(d6,plain,
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[c8,d5]) ).
cnf(d7,plain,
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d8,plain,
theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[c3,c7]) ).
cnf(d9,plain,
theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[c2,c7]) ).
cnf(d10,plain,
( ~ theorem(X1)
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[c8,d9]) ).
cnf(d11,plain,
( ~ theorem(or(X0,X2))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[d7,d10]) ).
cnf(d12,plain,
( ~ theorem(or(not(X0),X2))
| theorem(implies(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[c6,d11]) ).
cnf(d13,plain,
( theorem(implies(X0,or(X2,X1)))
| ~ theorem(implies(X0,X1)) ),
inference(demodulation,[status(thm)],[d12,c6]) ).
cnf(d14,plain,
( ~ theorem(X0)
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d13,c8]) ).
cnf(d15,plain,
( theorem(or(X2,or(X1,X0)))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
( theorem(or(X1,or(X2,X0)))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[d15,d7]) ).
cnf(d17,plain,
( ~ theorem(or(X1,X2))
| theorem(or(X2,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c6,d16]) ).
cnf(d18,plain,
( theorem(implies(X1,X0))
| ~ theorem(or(X0,implies(X1,X0))) ),
inference(resolution,[status(thm)],[d17,d6]) ).
cnf(d19,plain,
theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[d4,d9]) ).
cnf(d20,plain,
theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
theorem(or(X0,implies(or(X0,X1),X1))),
inference(resolution,[status(thm)],[d20,d4]) ).
cnf(d22,plain,
theorem(implies(X0,implies(or(not(X0),X1),X1))),
inference(superposition,[status(thm)],[c6,d21]) ).
cnf(d23,plain,
theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(demodulation,[status(thm)],[d22,c6]) ).
cnf(d24,plain,
( ~ theorem(X0)
| theorem(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[d23,c8]) ).
cnf(d25,plain,
and(X0,X1) = not(implies(X0,not(X1))),
inference(demodulation,[status(thm)],[c9,c6]) ).
cnf(d26,plain,
implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[d25,c6]) ).
cnf(d27,plain,
( ~ theorem(X0)
| theorem(or(and(X0,X1),not(X1))) ),
inference(superposition,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
theorem(or(X0,implies(or(X1,X0),X1))),
inference(resolution,[status(thm)],[d4,d8]) ).
cnf(d29,plain,
theorem(implies(X0,implies(or(X1,not(X0)),X1))),
inference(superposition,[status(thm)],[c6,d28]) ).
cnf(d30,plain,
( ~ theorem(X1)
| theorem(implies(or(X0,not(X1)),X0)) ),
inference(resolution,[status(thm)],[d29,c8]) ).
cnf(d31,plain,
( ~ theorem(or(X1,not(X0)))
| theorem(X1)
| ~ theorem(X0) ),
inference(resolution,[status(thm)],[d30,c8]) ).
cnf(d32,plain,
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[d8,c8]) ).
cnf(d33,plain,
( theorem(or(X1,not(X0)))
| ~ theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c6,d32]) ).
cnf(d34,plain,
( ~ theorem(implies(X1,not(X0)))
| theorem(implies(X0,not(X1))) ),
inference(superposition,[status(thm)],[c6,d33]) ).
cnf(d35,plain,
theorem(implies(X0,not(not(X0)))),
inference(resolution,[status(thm)],[d20,d34]) ).
cnf(d36,plain,
theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[c5,c7]) ).
cnf(d37,plain,
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[d36,c8]) ).
cnf(d38,plain,
( ~ theorem(or(X2,X0))
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d37,c8]) ).
cnf(d39,plain,
( ~ theorem(or(X0,X1))
| theorem(or(X0,not(not(X1)))) ),
inference(resolution,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
( ~ theorem(not(X1))
| theorem(X0)
| ~ theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[d39,d31]) ).
cnf(d41,plain,
( ~ theorem(X0)
| ~ theorem(not(not(X1)))
| theorem(and(X0,X1)) ),
inference(resolution,[status(thm)],[d40,d27]) ).
cnf(d42,plain,
( theorem(not(not(X0)))
| ~ theorem(or(not(not(X0)),X0)) ),
inference(resolution,[status(thm)],[d39,d6]) ).
cnf(d43,plain,
( ~ theorem(implies(not(X0),X0))
| theorem(not(not(X0))) ),
inference(demodulation,[status(thm)],[d42,c6]) ).
cnf(d44,plain,
theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[status(thm)],[c6,d8]) ).
cnf(d45,plain,
( ~ theorem(implies(X2,X1))
| theorem(implies(X2,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c6,d13]) ).
cnf(d46,plain,
( ~ theorem(not(implies(or(X1,X0),X1)))
| theorem(X0) ),
inference(resolution,[status(thm)],[d40,d28]) ).
cnf(d47,plain,
( theorem(X1)
| ~ theorem(and(or(not(X0),X1),X0)) ),
inference(superposition,[status(thm)],[d25,d46]) ).
cnf(d48,plain,
( ~ theorem(and(implies(X0,X1),X0))
| theorem(X1) ),
inference(demodulation,[status(thm)],[d47,c6]) ).
cnf(d49,plain,
( theorem(or(or(X2,X1),X0))
| ~ theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[d11,d32]) ).
cnf(d50,plain,
( ~ theorem(or(X2,X1))
| theorem(or(implies(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c6,d49]) ).
cnf(d51,plain,
( ~ theorem(or(X2,X1))
| theorem(or(X2,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c6,d11]) ).
cnf(d52,plain,
( theorem(implies(X0,X1))
| ~ theorem(or(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[d51,d6]) ).
cnf(d53,plain,
( ~ theorem(or(X1,X1))
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d52,d50]) ).
cnf(d54,plain,
( theorem(implies(X2,implies(X1,X0)))
| ~ theorem(or(X0,implies(X1,X0))) ),
inference(resolution,[status(thm)],[d17,d53]) ).
cnf(d55,plain,
theorem(implies(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[d19,d54]) ).
cnf(d56,plain,
theorem(not(not(implies(X0,X0)))),
inference(resolution,[status(thm)],[d43,d55]) ).
cnf(d57,plain,
( theorem(and(X0,implies(X1,X1)))
| ~ theorem(X0) ),
inference(resolution,[status(thm)],[d41,d56]) ).
cnf(d58,plain,
( theorem(X1)
| ~ theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[d57,d48]) ).
cnf(d59,plain,
( ~ theorem(implies(implies(X2,X2),X1))
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d58,d45]) ).
cnf(d60,plain,
theorem(implies(X0,or(X1,not(X1)))),
inference(resolution,[status(thm)],[d59,d44]) ).
cnf(d61,plain,
theorem(not(not(or(X0,not(X0))))),
inference(resolution,[status(thm)],[d60,d43]) ).
cnf(d62,plain,
( theorem(and(X0,or(X1,not(X1))))
| ~ theorem(X0) ),
inference(resolution,[status(thm)],[d61,d41]) ).
cnf(d63,plain,
equivalent(X2,implies(X0,not(X1))) = and(implies(X2,implies(X0,not(X1))),or(and(X0,X1),X2)),
inference(superposition,[status(thm)],[d26,c10]) ).
cnf(d64,plain,
( ~ theorem(implies(not(and(X0,X1)),implies(X0,not(X1))))
| theorem(equivalent(not(and(X0,X1)),implies(X0,not(X1)))) ),
inference(superposition,[status(thm)],[d63,d62]) ).
cnf(d65,plain,
theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(superposition,[status(thm)],[c6,d8]) ).
cnf(d66,plain,
( ~ theorem(or(X1,not(X0)))
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d65,c8]) ).
cnf(d67,plain,
( theorem(X1)
| ~ theorem(implies(or(X0,not(X0)),X1)) ),
inference(resolution,[status(thm)],[d62,d48]) ).
cnf(d68,plain,
( ~ theorem(implies(not(X0),X1))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[d67,d37]) ).
cnf(d69,plain,
theorem(or(X0,not(not(not(X0))))),
inference(resolution,[status(thm)],[d68,d35]) ).
cnf(d70,plain,
theorem(implies(not(not(X0)),X0)),
inference(resolution,[status(thm)],[d69,d66]) ).
cnf(d71,plain,
theorem(implies(not(and(X0,X1)),implies(X0,not(X1)))),
inference(superposition,[status(thm)],[d25,d70]) ).
cnf(d72,plain,
theorem(equivalent(not(and(X0,X1)),implies(X0,not(X1)))),
inference(resolution,[status(thm)],[d71,d64]) ).
cnf(d73,plain,
$false,
inference(resolution,[status(thm)],[d72,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL298-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/16.16 % Computer : n012.cluster.edu
% 0.04/16.16 % Model : x86_64 x86_64
% 0.04/16.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/16.16 % Memory : 8046.5625MB
% 0.04/16.16 % OS : Linux 6.8.0-71-generic
% 0.04/16.16 % CPULimit : 300
% 0.04/16.16 % WCLimit : 300
% 0.04/16.16 % DateTime : Fri Sep 25 22:12:48 UTC 2026
% 0.04/16.16 % CPUTime :
% 0.04/16.16 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.27/40.67 % SZS status Unsatisfiable for theBenchmark.p
% 3.27/40.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------