%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL246-3 : 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 : n008.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 07:54:12 AM UTC 2026
% Result : Unsatisfiable 8.19s 5.62s
% Output : CNFRefutation 8.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of clauses : 53 ( 37 unt; 0 nHn; 17 RR)
% Number of literals : 72 ( 6 equ; 21 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 110 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this,negated_conjecture,
~ theorem(implies(and(p,implies(p,q)),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(c0,plain,
~ theorem(implies(and(p,implies(p,q)),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(d0,plain,
theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[c3,c7]) ).
cnf(d1,plain,
theorem(implies(or(X1,not(X0)),implies(X0,X1))),
inference(superposition,[status(thm)],[c6,d0]) ).
cnf(d2,plain,
( ~ theorem(or(X1,not(X0)))
| theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d3,plain,
and(X0,X1) = not(implies(X0,not(X1))),
inference(demodulation,[status(thm)],[c9,c6]) ).
cnf(d4,plain,
implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[c5,c7]) ).
cnf(d6,plain,
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[d5,c8]) ).
cnf(d7,plain,
( ~ theorem(or(X2,X0))
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d6,c8]) ).
cnf(d8,plain,
theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[status(thm)],[c6,d0]) ).
cnf(d9,plain,
theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[c4,c7]) ).
cnf(d10,plain,
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[d9,c8]) ).
cnf(d11,plain,
( theorem(or(X1,or(not(X0),X2)))
| ~ theorem(implies(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[c6,d10]) ).
cnf(d12,plain,
( theorem(or(X2,implies(X0,X1)))
| ~ theorem(implies(X0,or(X2,X1))) ),
inference(demodulation,[status(thm)],[d11,c6]) ).
cnf(d13,plain,
theorem(or(X0,implies(implies(X1,X0),not(X1)))),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( theorem(or(X1,X2))
| ~ theorem(implies(implies(implies(X0,X1),not(X0)),X2)) ),
inference(resolution,[status(thm)],[d13,d7]) ).
cnf(d15,plain,
( theorem(or(X1,X2))
| ~ theorem(or(and(implies(X0,X1),X0),X2)) ),
inference(demodulation,[status(thm)],[d14,d4]) ).
cnf(d16,plain,
theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[c1,c7]) ).
cnf(d17,plain,
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[c8,d16]) ).
cnf(d18,plain,
theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[c2,c7]) ).
cnf(d19,plain,
theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[d12,d18]) ).
cnf(d20,plain,
( theorem(or(X2,X1))
| ~ theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[d7,d19]) ).
cnf(d21,plain,
theorem(or(X0,or(X1,not(X1)))),
inference(resolution,[status(thm)],[d20,d8]) ).
cnf(d22,plain,
theorem(or(X0,not(X0))),
inference(resolution,[status(thm)],[d21,d17]) ).
cnf(d23,plain,
axiom(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[status(thm)],[c6,c3]) ).
cnf(d24,plain,
axiom(implies(implies(X1,not(X0)),implies(X0,not(X1)))),
inference(superposition,[status(thm)],[c6,d23]) ).
cnf(d25,plain,
axiom(or(and(X0,X1),implies(X1,not(X0)))),
inference(demodulation,[status(thm)],[d24,d4]) ).
cnf(d26,plain,
theorem(or(and(X0,X1),implies(X1,not(X0)))),
inference(resolution,[status(thm)],[d25,c7]) ).
cnf(d27,plain,
( theorem(or(and(X1,X0),X2))
| ~ theorem(implies(implies(X0,not(X1)),X2)) ),
inference(resolution,[status(thm)],[d7,d26]) ).
cnf(d28,plain,
( theorem(or(and(X1,X0),X2))
| ~ theorem(or(and(X0,X1),X2)) ),
inference(demodulation,[status(thm)],[d27,d4]) ).
cnf(d29,plain,
theorem(or(and(X0,X1),not(and(X1,X0)))),
inference(resolution,[status(thm)],[d28,d22]) ).
cnf(d30,plain,
theorem(or(X0,not(and(X1,implies(X1,X0))))),
inference(resolution,[status(thm)],[d29,d15]) ).
cnf(d31,plain,
theorem(implies(and(X0,implies(X0,X1)),X1)),
inference(resolution,[status(thm)],[d30,d2]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[d31,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL246-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.46 % Computer : n008.cluster.edu
% 0.09/0.46 % Model : x86_64 x86_64
% 0.09/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.46 % Memory : 8046.5625MB
% 0.09/0.46 % OS : Linux 6.8.0-71-generic
% 0.09/0.47 % CPULimit : 300
% 0.09/0.47 % WCLimit : 300
% 0.09/0.47 % DateTime : Fri Sep 25 22:07:40 UTC 2026
% 0.09/0.47 % CPUTime :
% 0.09/0.47 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.19/5.62 % SZS status Unsatisfiable for theBenchmark.p
% 8.19/5.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------