%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL181-3 : TPTP v9.3.1. Released v2.3.0.
% 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 07:53:57 AM UTC 2026
% Result : Unsatisfiable 6.00s 20.99s
% Output : CNFRefutation 6.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of clauses : 62 ( 35 unt; 0 nHn; 25 RR)
% Number of literals : 94 ( 2 equ; 36 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 130 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this,negated_conjecture,
~ theorem(implies(implies(not(p),q),implies(not(q),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(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(c0,plain,
~ theorem(implies(implies(not(p),q),implies(not(q),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(c5,plain,
axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(clausification,[status(esa)],[axiom_1_6]) ).
cnf(c6,plain,
or(not(X0),X1) = implies(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(X0)
| theorem(X1)
| ~ theorem(implies(X0,X1)) ),
inference(clausification,[status(esa)],[rule_2]) ).
cnf(d0,plain,
theorem(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[c2,c7]) ).
cnf(d1,plain,
( ~ theorem(X1)
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[c8,d0]) ).
cnf(d2,plain,
theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[c4,c7]) ).
cnf(d3,plain,
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
( ~ theorem(or(X0,X2))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ theorem(or(X2,X1))
| theorem(or(X2,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c6,d4]) ).
cnf(d6,plain,
theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[c1,c7]) ).
cnf(d7,plain,
( ~ theorem(or(X0,X0))
| theorem(X0) ),
inference(resolution,[status(thm)],[c8,d6]) ).
cnf(d8,plain,
( theorem(implies(X0,X1))
| ~ theorem(or(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[d5,d7]) ).
cnf(d9,plain,
( ~ theorem(or(implies(X0,implies(X1,X2)),X2))
| theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
theorem(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[c3,c7]) ).
cnf(d11,plain,
( ~ theorem(or(X1,X0))
| theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[d10,c8]) ).
cnf(d12,plain,
theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[c5,c7]) ).
cnf(d13,plain,
( ~ theorem(implies(X1,X2))
| theorem(implies(or(X0,X1),or(X0,X2))) ),
inference(resolution,[status(thm)],[d12,c8]) ).
cnf(d14,plain,
( theorem(or(X1,or(not(X0),X2)))
| ~ theorem(implies(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[c6,d3]) ).
cnf(d15,plain,
( theorem(or(X2,implies(X0,X1)))
| ~ theorem(implies(X0,or(X2,X1))) ),
inference(demodulation,[status(thm)],[d14,c6]) ).
cnf(d16,plain,
( ~ theorem(implies(X1,X2))
| theorem(or(X0,implies(or(X0,X1),X2))) ),
inference(resolution,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
( theorem(or(implies(or(X2,X0),X1),X2))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d16,d11]) ).
cnf(d18,plain,
( theorem(implies(or(X2,X0),implies(X1,X2)))
| ~ theorem(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[d17,d9]) ).
cnf(d19,plain,
( ~ theorem(or(X2,X0))
| theorem(or(X2,X1))
| ~ theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d13,c8]) ).
cnf(d20,plain,
( theorem(or(not(X0),X2))
| ~ theorem(implies(X1,X2))
| ~ theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c6,d19]) ).
cnf(d21,plain,
( theorem(implies(X0,X1))
| ~ theorem(implies(X0,X2))
| ~ theorem(implies(X2,X1)) ),
inference(demodulation,[status(thm)],[d20,c6]) ).
cnf(d22,plain,
( theorem(or(not(X0),or(X2,X1)))
| ~ theorem(or(X2,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c6,d3]) ).
cnf(d23,plain,
( theorem(implies(X0,or(X1,X2)))
| ~ theorem(or(X1,implies(X0,X2))) ),
inference(demodulation,[status(thm)],[d22,c6]) ).
cnf(d24,plain,
theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[d15,d0]) ).
cnf(d25,plain,
theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[d24,d7]) ).
cnf(d26,plain,
theorem(or(X0,implies(or(X0,X1),X1))),
inference(resolution,[status(thm)],[d25,d15]) ).
cnf(d27,plain,
theorem(implies(X0,implies(or(not(X0),X1),X1))),
inference(superposition,[status(thm)],[c6,d26]) ).
cnf(d28,plain,
theorem(implies(X0,implies(implies(X0,X1),X1))),
inference(demodulation,[status(thm)],[d27,c6]) ).
cnf(d29,plain,
theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[status(thm)],[c6,d10]) ).
cnf(d30,plain,
( theorem(or(X2,X1))
| ~ theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[d19,d24]) ).
cnf(d31,plain,
theorem(or(X0,or(X1,not(X1)))),
inference(resolution,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
theorem(or(X0,not(X0))),
inference(resolution,[status(thm)],[d31,d7]) ).
cnf(d33,plain,
( theorem(or(X0,X1))
| ~ theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[d32,d19]) ).
cnf(d34,plain,
theorem(or(X0,implies(implies(not(X0),X1),X1))),
inference(resolution,[status(thm)],[d33,d28]) ).
cnf(d35,plain,
theorem(implies(implies(not(X0),X1),or(X0,X1))),
inference(resolution,[status(thm)],[d34,d23]) ).
cnf(d36,plain,
( theorem(implies(implies(not(X0),X1),X2))
| ~ theorem(implies(or(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d35,d21]) ).
cnf(d37,plain,
~ theorem(implies(or(p,q),implies(not(q),p))),
inference(resolution,[status(thm)],[d36,c0]) ).
cnf(d38,plain,
~ theorem(implies(q,implies(not(q),p))),
inference(resolution,[status(thm)],[d37,d18]) ).
cnf(d39,plain,
( theorem(implies(X1,X2))
| ~ theorem(implies(or(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d40,plain,
theorem(implies(X0,or(X0,X1))),
inference(resolution,[status(thm)],[d39,d10]) ).
cnf(d41,plain,
theorem(or(X0,implies(X0,X1))),
inference(resolution,[status(thm)],[d40,d15]) ).
cnf(d42,plain,
theorem(implies(X0,implies(not(X0),X1))),
inference(superposition,[status(thm)],[c6,d41]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[d42,d38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL181-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.54 % Computer : n005.cluster.edu
% 0.11/0.54 % Model : x86_64 x86_64
% 0.11/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.54 % Memory : 8046.5625MB
% 0.11/0.54 % OS : Linux 6.8.0-71-generic
% 0.11/0.54 % CPULimit : 300
% 0.11/0.54 % WCLimit : 300
% 0.11/0.54 % DateTime : Fri Sep 25 21:58:02 UTC 2026
% 0.11/0.54 % CPUTime :
% 0.11/0.54 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.00/20.99 % SZS status Unsatisfiable for theBenchmark.p
% 6.00/20.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------