%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL174-3 : 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 : n019.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 07:53:55 AM UTC 2026
% Result : Unsatisfiable 2.64s 3.31s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 23 ( 14 unt; 0 nHn; 12 RR)
% Number of literals : 34 ( 2 equ; 13 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; 3 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_this,negated_conjecture,
~ theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))) ).
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(p,q),implies(implies(q,r),implies(p,r)))),
inference(clausification,[status(esa)],[prove_this]) ).
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(d0,plain,
theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(resolution,[status(thm)],[c5,c7]) ).
cnf(d1,plain,
theorem(implies(implies(X1,X2),implies(implies(X0,X1),or(not(X0),X2)))),
inference(superposition,[status(thm)],[c6,d0]) ).
cnf(d2,plain,
theorem(implies(implies(X2,X1),implies(implies(X0,X2),implies(X0,X1)))),
inference(demodulation,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[c4,c7]) ).
cnf(d4,plain,
( ~ theorem(or(X1,or(X0,X2)))
| theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
( theorem(or(X1,or(not(X0),X2)))
| ~ theorem(implies(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[c6,d4]) ).
cnf(d6,plain,
( theorem(or(X2,implies(X0,X1)))
| ~ theorem(implies(X0,or(X2,X1))) ),
inference(demodulation,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
( theorem(or(not(X0),implies(X2,X1)))
| ~ theorem(implies(X2,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c6,d6]) ).
cnf(d8,plain,
( theorem(implies(X0,implies(X1,X2)))
| ~ theorem(implies(X1,implies(X0,X2))) ),
inference(demodulation,[status(thm)],[d7,c6]) ).
cnf(d9,plain,
theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL174-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n019.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 21:57:21 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.64/3.31 % SZS status Unsatisfiable for theBenchmark.p
% 2.64/3.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------