%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : REL003-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 08:24:12 AM UTC 2026
% Result : Unsatisfiable 17.02s 5.12s
% Output : CNFRefutation 17.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 42 ( 27 unt; 8 nHn; 17 RR)
% Number of literals : 57 ( 56 equ; 15 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(goals_14,negated_conjecture,
( join(converse(sk1),converse(sk2)) = converse(sk2)
| join(sk1,sk2) = sk2 ) ).
cnf(goals_17,negated_conjecture,
( join(converse(sk1),converse(sk2)) != converse(sk2)
| join(sk1,sk2) != sk2 ) ).
cnf(maddux1_join_commutativity_1,axiom,
join(X0,X1) = join(X1,X0) ).
cnf(composition_associativity_5,axiom,
composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2) ).
cnf(composition_identity_6,axiom,
composition(X0,one) = X0 ).
cnf(composition_distributivity_7,axiom,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X0)) = X0 ).
cnf(converse_additivity_9,axiom,
converse(join(X0,X1)) = join(converse(X0),converse(X1)) ).
cnf(converse_multiplicativity_10,axiom,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ).
cnf(c0,plain,
( join(converse(sk1),converse(sk2)) = converse(sk2)
| join(sk1,sk2) = sk2 ),
inference(clausification,[status(esa)],[goals_14]) ).
cnf(c1,plain,
( join(converse(sk1),converse(sk2)) != converse(sk2)
| join(sk1,sk2) != sk2 ),
inference(clausification,[status(esa)],[goals_17]) ).
cnf(c2,plain,
join(X0,X1) = join(X1,X0),
inference(clausification,[status(esa)],[maddux1_join_commutativity_1]) ).
cnf(c6,plain,
composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
inference(clausification,[status(esa)],[composition_associativity_5]) ).
cnf(c7,plain,
composition(X0,one) = X0,
inference(clausification,[status(esa)],[composition_identity_6]) ).
cnf(c8,plain,
composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
inference(clausification,[status(esa)],[composition_distributivity_7]) ).
cnf(c9,plain,
converse(converse(X0)) = X0,
inference(clausification,[status(esa)],[converse_idempotence_8]) ).
cnf(c10,plain,
converse(join(X0,X1)) = join(converse(X0),converse(X1)),
inference(clausification,[status(esa)],[converse_additivity_9]) ).
cnf(c11,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(clausification,[status(esa)],[converse_multiplicativity_10]) ).
cnf(d0,plain,
composition(join(X0,X1),one) = join(X0,composition(X1,one)),
inference(superposition,[status(thm)],[c7,c8]) ).
cnf(d1,plain,
join(X0,X1) = join(X0,composition(X1,one)),
inference(demodulation,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
join(X1,X0) = join(X1,X0),
inference(demodulation,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
( join(sk1,sk2) = sk2
| join(converse(sk2),converse(sk1)) = converse(sk2) ),
inference(demodulation,[status(thm)],[c0,c2]) ).
cnf(d4,plain,
( join(sk2,sk1) = sk2
| join(converse(sk2),converse(sk1)) = converse(sk2) ),
inference(demodulation,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
( join(sk2,sk1) = sk2
| converse(join(sk2,sk1)) = converse(sk2) ),
inference(demodulation,[status(thm)],[d4,c10]) ).
cnf(d6,plain,
( join(sk2,sk1) = sk2
| converse(converse(sk2)) = join(sk2,sk1) ),
inference(superposition,[status(thm)],[d5,c9]) ).
cnf(d7,plain,
( sk2 = join(sk2,sk1)
| join(sk2,sk1) = sk2 ),
inference(demodulation,[status(thm)],[d6,c9]) ).
cnf(d8,plain,
( sk2 = join(sk2,sk1)
| sk2 = join(sk2,sk1) ),
inference(superposition,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
( join(sk1,sk2) != sk2
| join(converse(sk2),converse(sk1)) != converse(sk2) ),
inference(demodulation,[status(thm)],[c1,c2]) ).
cnf(d10,plain,
( join(sk2,sk1) != sk2
| join(converse(sk2),converse(sk1)) != converse(sk2) ),
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
( join(sk2,sk1) != sk2
| converse(join(sk2,sk1)) != converse(sk2) ),
inference(demodulation,[status(thm)],[d10,c10]) ).
cnf(d12,plain,
( join(sk2,sk1) != sk2
| converse(sk2) != converse(sk2) ),
inference(demodulation,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( sk2 != sk2
| converse(sk2) != converse(sk2) ),
inference(demodulation,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
converse(composition(converse(X0),X1)) = composition(converse(X1),X0),
inference(superposition,[status(thm)],[c9,c11]) ).
cnf(d15,plain,
composition(X0,composition(X1,one)) = composition(X0,X1),
inference(superposition,[status(thm)],[c6,c7]) ).
cnf(d16,plain,
composition(X1,X0) = composition(X1,X0),
inference(demodulation,[status(thm)],[d15,c7]) ).
cnf(d17,plain,
X0 = composition(X0,one),
inference(superposition,[status(thm)],[c7,d16]) ).
cnf(d18,plain,
converse(converse(X0)) = composition(converse(one),X0),
inference(superposition,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
X0 = composition(converse(one),X0),
inference(demodulation,[status(thm)],[d18,c9]) ).
cnf(d20,plain,
converse(X0) = composition(converse(X0),one),
inference(superposition,[status(thm)],[d19,d14]) ).
cnf(d21,plain,
converse(X0) = converse(X0),
inference(demodulation,[status(thm)],[d20,c7]) ).
cnf(d22,plain,
sk2 != sk2,
inference(resolution,[status(thm)],[d21,d13]) ).
cnf(d23,plain,
$false,
inference(equality_resolution,[status(thm)],[d22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL003-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.39 % Computer : n001.cluster.edu
% 0.08/0.39 % Model : x86_64 x86_64
% 0.08/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.39 % Memory : 8046.5625MB
% 0.08/0.39 % OS : Linux 6.8.0-71-generic
% 0.08/0.39 % CPULimit : 300
% 0.08/0.39 % WCLimit : 300
% 0.08/0.39 % DateTime : Sat Sep 26 05:31:12 UTC 2026
% 0.08/0.40 % CPUTime :
% 0.08/0.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.02/5.12 % SZS status Unsatisfiable for theBenchmark.p
% 17.02/5.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------