%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LAT019-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 07:47:42 AM UTC 2026
% Result : Unsatisfiable 87.94s 14.32s
% Output : CNFRefutation 87.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 64 ( 64 unt; 0 nHn; 7 RR)
% Number of literals : 64 ( 63 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 143 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity_law,hypothesis,
meet(X0,join(X1,X2)) = join(meet(X0,X1),meet(X0,X2)) ).
cnf(prove_distributivity_law_dual,negated_conjecture,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)) ).
cnf(idempotence_of_meet,axiom,
meet(X0,X0) = X0 ).
cnf(idempotence_of_join,axiom,
join(X0,X0) = X0 ).
cnf(commutativity_of_meet,axiom,
meet(X0,X1) = meet(X1,X0) ).
cnf(commutativity_of_join,axiom,
join(X0,X1) = join(X1,X0) ).
cnf(associativity_of_meet,axiom,
meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)) ).
cnf(associativity_of_join,axiom,
join(join(X0,X1),X2) = join(X0,join(X1,X2)) ).
cnf(quasi_lattice1,axiom,
join(meet(X0,join(X1,X2)),meet(X0,X1)) = meet(X0,join(X1,X2)) ).
cnf(quasi_lattice2,axiom,
meet(join(X0,meet(X1,X2)),join(X0,X1)) = join(X0,meet(X1,X2)) ).
cnf(c0,plain,
join(meet(X0,X1),meet(X0,X2)) = meet(X0,join(X1,X2)),
inference(clausification,[status(esa)],[distributivity_law]) ).
cnf(c1,plain,
meet(join(a,b),join(a,c)) != join(a,meet(b,c)),
inference(clausification,[status(esa)],[prove_distributivity_law_dual]) ).
cnf(c2,plain,
meet(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_of_meet]) ).
cnf(c3,plain,
join(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_of_join]) ).
cnf(c4,plain,
meet(X0,X1) = meet(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_meet]) ).
cnf(c5,plain,
join(X0,X1) = join(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_join]) ).
cnf(c6,plain,
meet(X0,meet(X1,X2)) = meet(meet(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_of_meet]) ).
cnf(c7,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_of_join]) ).
cnf(c8,plain,
meet(X0,join(X1,X2)) = join(meet(X0,join(X1,X2)),meet(X0,X1)),
inference(clausification,[status(esa)],[quasi_lattice1]) ).
cnf(c9,plain,
join(X0,meet(X1,X2)) = meet(join(X0,meet(X1,X2)),join(X0,X1)),
inference(clausification,[status(esa)],[quasi_lattice2]) ).
cnf(d0,plain,
X0 = meet(X0,X0),
inference(superposition,[status(thm)],[c2,c4]) ).
cnf(d1,plain,
meet(X0,meet(X0,X1)) = meet(X0,X1),
inference(superposition,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
join(meet(X0,X1),meet(X0,X2)) = meet(X0,join(meet(X0,X1),X2)),
inference(superposition,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
meet(X0,join(X1,X2)) = meet(X0,join(meet(X0,X1),X2)),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
join(meet(X0,X2),meet(X0,X1)) = meet(X0,join(X1,X2)),
inference(superposition,[status(thm)],[c5,c0]) ).
cnf(d5,plain,
meet(X0,join(X2,X1)) = meet(X0,join(X1,X2)),
inference(superposition,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
meet(X0,join(X2,X1)) = meet(join(X1,X2),X0),
inference(superposition,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
join(meet(X0,X2),meet(X0,X1)) = meet(X0,join(X2,meet(X0,X1))),
inference(superposition,[status(thm)],[d1,c0]) ).
cnf(d8,plain,
meet(X0,join(X1,X2)) = meet(X0,join(X1,meet(X0,X2))),
inference(demodulation,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
join(X0,meet(X1,X2)) = meet(join(X0,X1),join(X0,meet(X1,X2))),
inference(demodulation,[status(thm)],[c9,c4]) ).
cnf(d10,plain,
X0 = join(X0,X0),
inference(superposition,[status(thm)],[c3,c5]) ).
cnf(d11,plain,
join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[d10,c7]) ).
cnf(d12,plain,
join(X0,meet(join(X0,X1),X2)) = meet(join(X0,X1),join(X0,meet(join(X0,X1),X2))),
inference(superposition,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
join(X0,meet(join(X0,X1),X2)) = meet(join(X0,X1),join(X0,X2)),
inference(demodulation,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
meet(X0,meet(X1,X2)) = meet(X2,meet(X0,X1)),
inference(superposition,[status(thm)],[c6,c4]) ).
cnf(d15,plain,
meet(X2,meet(X1,X0)) = meet(X1,meet(X2,X0)),
inference(superposition,[status(thm)],[c4,d14]) ).
cnf(d16,plain,
meet(X0,X1) = meet(X0,join(X1,X1)),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d17,plain,
meet(X1,X0) = meet(X1,X0),
inference(demodulation,[status(thm)],[d16,c3]) ).
cnf(d18,plain,
meet(X0,X1) = meet(X0,meet(X0,X1)),
inference(superposition,[status(thm)],[d1,d17]) ).
cnf(d19,plain,
join(X2,meet(X0,meet(X0,X1))) = meet(join(X2,X0),join(X2,meet(X0,X1))),
inference(superposition,[status(thm)],[d18,d9]) ).
cnf(d20,plain,
join(X2,meet(X0,X1)) = meet(join(X2,X0),join(X2,meet(X0,X1))),
inference(demodulation,[status(thm)],[d19,d1]) ).
cnf(d21,plain,
join(X0,meet(X1,X2)) = join(X0,meet(join(X0,X1),meet(X1,X2))),
inference(demodulation,[status(thm)],[d20,d13]) ).
cnf(d22,plain,
join(X0,meet(X1,X2)) = join(X0,meet(X1,meet(join(X0,X1),X2))),
inference(demodulation,[status(thm)],[d21,d15]) ).
cnf(d23,plain,
meet(X0,meet(X0,X1)) = meet(X1,X0),
inference(superposition,[status(thm)],[d0,d14]) ).
cnf(d24,plain,
meet(join(X0,X1),join(X0,meet(X1,X2))) = meet(join(X0,meet(X1,X2)),join(X0,X1)),
inference(superposition,[status(thm)],[d9,d23]) ).
cnf(d25,plain,
join(X0,meet(join(X0,X1),meet(X1,X2))) = meet(join(X0,meet(X1,X2)),join(X0,X1)),
inference(demodulation,[status(thm)],[d24,d13]) ).
cnf(d26,plain,
join(X0,meet(X1,meet(join(X0,X1),X2))) = meet(join(X0,meet(X1,X2)),join(X0,X1)),
inference(demodulation,[status(thm)],[d25,d15]) ).
cnf(d27,plain,
join(X0,meet(X1,X2)) = meet(join(X0,meet(X1,X2)),join(X0,X1)),
inference(demodulation,[status(thm)],[d26,d22]) ).
cnf(d28,plain,
join(X0,meet(X1,X2)) = join(X0,meet(join(X0,meet(X1,X2)),X1)),
inference(demodulation,[status(thm)],[d27,d13]) ).
cnf(d29,plain,
join(X0,meet(X1,X2)) = join(X0,meet(X1,join(meet(X1,X2),X0))),
inference(demodulation,[status(thm)],[d28,d6]) ).
cnf(d30,plain,
join(X2,meet(X0,X1)) = join(X2,meet(X0,join(X1,X2))),
inference(demodulation,[status(thm)],[d29,d3]) ).
cnf(d31,plain,
join(a,meet(join(a,b),c)) != join(a,meet(b,c)),
inference(demodulation,[status(thm)],[c1,d13]) ).
cnf(d32,plain,
join(a,meet(c,join(b,a))) != join(a,meet(b,c)),
inference(demodulation,[status(thm)],[d31,d6]) ).
cnf(d33,plain,
join(a,meet(c,b)) != join(a,meet(b,c)),
inference(demodulation,[status(thm)],[d32,d30]) ).
cnf(d34,plain,
join(a,meet(b,c)) != join(a,meet(b,c)),
inference(demodulation,[status(thm)],[d33,c4]) ).
cnf(d35,plain,
join(X0,join(X1,X0)) = join(X0,X1),
inference(superposition,[status(thm)],[c5,d11]) ).
cnf(d36,plain,
meet(X0,join(X1,X2)) = meet(X0,join(join(X1,X2),X1)),
inference(demodulation,[status(thm)],[c8,c0]) ).
cnf(d37,plain,
meet(X2,join(X0,X1)) = meet(X2,join(X0,join(X1,X0))),
inference(demodulation,[status(thm)],[d36,c7]) ).
cnf(d38,plain,
join(X0,join(X1,X0)) = meet(join(X0,join(X1,X0)),join(X0,X1)),
inference(superposition,[status(thm)],[d37,d0]) ).
cnf(d39,plain,
join(X0,X1) = meet(join(X0,join(X1,X0)),join(X0,X1)),
inference(demodulation,[status(thm)],[d38,d35]) ).
cnf(d40,plain,
join(X0,X1) = meet(join(X0,X1),join(X0,join(X1,X0))),
inference(demodulation,[status(thm)],[d39,c4]) ).
cnf(d41,plain,
join(X0,X1) = meet(join(X0,X1),join(X0,X1)),
inference(demodulation,[status(thm)],[d40,d35]) ).
cnf(d42,plain,
join(X0,X1) = join(X0,X1),
inference(demodulation,[status(thm)],[d41,c2]) ).
cnf(d43,plain,
$false,
inference(resolution,[status(thm)],[d42,d34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT019-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n002.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 19:59:50 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 87.94/14.32 % SZS status Unsatisfiable for theBenchmark.p
% 87.94/14.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------