%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LAT040-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 07:47:44 AM UTC 2026
% Result : Unsatisfiable 27.22s 5.88s
% Output : CNFRefutation 27.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of clauses : 58 ( 58 unt; 0 nHn; 24 RR)
% Number of literals : 58 ( 57 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 81 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(dist_join,hypothesis,
join(X0,meet(X1,X2)) = meet(join(X0,X1),join(X0,X2)) ).
cnf(dist_meet,hypothesis,
meet(X0,join(X1,X2)) = join(meet(X0,X1),meet(X0,X2)) ).
cnf(lhs1,hypothesis,
join(xx,yy) = join(xx,zz) ).
cnf(lhs2,hypothesis,
meet(xx,yy) = meet(xx,zz) ).
cnf(rhs,negated_conjecture,
yy != zz ).
cnf(idempotence_of_meet,axiom,
meet(X0,X0) = X0 ).
cnf(absorption1,axiom,
meet(X0,join(X0,X1)) = X0 ).
cnf(absorption2,axiom,
join(X0,meet(X0,X1)) = 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(c0,plain,
join(X0,meet(X1,X2)) = meet(join(X0,X1),join(X0,X2)),
inference(clausification,[status(esa)],[dist_join]) ).
cnf(c1,plain,
meet(X0,join(X1,X2)) = join(meet(X0,X1),meet(X0,X2)),
inference(clausification,[status(esa)],[dist_meet]) ).
cnf(c2,plain,
join(xx,yy) = join(xx,zz),
inference(clausification,[status(esa)],[lhs1]) ).
cnf(c3,plain,
meet(xx,yy) = meet(xx,zz),
inference(clausification,[status(esa)],[lhs2]) ).
cnf(c4,plain,
yy != zz,
inference(clausification,[status(esa)],[rhs]) ).
cnf(c5,plain,
meet(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_of_meet]) ).
cnf(c7,plain,
meet(X0,join(X0,X1)) = X0,
inference(clausification,[status(esa)],[absorption1]) ).
cnf(c8,plain,
join(X0,meet(X0,X1)) = X0,
inference(clausification,[status(esa)],[absorption2]) ).
cnf(c9,plain,
meet(X0,X1) = meet(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_meet]) ).
cnf(c10,plain,
join(X0,X1) = join(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_join]) ).
cnf(c11,plain,
meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
inference(clausification,[status(esa)],[associativity_of_meet]) ).
cnf(c12,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(clausification,[status(esa)],[associativity_of_join]) ).
cnf(d0,plain,
join(X0,meet(X1,X0)) = X0,
inference(superposition,[status(thm)],[c9,c8]) ).
cnf(d1,plain,
join(X0,meet(X1,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c5,c0]) ).
cnf(d2,plain,
join(X1,X0) = join(X1,X0),
inference(demodulation,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
X0 = join(X0,meet(X1,X0)),
inference(superposition,[status(thm)],[d0,d2]) ).
cnf(d4,plain,
meet(X0,join(X1,X0)) = X0,
inference(superposition,[status(thm)],[c10,c7]) ).
cnf(d5,plain,
meet(X0,join(X2,X1)) = join(meet(X0,X2),meet(X1,X0)),
inference(superposition,[status(thm)],[c9,c1]) ).
cnf(d6,plain,
join(zz,meet(xx,yy)) = zz,
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d7,plain,
meet(meet(xx,yy),zz) = meet(xx,yy),
inference(superposition,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
meet(xx,meet(yy,zz)) = meet(xx,yy),
inference(demodulation,[status(thm)],[d7,c11]) ).
cnf(d9,plain,
join(meet(yy,zz),meet(xx,yy)) = meet(yy,zz),
inference(superposition,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
meet(yy,join(zz,xx)) = meet(yy,zz),
inference(demodulation,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
meet(yy,join(xx,zz)) = meet(yy,zz),
inference(demodulation,[status(thm)],[d10,c10]) ).
cnf(d12,plain,
meet(yy,join(xx,yy)) = meet(yy,zz),
inference(demodulation,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
yy = meet(yy,zz),
inference(demodulation,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
zz = join(zz,yy),
inference(superposition,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
zz = join(yy,zz),
inference(demodulation,[status(thm)],[d14,c10]) ).
cnf(d16,plain,
join(join(X0,X1),X0) = join(X0,X1),
inference(superposition,[status(thm)],[c7,d0]) ).
cnf(d17,plain,
join(X0,join(X1,X0)) = join(X0,X1),
inference(demodulation,[status(thm)],[d16,c12]) ).
cnf(d18,plain,
join(X0,meet(X2,join(X1,X0))) = meet(join(X0,X2),join(X0,X1)),
inference(superposition,[status(thm)],[d17,c0]) ).
cnf(d19,plain,
join(X0,meet(X1,join(X2,X0))) = join(X0,meet(X1,X2)),
inference(demodulation,[status(thm)],[d18,c0]) ).
cnf(d20,plain,
meet(zz,join(xx,yy)) = zz,
inference(superposition,[status(thm)],[c2,d4]) ).
cnf(d21,plain,
join(yy,zz) = join(yy,meet(zz,xx)),
inference(superposition,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
zz = join(yy,meet(zz,xx)),
inference(demodulation,[status(thm)],[d21,d15]) ).
cnf(d23,plain,
zz = join(yy,meet(xx,zz)),
inference(demodulation,[status(thm)],[d22,c9]) ).
cnf(d24,plain,
zz = join(yy,meet(xx,yy)),
inference(demodulation,[status(thm)],[d23,c3]) ).
cnf(d25,plain,
zz = yy,
inference(demodulation,[status(thm)],[d24,d0]) ).
cnf(d26,plain,
yy != yy,
inference(demodulation,[status(thm)],[c4,d25]) ).
cnf(d27,plain,
join(X0,meet(X2,meet(X0,X1))) = meet(join(X0,X2),X0),
inference(superposition,[status(thm)],[c8,c0]) ).
cnf(d28,plain,
join(X0,meet(X1,meet(X0,X2))) = meet(X0,join(X0,X1)),
inference(demodulation,[status(thm)],[d27,c9]) ).
cnf(d29,plain,
join(X0,meet(X1,meet(X0,X2))) = X0,
inference(demodulation,[status(thm)],[d28,c7]) ).
cnf(d30,plain,
join(X1,meet(meet(X1,X2),X0)) = X1,
inference(superposition,[status(thm)],[c9,d29]) ).
cnf(d31,plain,
join(X0,meet(X0,meet(X1,X2))) = X0,
inference(demodulation,[status(thm)],[d30,c11]) ).
cnf(d32,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d31,c8]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d32,d26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT040-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 19:59:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.22/5.88 % SZS status Unsatisfiable for theBenchmark.p
% 27.22/5.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------