%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP146-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 07:23:15 AM UTC 2026
% Result : Unsatisfiable 16.42s 3.65s
% Output : CNFRefutation 16.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 15 RR)
% Number of literals : 24 ( 23 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 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 : 19 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ax_lub1a_1,hypothesis,
'least$uupper$ubound'(a,c) = c ).
cnf(ax_lub1a_2,hypothesis,
'least$uupper$ubound'(b,c) = c ).
cnf(prove_ax_lub1a,negated_conjecture,
'least$uupper$ubound'('least$uupper$ubound'(a,b),c) != c ).
cnf(symmetry_of_lub,axiom,
'least$uupper$ubound'(X0,X1) = 'least$uupper$ubound'(X1,X0) ).
cnf(associativity_of_lub,axiom,
'least$uupper$ubound'(X0,'least$uupper$ubound'(X1,X2)) = 'least$uupper$ubound'('least$uupper$ubound'(X0,X1),X2) ).
cnf(idempotence_of_gld,axiom,
'greatest$ulower$ubound'(X0,X0) = X0 ).
cnf(glb_absorbtion,axiom,
'greatest$ulower$ubound'(X0,'least$uupper$ubound'(X0,X1)) = X0 ).
cnf(c0,plain,
'least$uupper$ubound'(a,c) = c,
inference(clausification,[status(esa)],[ax_lub1a_1]) ).
cnf(c1,plain,
'least$uupper$ubound'(b,c) = c,
inference(clausification,[status(esa)],[ax_lub1a_2]) ).
cnf(c2,plain,
'least$uupper$ubound'('least$uupper$ubound'(a,b),c) != c,
inference(clausification,[status(esa)],[prove_ax_lub1a]) ).
cnf(c7,plain,
'least$uupper$ubound'(X0,X1) = 'least$uupper$ubound'(X1,X0),
inference(clausification,[status(esa)],[symmetry_of_lub]) ).
cnf(c9,plain,
'least$uupper$ubound'('least$uupper$ubound'(X0,X1),X2) = 'least$uupper$ubound'(X0,'least$uupper$ubound'(X1,X2)),
inference(clausification,[status(esa)],[associativity_of_lub]) ).
cnf(c11,plain,
'greatest$ulower$ubound'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_of_gld]) ).
cnf(c13,plain,
'greatest$ulower$ubound'(X0,'least$uupper$ubound'(X0,X1)) = X0,
inference(clausification,[status(esa)],[glb_absorbtion]) ).
cnf(d0,plain,
'least$uupper$ubound'(c,b) = c,
inference(demodulation,[status(thm)],[c1,c7]) ).
cnf(d1,plain,
'least$uupper$ubound'(X0,'least$uupper$ubound'(X1,X2)) = 'least$uupper$ubound'(X2,'least$uupper$ubound'(X0,X1)),
inference(superposition,[status(thm)],[c9,c7]) ).
cnf(d2,plain,
'least$uupper$ubound'(c,'least$uupper$ubound'(a,b)) != c,
inference(demodulation,[status(thm)],[c2,c7]) ).
cnf(d3,plain,
'least$uupper$ubound'(a,'least$uupper$ubound'(b,c)) != c,
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'least$uupper$ubound'(a,'least$uupper$ubound'(c,b)) != c,
inference(demodulation,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
'least$uupper$ubound'(a,c) != c,
inference(demodulation,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
c != c,
inference(demodulation,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
'greatest$ulower$ubound'(c,c) = c,
inference(superposition,[status(thm)],[d0,c13]) ).
cnf(d8,plain,
c = c,
inference(demodulation,[status(thm)],[d7,c11]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP146-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n017.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:27:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.42/3.65 % SZS status Unsatisfiable for theBenchmark.p
% 16.42/3.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------