%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP186-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 07:23:23 AM UTC 2026
% Result : Unsatisfiable 41.46s 23.18s
% Output : CNFRefutation 41.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 6 RR)
% Number of literals : 30 ( 29 equ; 5 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p23x_2,hypothesis,
inverse(inverse(X0)) = X0 ).
cnf(prove_p23x,negated_conjecture,
'least$uupper$ubound'(multiply(a,b),identity) != multiply(a,'least$uupper$ubound'(inverse(a),b)) ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(symmetry_of_glb,axiom,
'greatest$ulower$ubound'(X0,X1) = 'greatest$ulower$ubound'(X1,X0) ).
cnf(symmetry_of_lub,axiom,
'least$uupper$ubound'(X0,X1) = 'least$uupper$ubound'(X1,X0) ).
cnf(associativity_of_glb,axiom,
'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'(X1,X2)) = 'greatest$ulower$ubound'('greatest$ulower$ubound'(X0,X1),X2) ).
cnf(lub_absorbtion,axiom,
'least$uupper$ubound'(X0,'greatest$ulower$ubound'(X0,X1)) = X0 ).
cnf(monotony_lub1,axiom,
multiply(X0,'least$uupper$ubound'(X1,X2)) = 'least$uupper$ubound'(multiply(X0,X1),multiply(X0,X2)) ).
cnf(c1,plain,
inverse(inverse(X0)) = X0,
inference(clausification,[status(esa)],[p23x_2]) ).
cnf(c3,plain,
'least$uupper$ubound'(multiply(a,b),identity) != multiply(a,'least$uupper$ubound'(inverse(a),b)),
inference(clausification,[status(esa)],[prove_p23x]) ).
cnf(c5,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c7,plain,
'greatest$ulower$ubound'(X0,X1) = 'greatest$ulower$ubound'(X1,X0),
inference(clausification,[status(esa)],[symmetry_of_glb]) ).
cnf(c8,plain,
'least$uupper$ubound'(X0,X1) = 'least$uupper$ubound'(X1,X0),
inference(clausification,[status(esa)],[symmetry_of_lub]) ).
cnf(c9,plain,
'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'(X1,X2)) = 'greatest$ulower$ubound'('greatest$ulower$ubound'(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_of_glb]) ).
cnf(c13,plain,
'least$uupper$ubound'(X0,'greatest$ulower$ubound'(X0,X1)) = X0,
inference(clausification,[status(esa)],[lub_absorbtion]) ).
cnf(c15,plain,
multiply(X0,'least$uupper$ubound'(X1,X2)) = 'least$uupper$ubound'(multiply(X0,X1),multiply(X0,X2)),
inference(clausification,[status(esa)],[monotony_lub1]) ).
cnf(d0,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c1,c5]) ).
cnf(d1,plain,
multiply(X0,'least$uupper$ubound'(X1,inverse(X0))) = 'least$uupper$ubound'(multiply(X0,X1),identity),
inference(superposition,[status(thm)],[d0,c15]) ).
cnf(d2,plain,
multiply(X0,'least$uupper$ubound'(X1,inverse(X0))) = 'least$uupper$ubound'(identity,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d1,c8]) ).
cnf(d3,plain,
'least$uupper$ubound'(identity,multiply(a,b)) != multiply(a,'least$uupper$ubound'(inverse(a),b)),
inference(demodulation,[status(thm)],[c3,c8]) ).
cnf(d4,plain,
'least$uupper$ubound'(identity,multiply(a,b)) != multiply(a,'least$uupper$ubound'(b,inverse(a))),
inference(demodulation,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
'least$uupper$ubound'(identity,multiply(a,b)) != 'least$uupper$ubound'(identity,multiply(a,b)),
inference(demodulation,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
'least$uupper$ubound'(X0,'greatest$ulower$ubound'(X1,X0)) = X0,
inference(superposition,[status(thm)],[c7,c13]) ).
cnf(d7,plain,
'least$uupper$ubound'(X2,'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'(X1,X2))) = X2,
inference(superposition,[status(thm)],[c9,d6]) ).
cnf(d8,plain,
'least$uupper$ubound'(X2,'greatest$ulower$ubound'('greatest$ulower$ubound'(X1,X2),X0)) = X2,
inference(superposition,[status(thm)],[c7,d7]) ).
cnf(d9,plain,
'least$uupper$ubound'(X1,'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'(X1,X2))) = X1,
inference(demodulation,[status(thm)],[d8,c9]) ).
cnf(d10,plain,
'least$uupper$ubound'(X1,'greatest$ulower$ubound'('greatest$ulower$ubound'(X1,X2),X0)) = X1,
inference(superposition,[status(thm)],[c7,d9]) ).
cnf(d11,plain,
'least$uupper$ubound'(X0,'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'(X1,X2))) = X0,
inference(demodulation,[status(thm)],[d10,c9]) ).
cnf(d12,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d11,c13]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP186-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n018.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Fri Sep 25 14:38:56 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 41.46/23.18 % SZS status Unsatisfiable for theBenchmark.p
% 41.46/23.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------