%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP167-5 : 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 : n020.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 07:23:18 AM UTC 2026
% Result : Unsatisfiable 50.31s 6.50s
% Output : CNFRefutation 50.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 4 RR)
% Number of literals : 43 ( 42 equ; 2 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p10,axiom,
inverse('least$uupper$ubound'(X0,X1)) = 'greatest$ulower$ubound'(inverse(X0),inverse(X1)) ).
cnf(lat4_1,axiom,
'positive$upart'(X0) = 'least$uupper$ubound'(X0,identity) ).
cnf(lat4_2,axiom,
'negative$upart'(X0) = 'greatest$ulower$ubound'(X0,identity) ).
cnf(prove_lat4,negated_conjecture,
a != multiply('positive$upart'(a),'negative$upart'(a)) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(left_inverse,axiom,
multiply(inverse(X0),X0) = identity ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
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(monotony_glb2,axiom,
multiply('greatest$ulower$ubound'(X0,X1),X2) = 'greatest$ulower$ubound'(multiply(X0,X2),multiply(X1,X2)) ).
cnf(c0,plain,
inverse('least$uupper$ubound'(X0,X1)) = 'greatest$ulower$ubound'(inverse(X0),inverse(X1)),
inference(clausification,[status(esa)],[p10]) ).
cnf(c1,plain,
'positive$upart'(X0) = 'least$uupper$ubound'(X0,identity),
inference(clausification,[status(esa)],[lat4_1]) ).
cnf(c2,plain,
'negative$upart'(X0) = 'greatest$ulower$ubound'(X0,identity),
inference(clausification,[status(esa)],[lat4_2]) ).
cnf(c5,plain,
a != multiply('positive$upart'(a),'negative$upart'(a)),
inference(clausification,[status(esa)],[prove_lat4]) ).
cnf(c6,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c7,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c8,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(c9,plain,
'greatest$ulower$ubound'(X0,X1) = 'greatest$ulower$ubound'(X1,X0),
inference(clausification,[status(esa)],[symmetry_of_glb]) ).
cnf(c10,plain,
'least$uupper$ubound'(X0,X1) = 'least$uupper$ubound'(X1,X0),
inference(clausification,[status(esa)],[symmetry_of_lub]) ).
cnf(c20,plain,
multiply('greatest$ulower$ubound'(X0,X1),X2) = 'greatest$ulower$ubound'(multiply(X0,X2),multiply(X1,X2)),
inference(clausification,[status(esa)],[monotony_glb2]) ).
cnf(d0,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c7,c8]) ).
cnf(d1,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[d1,d1]) ).
cnf(d3,plain,
X1 = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'negative$upart'(X0) = 'greatest$ulower$ubound'(identity,X0),
inference(superposition,[status(thm)],[c9,c2]) ).
cnf(d5,plain,
'positive$upart'(X0) = 'least$uupper$ubound'(identity,X0),
inference(superposition,[status(thm)],[c10,c1]) ).
cnf(d6,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d7,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d6,c6]) ).
cnf(d8,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c7,d7]) ).
cnf(d9,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c6,d7]) ).
cnf(d10,plain,
X0 = multiply(inverse(identity),X0),
inference(superposition,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
X0 = multiply(inverse(inverse(identity)),X0),
inference(superposition,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
identity = inverse(identity),
inference(superposition,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
inverse('least$uupper$ubound'(identity,X0)) = 'greatest$ulower$ubound'(identity,inverse(X0)),
inference(superposition,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
inverse('positive$upart'(X0)) = 'greatest$ulower$ubound'(identity,inverse(X0)),
inference(demodulation,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
inverse('positive$upart'(X0)) = 'negative$upart'(inverse(X0)),
inference(demodulation,[status(thm)],[d14,d4]) ).
cnf(d16,plain,
multiply('greatest$ulower$ubound'(identity,X1),X0) = 'greatest$ulower$ubound'(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[c6,c20]) ).
cnf(d17,plain,
multiply('negative$upart'(X0),X1) = 'greatest$ulower$ubound'(X1,multiply(X0,X1)),
inference(demodulation,[status(thm)],[d16,d4]) ).
cnf(d18,plain,
multiply('negative$upart'(inverse(X0)),X0) = 'greatest$ulower$ubound'(X0,identity),
inference(superposition,[status(thm)],[d8,d17]) ).
cnf(d19,plain,
multiply(inverse('positive$upart'(X0)),X0) = 'greatest$ulower$ubound'(X0,identity),
inference(demodulation,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
multiply(inverse('positive$upart'(X0)),X0) = 'negative$upart'(X0),
inference(demodulation,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
X0 = multiply('positive$upart'(X0),'negative$upart'(X0)),
inference(superposition,[status(thm)],[d20,d3]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d21,c5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 14:34:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 50.31/6.50 % SZS status Unsatisfiable for theBenchmark.p
% 50.31/6.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------