%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP168-2 : 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 : n007.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 12.63s 4.24s
% Output : CNFRefutation 12.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 8 RR)
% Number of literals : 18 ( 17 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; 4 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p01b_1,hypothesis,
'greatest$ulower$ubound'(a,b) = a ).
cnf(prove_p01b,negated_conjecture,
'greatest$ulower$ubound'(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(a,c)) ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
cnf(associativity,axiom,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)) ).
cnf(monotony_glb1,axiom,
multiply(X0,'greatest$ulower$ubound'(X1,X2)) = 'greatest$ulower$ubound'(multiply(X0,X1),multiply(X0,X2)) ).
cnf(monotony_glb2,axiom,
multiply('greatest$ulower$ubound'(X0,X1),X2) = 'greatest$ulower$ubound'(multiply(X0,X2),multiply(X1,X2)) ).
cnf(c0,plain,
'greatest$ulower$ubound'(a,b) = a,
inference(clausification,[status(esa)],[p01b_1]) ).
cnf(c1,plain,
'greatest$ulower$ubound'(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(a,c)),
inference(clausification,[status(esa)],[prove_p01b]) ).
cnf(c2,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c4,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(c14,plain,
multiply(X0,'greatest$ulower$ubound'(X1,X2)) = 'greatest$ulower$ubound'(multiply(X0,X1),multiply(X0,X2)),
inference(clausification,[status(esa)],[monotony_glb1]) ).
cnf(c16,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(inverse(c),'greatest$ulower$ubound'(multiply(a,c),multiply(b,c))) != multiply(inverse(c),multiply(a,c)),
inference(demodulation,[status(thm)],[c1,c14]) ).
cnf(d1,plain,
multiply(inverse(c),multiply('greatest$ulower$ubound'(a,b),c)) != multiply(inverse(c),multiply(a,c)),
inference(demodulation,[status(thm)],[d0,c16]) ).
cnf(d2,plain,
multiply(inverse(c),multiply(a,c)) != multiply(inverse(c),multiply(a,c)),
inference(demodulation,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c2,c4]) ).
cnf(d4,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP168-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.64 % Computer : n007.cluster.edu
% 0.17/0.64 % Model : x86_64 x86_64
% 0.17/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.64 % Memory : 8046.5625MB
% 0.17/0.64 % OS : Linux 6.8.0-71-generic
% 0.17/0.64 % CPULimit : 300
% 0.17/0.64 % WCLimit : 300
% 0.17/0.64 % DateTime : Fri Sep 25 14:31:08 UTC 2026
% 0.22/0.65 % CPUTime :
% 0.22/0.65 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.63/4.24 % SZS status Unsatisfiable for theBenchmark.p
% 12.63/4.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------