%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP171-2 : 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 : 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 07:23:19 AM UTC 2026
% Result : Unsatisfiable 39.45s 14.95s
% Output : CNFRefutation 39.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 11 RR)
% Number of literals : 39 ( 38 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p04c_1,hypothesis,
'least$uupper$ubound'(identity,a) = a ).
cnf(p04c_2,hypothesis,
'least$uupper$ubound'(identity,b) = b ).
cnf(prove_p04c,negated_conjecture,
'greatest$ulower$ubound'(identity,multiply(a,b)) != identity ).
cnf(left_identity,axiom,
multiply(identity,X0) = X0 ).
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(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_lub,axiom,
'least$uupper$ubound'(X0,X0) = X0 ).
cnf(lub_absorbtion,axiom,
'least$uupper$ubound'(X0,'greatest$ulower$ubound'(X0,X1)) = X0 ).
cnf(glb_absorbtion,axiom,
'greatest$ulower$ubound'(X0,'least$uupper$ubound'(X0,X1)) = X0 ).
cnf(monotony_lub2,axiom,
multiply('least$uupper$ubound'(X0,X1),X2) = 'least$uupper$ubound'(multiply(X0,X2),multiply(X1,X2)) ).
cnf(c0,plain,
'least$uupper$ubound'(identity,a) = a,
inference(clausification,[status(esa)],[p04c_1]) ).
cnf(c1,plain,
'least$uupper$ubound'(identity,b) = b,
inference(clausification,[status(esa)],[p04c_2]) ).
cnf(c2,plain,
'greatest$ulower$ubound'(identity,multiply(a,b)) != identity,
inference(clausification,[status(esa)],[prove_p04c]) ).
cnf(c3,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c5,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(c6,plain,
'greatest$ulower$ubound'(X0,X1) = 'greatest$ulower$ubound'(X1,X0),
inference(clausification,[status(esa)],[symmetry_of_glb]) ).
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'(X0,'least$uupper$ubound'(X1,X2)) = 'least$uupper$ubound'('least$uupper$ubound'(X0,X1),X2),
inference(clausification,[status(esa)],[associativity_of_lub]) ).
cnf(c10,plain,
'least$uupper$ubound'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_of_lub]) ).
cnf(c12,plain,
'least$uupper$ubound'(X0,'greatest$ulower$ubound'(X0,X1)) = X0,
inference(clausification,[status(esa)],[lub_absorbtion]) ).
cnf(c13,plain,
'greatest$ulower$ubound'(X0,'least$uupper$ubound'(X0,X1)) = X0,
inference(clausification,[status(esa)],[glb_absorbtion]) ).
cnf(c16,plain,
multiply('least$uupper$ubound'(X0,X1),X2) = 'least$uupper$ubound'(multiply(X0,X2),multiply(X1,X2)),
inference(clausification,[status(esa)],[monotony_lub2]) ).
cnf(d0,plain,
'least$uupper$ubound'(identity,'least$uupper$ubound'(b,X0)) = 'least$uupper$ubound'(b,X0),
inference(superposition,[status(thm)],[c1,c9]) ).
cnf(d1,plain,
'greatest$ulower$ubound'(identity,'least$uupper$ubound'(b,X0)) = identity,
inference(superposition,[status(thm)],[d0,c13]) ).
cnf(d2,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c3,c5]) ).
cnf(d3,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c3,d3]) ).
cnf(d5,plain,
multiply('least$uupper$ubound'(identity,X1),X0) = 'least$uupper$ubound'(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[d4,c16]) ).
cnf(d6,plain,
'greatest$ulower$ubound'(identity,multiply('least$uupper$ubound'(identity,X0),b)) = identity,
inference(superposition,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
'least$uupper$ubound'(X0,'greatest$ulower$ubound'(X1,X0)) = X0,
inference(superposition,[status(thm)],[c6,c12]) ).
cnf(d8,plain,
'least$uupper$ubound'('least$uupper$ubound'(X0,X1),X0) = 'least$uupper$ubound'(X0,X1),
inference(superposition,[status(thm)],[c13,d7]) ).
cnf(d9,plain,
'least$uupper$ubound'(X0,'least$uupper$ubound'(X1,X0)) = 'least$uupper$ubound'(X0,X1),
inference(demodulation,[status(thm)],[d8,c9]) ).
cnf(d10,plain,
'least$uupper$ubound'(a,a) = 'least$uupper$ubound'(a,identity),
inference(superposition,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
a = 'least$uupper$ubound'(a,identity),
inference(demodulation,[status(thm)],[d10,c10]) ).
cnf(d12,plain,
a = 'least$uupper$ubound'(identity,a),
inference(demodulation,[status(thm)],[d11,c7]) ).
cnf(d13,plain,
'greatest$ulower$ubound'(identity,multiply(a,b)) = identity,
inference(superposition,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[c2,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP171-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.45 % Computer : n020.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Fri Sep 25 14:34:39 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.45/14.95 % SZS status Unsatisfiable for theBenchmark.p
% 39.45/14.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------