%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP172-2 : 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 : 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 07:23:19 AM UTC 2026
% Result : Unsatisfiable 51.80s 11.94s
% Output : CNFRefutation 51.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 63 ( 63 unt; 0 nHn; 17 RR)
% Number of literals : 63 ( 62 equ; 3 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 : 88 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p04d_1,hypothesis,
'greatest$ulower$ubound'(identity,a) = identity ).
cnf(p04d_2,hypothesis,
'greatest$ulower$ubound'(identity,b) = identity ).
cnf(prove_p04d,negated_conjecture,
'least$uupper$ubound'(identity,multiply(a,b)) != multiply(a,b) ).
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_glb,axiom,
'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'(X1,X2)) = 'greatest$ulower$ubound'('greatest$ulower$ubound'(X0,X1),X2) ).
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(idempotence_of_gld,axiom,
'greatest$ulower$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,
'greatest$ulower$ubound'(identity,a) = identity,
inference(clausification,[status(esa)],[p04d_1]) ).
cnf(c1,plain,
'greatest$ulower$ubound'(identity,b) = identity,
inference(clausification,[status(esa)],[p04d_2]) ).
cnf(c2,plain,
'least$uupper$ubound'(identity,multiply(a,b)) != multiply(a,b),
inference(clausification,[status(esa)],[prove_p04d]) ).
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(c8,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(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(c11,plain,
'greatest$ulower$ubound'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_of_gld]) ).
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'(X0,'greatest$ulower$ubound'(X1,X0)) = X0,
inference(superposition,[status(thm)],[c6,c12]) ).
cnf(d1,plain,
'least$uupper$ubound'('least$uupper$ubound'(X0,X1),X0) = 'least$uupper$ubound'(X0,X1),
inference(superposition,[status(thm)],[c13,d0]) ).
cnf(d2,plain,
'least$uupper$ubound'(X0,'least$uupper$ubound'(X0,X1)) = 'least$uupper$ubound'(X0,X1),
inference(demodulation,[status(thm)],[d1,c7]) ).
cnf(d3,plain,
'least$uupper$ubound'(X0,X0) = 'least$uupper$ubound'(X0,'greatest$ulower$ubound'(X0,X1)),
inference(superposition,[status(thm)],[c12,d2]) ).
cnf(d4,plain,
X0 = 'least$uupper$ubound'(X0,'greatest$ulower$ubound'(X0,X1)),
inference(demodulation,[status(thm)],[d3,c10]) ).
cnf(d5,plain,
X0 = 'least$uupper$ubound'(X0,'greatest$ulower$ubound'(X1,X0)),
inference(superposition,[status(thm)],[c6,d4]) ).
cnf(d6,plain,
'greatest$ulower$ubound'(X0,'least$uupper$ubound'(X1,X0)) = X0,
inference(superposition,[status(thm)],[c7,c13]) ).
cnf(d7,plain,
'greatest$ulower$ubound'('greatest$ulower$ubound'(X1,X0),X0) = 'greatest$ulower$ubound'(X1,X0),
inference(superposition,[status(thm)],[d0,d6]) ).
cnf(d8,plain,
'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'(X1,X1)) = 'greatest$ulower$ubound'(X0,X1),
inference(demodulation,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
'greatest$ulower$ubound'(X1,X0) = 'greatest$ulower$ubound'(X1,X0),
inference(demodulation,[status(thm)],[d8,c11]) ).
cnf(d10,plain,
X0 = 'greatest$ulower$ubound'(X0,'least$uupper$ubound'(X0,X1)),
inference(superposition,[status(thm)],[c13,d9]) ).
cnf(d11,plain,
'least$uupper$ubound'('least$uupper$ubound'(X1,X0),X0) = 'least$uupper$ubound'(X1,X0),
inference(superposition,[status(thm)],[d6,d0]) ).
cnf(d12,plain,
'least$uupper$ubound'(X1,'least$uupper$ubound'(X0,X1)) = 'least$uupper$ubound'(X0,X1),
inference(demodulation,[status(thm)],[d11,c7]) ).
cnf(d13,plain,
'least$uupper$ubound'(b,identity) = b,
inference(superposition,[status(thm)],[c1,d0]) ).
cnf(d14,plain,
'least$uupper$ubound'(identity,b) = b,
inference(demodulation,[status(thm)],[d13,c7]) ).
cnf(d15,plain,
'least$uupper$ubound'(b,b) = 'least$uupper$ubound'(identity,b),
inference(superposition,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
b = 'least$uupper$ubound'(identity,b),
inference(demodulation,[status(thm)],[d15,c10]) ).
cnf(d17,plain,
'least$uupper$ubound'(identity,'least$uupper$ubound'(b,X0)) = 'least$uupper$ubound'(b,X0),
inference(superposition,[status(thm)],[d16,c9]) ).
cnf(d18,plain,
identity = 'greatest$ulower$ubound'(identity,'least$uupper$ubound'(b,X0)),
inference(superposition,[status(thm)],[d17,d10]) ).
cnf(d19,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c3,c5]) ).
cnf(d20,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d19,c3]) ).
cnf(d21,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c3,d20]) ).
cnf(d22,plain,
multiply('least$uupper$ubound'(identity,X1),X0) = 'least$uupper$ubound'(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[d21,c16]) ).
cnf(d23,plain,
identity = 'greatest$ulower$ubound'(identity,multiply('least$uupper$ubound'(identity,X0),b)),
inference(superposition,[status(thm)],[d22,d18]) ).
cnf(d24,plain,
'least$uupper$ubound'(a,identity) = a,
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d25,plain,
'least$uupper$ubound'(identity,a) = a,
inference(demodulation,[status(thm)],[d24,c7]) ).
cnf(d26,plain,
identity = 'greatest$ulower$ubound'(identity,multiply(a,b)),
inference(superposition,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
multiply(a,b) = 'least$uupper$ubound'(multiply(a,b),identity),
inference(superposition,[status(thm)],[d26,d5]) ).
cnf(d28,plain,
multiply(a,b) = 'least$uupper$ubound'(identity,multiply(a,b)),
inference(demodulation,[status(thm)],[d27,c7]) ).
cnf(d29,plain,
multiply(a,b) != multiply(a,b),
inference(demodulation,[status(thm)],[c2,d28]) ).
cnf(d30,plain,
'least$uupper$ubound'(X2,'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'(X1,X2))) = X2,
inference(superposition,[status(thm)],[c8,d0]) ).
cnf(d31,plain,
'greatest$ulower$ubound'(identity,'greatest$ulower$ubound'(b,X0)) = 'greatest$ulower$ubound'(identity,X0),
inference(superposition,[status(thm)],[c1,c8]) ).
cnf(d32,plain,
'least$uupper$ubound'(X0,'greatest$ulower$ubound'(identity,X0)) = X0,
inference(superposition,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d32,d0]) ).
cnf(d34,plain,
$false,
inference(resolution,[status(thm)],[d33,d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP172-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n018.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 25 14:35:51 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 51.80/11.94 % SZS status Unsatisfiable for theBenchmark.p
% 51.80/11.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------