%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 69.05s 10.33s
% Output : CNFRefutation 69.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of clauses : 72 ( 72 unt; 0 nHn; 17 RR)
% Number of literals : 72 ( 71 equ; 3 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 : 115 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p02a_1,hypothesis,
'least$uupper$ubound'(inverse(a),inverse(b)) = inverse(b) ).
cnf(prove_p02a,negated_conjecture,
'least$uupper$ubound'(a,b) != 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(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(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_lub1,axiom,
multiply(X0,'least$uupper$ubound'(X1,X2)) = 'least$uupper$ubound'(multiply(X0,X1),multiply(X0,X2)) ).
cnf(monotony_glb1,axiom,
multiply(X0,'greatest$ulower$ubound'(X1,X2)) = 'greatest$ulower$ubound'(multiply(X0,X1),multiply(X0,X2)) ).
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'(inverse(a),inverse(b)) = inverse(b),
inference(clausification,[status(esa)],[p02a_1]) ).
cnf(c1,plain,
'least$uupper$ubound'(a,b) != a,
inference(clausification,[status(esa)],[prove_p02a]) ).
cnf(c2,plain,
multiply(identity,X0) = X0,
inference(clausification,[status(esa)],[left_identity]) ).
cnf(c3,plain,
multiply(inverse(X0),X0) = identity,
inference(clausification,[status(esa)],[left_inverse]) ).
cnf(c4,plain,
multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(clausification,[status(esa)],[associativity]) ).
cnf(c5,plain,
'greatest$ulower$ubound'(X0,X1) = 'greatest$ulower$ubound'(X1,X0),
inference(clausification,[status(esa)],[symmetry_of_glb]) ).
cnf(c6,plain,
'least$uupper$ubound'(X0,X1) = 'least$uupper$ubound'(X1,X0),
inference(clausification,[status(esa)],[symmetry_of_lub]) ).
cnf(c7,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(c8,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(c9,plain,
'least$uupper$ubound'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_of_lub]) ).
cnf(c11,plain,
'least$uupper$ubound'(X0,'greatest$ulower$ubound'(X0,X1)) = X0,
inference(clausification,[status(esa)],[lub_absorbtion]) ).
cnf(c12,plain,
'greatest$ulower$ubound'(X0,'least$uupper$ubound'(X0,X1)) = X0,
inference(clausification,[status(esa)],[glb_absorbtion]) ).
cnf(c13,plain,
multiply(X0,'least$uupper$ubound'(X1,X2)) = 'least$uupper$ubound'(multiply(X0,X1),multiply(X0,X2)),
inference(clausification,[status(esa)],[monotony_lub1]) ).
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(c15,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)],[c5,c11]) ).
cnf(d1,plain,
'greatest$ulower$ubound'(X0,'least$uupper$ubound'(X1,X0)) = X0,
inference(superposition,[status(thm)],[c6,c12]) ).
cnf(d2,plain,
'least$uupper$ubound'('least$uupper$ubound'(X1,X0),X0) = 'least$uupper$ubound'(X1,X0),
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
'least$uupper$ubound'(X0,'least$uupper$ubound'(X1,X1)) = 'least$uupper$ubound'(X0,X1),
inference(demodulation,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
'least$uupper$ubound'(X1,X0) = 'least$uupper$ubound'(X1,X0),
inference(demodulation,[status(thm)],[d3,c9]) ).
cnf(d5,plain,
X0 = 'least$uupper$ubound'(X0,'greatest$ulower$ubound'(X0,X1)),
inference(superposition,[status(thm)],[c11,d4]) ).
cnf(d6,plain,
multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[status(thm)],[c3,c4]) ).
cnf(d7,plain,
X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(demodulation,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[d7,d7]) ).
cnf(d9,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c2,c4]) ).
cnf(d10,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d9,c2]) ).
cnf(d11,plain,
identity = multiply(inverse(X0),X0),
inference(superposition,[status(thm)],[c3,d10]) ).
cnf(d12,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
X1 = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d15,plain,
multiply(X0,'greatest$ulower$ubound'(X1,X2)) = 'greatest$ulower$ubound'(multiply(X0,X2),multiply(X0,X1)),
inference(superposition,[status(thm)],[c14,c5]) ).
cnf(d16,plain,
multiply(X0,'greatest$ulower$ubound'(X1,X2)) = multiply(X0,'greatest$ulower$ubound'(X2,X1)),
inference(superposition,[status(thm)],[d15,c14]) ).
cnf(d17,plain,
multiply(inverse(X0),'greatest$ulower$ubound'(X0,X1)) = 'greatest$ulower$ubound'(identity,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d11,c14]) ).
cnf(d18,plain,
multiply(inverse(X0),'least$uupper$ubound'(X1,X0)) = 'least$uupper$ubound'(multiply(inverse(X0),X1),identity),
inference(superposition,[status(thm)],[d11,c13]) ).
cnf(d19,plain,
multiply(inverse(X0),'least$uupper$ubound'(X1,X0)) = 'least$uupper$ubound'(identity,multiply(inverse(X0),X1)),
inference(demodulation,[status(thm)],[d18,c6]) ).
cnf(d20,plain,
'greatest$ulower$ubound'(identity,multiply(inverse(X0),'least$uupper$ubound'(X1,X0))) = identity,
inference(superposition,[status(thm)],[d19,c12]) ).
cnf(d21,plain,
'least$uupper$ubound'(multiply(X0,X2),multiply(X0,X1)) = multiply(X0,'least$uupper$ubound'(X1,X2)),
inference(superposition,[status(thm)],[c13,c6]) ).
cnf(d22,plain,
multiply(X0,'least$uupper$ubound'(X1,X2)) = multiply(X0,'least$uupper$ubound'(X2,X1)),
inference(superposition,[status(thm)],[d21,c13]) ).
cnf(d23,plain,
multiply(inverse(X0),'least$uupper$ubound'(X0,X1)) = 'least$uupper$ubound'(identity,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[d11,c13]) ).
cnf(d24,plain,
multiply('least$uupper$ubound'(inverse(X0),X1),X0) = 'least$uupper$ubound'(identity,multiply(X1,X0)),
inference(superposition,[status(thm)],[d11,c15]) ).
cnf(d25,plain,
inverse(b) = 'least$uupper$ubound'(inverse(a),inverse(b)),
inference(superposition,[status(thm)],[c0,d4]) ).
cnf(d26,plain,
multiply(inverse(b),a) = 'least$uupper$ubound'(identity,multiply(inverse(b),a)),
inference(superposition,[status(thm)],[d25,d24]) ).
cnf(d27,plain,
multiply(inverse(b),a) = multiply(inverse(b),'least$uupper$ubound'(b,a)),
inference(demodulation,[status(thm)],[d26,d23]) ).
cnf(d28,plain,
multiply(inverse(b),a) = multiply(inverse(b),'least$uupper$ubound'(a,b)),
inference(demodulation,[status(thm)],[d27,d22]) ).
cnf(d29,plain,
'greatest$ulower$ubound'(identity,multiply(inverse(b),a)) = identity,
inference(superposition,[status(thm)],[d28,d20]) ).
cnf(d30,plain,
multiply(inverse(b),'greatest$ulower$ubound'(b,a)) = identity,
inference(demodulation,[status(thm)],[d29,d17]) ).
cnf(d31,plain,
multiply(inverse(b),'greatest$ulower$ubound'(a,b)) = identity,
inference(demodulation,[status(thm)],[d30,d16]) ).
cnf(d32,plain,
'greatest$ulower$ubound'(a,b) = multiply(b,identity),
inference(superposition,[status(thm)],[d31,d14]) ).
cnf(d33,plain,
'greatest$ulower$ubound'(a,b) = b,
inference(demodulation,[status(thm)],[d32,d13]) ).
cnf(d34,plain,
a = 'least$uupper$ubound'(a,b),
inference(superposition,[status(thm)],[d33,d5]) ).
cnf(d35,plain,
a != a,
inference(demodulation,[status(thm)],[c1,d34]) ).
cnf(d36,plain,
'least$uupper$ubound'(X2,'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'(X1,X2))) = X2,
inference(superposition,[status(thm)],[c7,d0]) ).
cnf(d37,plain,
'greatest$ulower$ubound'(inverse(a),inverse(b)) = inverse(a),
inference(superposition,[status(thm)],[c0,c12]) ).
cnf(d38,plain,
'greatest$ulower$ubound'(inverse(a),'greatest$ulower$ubound'(inverse(b),X0)) = 'greatest$ulower$ubound'(inverse(a),X0),
inference(superposition,[status(thm)],[d37,c7]) ).
cnf(d39,plain,
'least$uupper$ubound'(X0,'greatest$ulower$ubound'(inverse(a),X0)) = X0,
inference(superposition,[status(thm)],[d38,d36]) ).
cnf(d40,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d39,d0]) ).
cnf(d41,plain,
$false,
inference(resolution,[status(thm)],[d40,d35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 14:34:10 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 69.05/10.33 % SZS status Unsatisfiable for theBenchmark.p
% 69.05/10.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------