%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP191-2 : 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 : n015.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 07:23:24 AM UTC 2026
% Result : Unsatisfiable 36.08s 33.96s
% Output : CNFRefutation 36.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 54 ( 54 unt; 0 nHn; 11 RR)
% Number of literals : 54 ( 53 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 83 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(p39d_1,hypothesis,
'greatest$ulower$ubound'(a,b) = b ).
cnf(prove_p39d,negated_conjecture,
'least$uupper$ubound'(inverse(a),inverse(b)) != inverse(b) ).
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(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_lub1,axiom,
multiply(X0,'least$uupper$ubound'(X1,X2)) = 'least$uupper$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,
'greatest$ulower$ubound'(a,b) = b,
inference(clausification,[status(esa)],[p39d_1]) ).
cnf(c1,plain,
'least$uupper$ubound'(inverse(a),inverse(b)) != inverse(b),
inference(clausification,[status(esa)],[prove_p39d]) ).
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(X0,multiply(X1,X2)) = multiply(multiply(X0,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'('greatest$ulower$ubound'(X0,X1),X2) = 'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'(X1,X2)),
inference(clausification,[status(esa)],[associativity_of_glb]) ).
cnf(c10,plain,
'greatest$ulower$ubound'(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence_of_gld]) ).
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,
'least$uupper$ubound'(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,'least$uupper$ubound'(X1,X2)),
inference(clausification,[status(esa)],[monotony_lub1]) ).
cnf(c15,plain,
'least$uupper$ubound'(multiply(X0,X1),multiply(X2,X1)) = multiply('least$uupper$ubound'(X0,X2),X1),
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,
multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c3,c4]) ).
cnf(d2,plain,
multiply(inverse(X1),multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[d2,d2]) ).
cnf(d4,plain,
multiply(identity,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c2,c4]) ).
cnf(d5,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c3,d2]) ).
cnf(d7,plain,
X0 = multiply(inverse(inverse(X0)),identity),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
X0 = multiply(X0,identity),
inference(demodulation,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
'greatest$ulower$ubound'(X0,X2) = 'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'('least$uupper$ubound'(X0,X1),X2)),
inference(superposition,[status(thm)],[c12,c7]) ).
cnf(d10,plain,
'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'(X1,'greatest$ulower$ubound'(X0,X1))) = 'greatest$ulower$ubound'(X0,X1),
inference(superposition,[status(thm)],[c7,c10]) ).
cnf(d11,plain,
'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'('least$uupper$ubound'(X0,X1),X0)) = 'greatest$ulower$ubound'(X0,'least$uupper$ubound'(X0,X1)),
inference(superposition,[status(thm)],[c12,d10]) ).
cnf(d12,plain,
'greatest$ulower$ubound'(X0,X0) = 'greatest$ulower$ubound'(X0,'least$uupper$ubound'(X0,X1)),
inference(demodulation,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
X0 = 'greatest$ulower$ubound'(X0,'least$uupper$ubound'(X0,X1)),
inference(demodulation,[status(thm)],[d12,c10]) ).
cnf(d14,plain,
'least$uupper$ubound'(X0,multiply(X1,X0)) = multiply('least$uupper$ubound'(identity,X1),X0),
inference(superposition,[status(thm)],[c2,c15]) ).
cnf(d15,plain,
X0 = 'greatest$ulower$ubound'(X0,multiply('least$uupper$ubound'(identity,X1),X0)),
inference(superposition,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
'least$uupper$ubound'(multiply(inverse(X0),X1),identity) = multiply(inverse(X0),'least$uupper$ubound'(X1,X0)),
inference(superposition,[status(thm)],[c3,c13]) ).
cnf(d17,plain,
'least$uupper$ubound'(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),'least$uupper$ubound'(X1,X0)),
inference(demodulation,[status(thm)],[d16,c6]) ).
cnf(d18,plain,
'least$uupper$ubound'(a,b) = a,
inference(superposition,[status(thm)],[c0,c11]) ).
cnf(d19,plain,
'least$uupper$ubound'(identity,multiply(inverse(b),a)) = multiply(inverse(b),a),
inference(superposition,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
X0 = 'greatest$ulower$ubound'(X0,multiply(multiply(inverse(b),a),X0)),
inference(superposition,[status(thm)],[d19,d15]) ).
cnf(d21,plain,
X0 = 'greatest$ulower$ubound'(X0,multiply(inverse(b),multiply(a,X0))),
inference(demodulation,[status(thm)],[d20,c4]) ).
cnf(d22,plain,
multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[d3,c3]) ).
cnf(d23,plain,
inverse(a) = 'greatest$ulower$ubound'(inverse(a),multiply(inverse(b),identity)),
inference(superposition,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
inverse(a) = 'greatest$ulower$ubound'(inverse(a),inverse(b)),
inference(demodulation,[status(thm)],[d23,d8]) ).
cnf(d25,plain,
'least$uupper$ubound'(inverse(b),inverse(a)) = inverse(b),
inference(superposition,[status(thm)],[d24,d0]) ).
cnf(d26,plain,
'least$uupper$ubound'(inverse(a),inverse(b)) = inverse(b),
inference(demodulation,[status(thm)],[d25,c6]) ).
cnf(d27,plain,
$false,
inference(resolution,[status(thm)],[c1,d26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP191-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.57 % Computer : n015.cluster.edu
% 0.12/0.57 % Model : x86_64 x86_64
% 0.12/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.57 % Memory : 8046.5625MB
% 0.12/0.57 % OS : Linux 6.8.0-71-generic
% 0.12/0.58 % CPULimit : 300
% 0.12/0.58 % WCLimit : 300
% 0.12/0.58 % DateTime : Fri Sep 25 14:40:14 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.12/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.08/33.96 % SZS status Unsatisfiable for theBenchmark.p
% 36.08/33.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------