%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP166-3 : 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 : n014.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 07:23:17 AM UTC 2026
% Result : Unsatisfiable 37.29s 6.51s
% Output : CNFRefutation 37.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 12 RR)
% Number of literals : 38 ( 37 equ; 4 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 : 53 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(lat3a_1,hypothesis,
'least$uupper$ubound'(a,identity) = a ).
cnf(lat3a_2,hypothesis,
'least$uupper$ubound'(b,identity) = b ).
cnf(prove_lat3a,negated_conjecture,
'least$uupper$ubound'(a,multiply(b,a)) != multiply(b,a) ).
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(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'(a,identity) = a,
inference(clausification,[status(esa)],[lat3a_1]) ).
cnf(c1,plain,
'least$uupper$ubound'(b,identity) = b,
inference(clausification,[status(esa)],[lat3a_2]) ).
cnf(c2,plain,
'least$uupper$ubound'(a,multiply(b,a)) != multiply(b,a),
inference(clausification,[status(esa)],[prove_lat3a]) ).
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(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,b) = b,
inference(demodulation,[status(thm)],[c1,c7]) ).
cnf(d1,plain,
multiply(X0,X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c3,c5]) ).
cnf(d2,plain,
multiply(X0,X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
X0 = multiply(identity,X0),
inference(superposition,[status(thm)],[c3,d2]) ).
cnf(d4,plain,
multiply('least$uupper$ubound'(identity,X1),X0) = 'least$uupper$ubound'(X0,multiply(X1,X0)),
inference(superposition,[status(thm)],[d3,c16]) ).
cnf(d5,plain,
multiply('least$uupper$ubound'(identity,b),a) != multiply(b,a),
inference(demodulation,[status(thm)],[c2,d4]) ).
cnf(d6,plain,
multiply(b,a) != multiply(b,a),
inference(demodulation,[status(thm)],[d5,d0]) ).
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'(X2,'greatest$ulower$ubound'(X0,'greatest$ulower$ubound'(X1,X2))) = X2,
inference(superposition,[status(thm)],[c8,d7]) ).
cnf(d9,plain,
'greatest$ulower$ubound'(X0,'least$uupper$ubound'(X1,X0)) = X0,
inference(superposition,[status(thm)],[c7,c13]) ).
cnf(d10,plain,
'greatest$ulower$ubound'(identity,a) = identity,
inference(superposition,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
'greatest$ulower$ubound'(a,identity) = identity,
inference(demodulation,[status(thm)],[d10,c6]) ).
cnf(d12,plain,
'greatest$ulower$ubound'(a,'greatest$ulower$ubound'(identity,X0)) = 'greatest$ulower$ubound'(identity,X0),
inference(superposition,[status(thm)],[d11,c8]) ).
cnf(d13,plain,
'least$uupper$ubound'(X0,'greatest$ulower$ubound'(identity,X0)) = X0,
inference(superposition,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d13,d7]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n014.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 14:33:03 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.29/6.51 % SZS status Unsatisfiable for theBenchmark.p
% 37.29/6.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------