%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP168-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 : Thu Sep 24 12:32:56 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 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 : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] : multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Y,Z,X] : multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f31,plain,
! [X0,X1,X2] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f33,plain,
least_upper_bound(a,b) = b,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
least_upper_bound(multiply(inverse(c),multiply(a,c)),multiply(inverse(c),multiply(b,c))) != multiply(inverse(c),multiply(b,c)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f43,plain,
least_upper_bound(b,a) = b,
inference(forward_demodulation,[status(thm)],[f22,f33]) ).
fof(f44,plain,
multiply(inverse(c),least_upper_bound(multiply(a,c),multiply(b,c))) != multiply(inverse(c),multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f29,f34]) ).
fof(f45,plain,
multiply(inverse(c),multiply(least_upper_bound(a,b),c)) != multiply(inverse(c),multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f31,f44]) ).
fof(f46,plain,
multiply(inverse(c),multiply(least_upper_bound(b,a),c)) != multiply(inverse(c),multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f22,f45]) ).
fof(f47,plain,
multiply(inverse(c),multiply(b,c)) != multiply(inverse(c),multiply(b,c)),
inference(forward_demodulation,[status(thm)],[f43,f46]) ).
fof(f48,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP168-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:03:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.037707 seconds
% 0.13/0.41 % CPU time: 0.027590 seconds
% 0.13/0.41 % Total memory used: 679.920 KB
% 0.13/0.41 % Net memory used: 659.312 KB
%------------------------------------------------------------------------------