%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP181-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:33:00 PM UTC 2026
% Result : Unsatisfiable 5.64s 1.38s
% Output : CNFRefutation 5.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 51 ( 51 unt; 0 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] : multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
! [X] : inverse(inverse(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
! [X,Y] : inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
! [X,Y] : inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f35,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(f36,plain,
! [X0,X1,X2] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f39,plain,
inverse(identity) = identity,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f40,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f41,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f42,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f43,plain,
least_upper_bound(a,c) = least_upper_bound(b,c),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f45,plain,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f46,plain,
a != b,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f50,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f40,f25]) ).
fof(f57,plain,
greatest_lower_bound(b,c) = greatest_lower_bound(c,a),
inference(paramodulation,[status(thm)],[f42,f27]) ).
fof(f79,plain,
! [X0,X1] : multiply(identity,X0) = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f50,f26]) ).
fof(f80,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f24,f79]) ).
fof(f183,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f25,f35]) ).
fof(f214,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f25,f36]) ).
fof(f218,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),identity),
inference(paramodulation,[status(thm)],[f25,f36]) ).
fof(f459,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f40,f41]) ).
fof(f461,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f41,f80]) ).
fof(f774,plain,
! [X0] : inverse(least_upper_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0)),
inference(paramodulation,[status(thm)],[f39,f45]) ).
fof(f5406,plain,
multiply(inverse(a),least_upper_bound(b,c)) = least_upper_bound(identity,multiply(inverse(a),c)),
inference(paramodulation,[status(thm)],[f43,f183]) ).
fof(f5426,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(least_upper_bound(X0,X1),inverse(least_upper_bound(identity,multiply(inverse(X0),X1)))),
inference(paramodulation,[status(thm)],[f183,f461]) ).
fof(f5486,plain,
! [X0,X1] : X0 = multiply(least_upper_bound(X0,X1),inverse(least_upper_bound(identity,multiply(inverse(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f40,f5426]) ).
fof(f5487,plain,
! [X0,X1] : X0 = multiply(least_upper_bound(X0,X1),greatest_lower_bound(identity,inverse(multiply(inverse(X0),X1)))),
inference(forward_demodulation,[status(thm)],[f774,f5486]) ).
fof(f5488,plain,
! [X0,X1] : X0 = multiply(least_upper_bound(X0,X1),greatest_lower_bound(identity,multiply(inverse(X1),X0))),
inference(forward_demodulation,[status(thm)],[f459,f5487]) ).
fof(f6765,plain,
multiply(inverse(c),greatest_lower_bound(b,c)) = greatest_lower_bound(identity,multiply(inverse(c),a)),
inference(paramodulation,[status(thm)],[f57,f214]) ).
fof(f6828,plain,
greatest_lower_bound(multiply(inverse(c),b),identity) = greatest_lower_bound(identity,multiply(inverse(c),a)),
inference(forward_demodulation,[status(thm)],[f218,f6765]) ).
fof(f6978,plain,
inverse(inverse(a)) = multiply(least_upper_bound(b,c),inverse(least_upper_bound(identity,multiply(inverse(a),c)))),
inference(paramodulation,[status(thm)],[f5406,f461]) ).
fof(f7002,plain,
a = multiply(least_upper_bound(b,c),inverse(least_upper_bound(identity,multiply(inverse(a),c)))),
inference(forward_demodulation,[status(thm)],[f40,f6978]) ).
fof(f7003,plain,
a = multiply(least_upper_bound(b,c),greatest_lower_bound(identity,inverse(multiply(inverse(a),c)))),
inference(forward_demodulation,[status(thm)],[f774,f7002]) ).
fof(f7004,plain,
a = multiply(least_upper_bound(b,c),greatest_lower_bound(identity,multiply(inverse(c),a))),
inference(forward_demodulation,[status(thm)],[f459,f7003]) ).
fof(f8287,plain,
greatest_lower_bound(identity,multiply(inverse(c),b)) = greatest_lower_bound(identity,multiply(inverse(c),a)),
inference(paramodulation,[status(thm)],[f27,f6828]) ).
fof(f8314,plain,
a = multiply(least_upper_bound(b,c),greatest_lower_bound(identity,multiply(inverse(c),b))),
inference(backward_demodulation,[status(thm)],[f8287,f7004]) ).
fof(f8354,plain,
a = b,
inference(forward_demodulation,[status(thm)],[f5488,f8314]) ).
fof(f8355,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f8354,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP181-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:03:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 5.64/1.38 % Refutation found
% 5.64/1.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.64/1.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.51/1.42 % Elapsed time: 1.059095 seconds
% 3.51/1.42 % CPU time: 8.105594 seconds
% 3.51/1.42 % Total memory used: 98.858 MB
% 3.51/1.42 % Net memory used: 96.961 MB
%------------------------------------------------------------------------------