%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP167-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.59s 0.64s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 37 unt; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Y,Z,X] : multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B] : inverse(least_upper_bound(A,B)) = greatest_lower_bound(inverse(A),inverse(B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] : positive_part(X) = least_upper_bound(X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] : negative_part(X) = greatest_lower_bound(X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f23,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f25,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f37,plain,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f38,plain,
! [X0] : positive_part(X0) = least_upper_bound(X0,identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f39,plain,
! [X0] : negative_part(X0) = greatest_lower_bound(X0,identity),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f42,plain,
a != multiply(positive_part(a),negative_part(a)),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f351,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f22,f36]) ).
fof(f451,plain,
! [X0,X1] : multiply(negative_part(X0),X1) = greatest_lower_bound(multiply(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f39,f351]) ).
fof(f453,plain,
! [X0,X1] : multiply(negative_part(X0),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f25,f451]) ).
fof(f678,plain,
! [X0] : multiply(negative_part(inverse(X0)),X0) = greatest_lower_bound(X0,identity),
inference(paramodulation,[status(thm)],[f23,f453]) ).
fof(f699,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f23,f24]) ).
fof(f705,plain,
! [X0] : multiply(negative_part(inverse(X0)),X0) = negative_part(X0),
inference(forward_demodulation,[status(thm)],[f39,f678]) ).
fof(f720,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f22,f699]) ).
fof(f1720,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f720,f720]) ).
fof(f1722,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f23,f720]) ).
fof(f1777,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f1720,f1722]) ).
fof(f1849,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f23,f1777]) ).
fof(f2176,plain,
! [X0] : inverse(least_upper_bound(X0,identity)) = greatest_lower_bound(inverse(X0),identity),
inference(paramodulation,[status(thm)],[f1849,f37]) ).
fof(f2184,plain,
! [X0] : inverse(positive_part(X0)) = greatest_lower_bound(inverse(X0),identity),
inference(forward_demodulation,[status(thm)],[f38,f2176]) ).
fof(f2188,plain,
! [X0] : multiply(inverse(positive_part(X0)),X0) = negative_part(X0),
inference(backward_demodulation,[status(thm)],[f2189,f705]) ).
fof(f2189,plain,
! [X0] : inverse(positive_part(X0)) = negative_part(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f39,f2184]) ).
fof(f2367,plain,
! [X0] : X0 = multiply(inverse(inverse(positive_part(X0))),negative_part(X0)),
inference(paramodulation,[status(thm)],[f2188,f720]) ).
fof(f2411,plain,
a != a,
inference(backward_demodulation,[status(thm)],[f2412,f42]) ).
fof(f2412,plain,
! [X0] : X0 = multiply(positive_part(X0),negative_part(X0)),
inference(forward_demodulation,[status(thm)],[f1720,f2367]) ).
fof(f2443,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2411]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.51 % Computer : n003.cluster.edu
% 0.10/0.51 % Model : x86_64 x86_64
% 0.10/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.51 % Memory : 8046.5625MB
% 0.10/0.51 % OS : Linux 6.8.0-71-generic
% 0.10/0.51 % CPULimit : 300
% 0.10/0.51 % WCLimit : 300
% 0.10/0.51 % DateTime : Sun Sep 20 20:04:45 UTC 2026
% 0.10/0.51 % CPUTime :
% 0.10/0.52 % Drodi V4.1.1
% 0.59/0.64 % Refutation found
% 0.59/0.64 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.59/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.59/0.65 % Elapsed time: 0.132721 seconds
% 0.59/0.65 % CPU time: 0.893419 seconds
% 0.59/0.65 % Total memory used: 31.796 MB
% 0.59/0.65 % Net memory used: 31.336 MB
%------------------------------------------------------------------------------