%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP175-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:32:58 PM UTC 2026
% Result : Unsatisfiable 0.04s 5.32s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 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 : 20 ( 20 !; 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(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(f15,axiom,
! [Y,Z,X] : multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f30,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(f32,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(f33,plain,
greatest_lower_bound(identity,b) = identity,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
greatest_lower_bound(identity,multiply(inverse(a),multiply(b,a))) != identity,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f155,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f19,f30]) ).
fof(f177,plain,
multiply(inverse(a),greatest_lower_bound(a,multiply(b,a))) != identity,
inference(backward_demodulation,[status(thm)],[f155,f34]) ).
fof(f198,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f18,f32]) ).
fof(f218,plain,
multiply(inverse(a),multiply(greatest_lower_bound(identity,b),a)) != identity,
inference(backward_demodulation,[status(thm)],[f198,f177]) ).
fof(f232,plain,
multiply(inverse(a),multiply(identity,a)) != identity,
inference(forward_demodulation,[status(thm)],[f33,f218]) ).
fof(f233,plain,
multiply(inverse(a),a) != identity,
inference(forward_demodulation,[status(thm)],[f18,f232]) ).
fof(f234,plain,
identity != identity,
inference(forward_demodulation,[status(thm)],[f19,f233]) ).
fof(f235,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP175-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/5.31 % Computer : n012.cluster.edu
% 0.04/5.31 % Model : x86_64 x86_64
% 0.04/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.31 % Memory : 8046.5625MB
% 0.04/5.31 % OS : Linux 6.8.0-71-generic
% 0.04/5.31 % CPULimit : 300
% 0.04/5.31 % WCLimit : 300
% 0.04/5.31 % DateTime : Sun Sep 20 20:03:59 UTC 2026
% 0.04/5.31 % CPUTime :
% 0.04/5.32 % Drodi V4.1.1
% 0.04/5.32 % Refutation found
% 0.04/5.32 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.04/5.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.04/5.33 % Elapsed time: 0.016022 seconds
% 0.04/5.33 % CPU time: 0.039283 seconds
% 0.04/5.33 % Total memory used: 2.695 MB
% 0.04/5.33 % Net memory used: 2.653 MB
%------------------------------------------------------------------------------