%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP166-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 12:32:55 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 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 : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
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(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(f17,hypothesis,
greatest_lower_bound(b,identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
greatest_lower_bound(a,multiply(b,a)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f33,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(f35,plain,
greatest_lower_bound(b,identity) = identity,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f36,plain,
greatest_lower_bound(a,multiply(b,a)) != a,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
greatest_lower_bound(identity,b) = identity,
inference(forward_demodulation,[status(thm)],[f22,f35]) ).
fof(f239,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X1,X2),multiply(X0,X2)),
inference(paramodulation,[status(thm)],[f22,f33]) ).
fof(f252,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = multiply(greatest_lower_bound(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f33,f239]) ).
fof(f261,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f19,f33]) ).
fof(f266,plain,
multiply(greatest_lower_bound(b,identity),a) != a,
inference(backward_demodulation,[status(thm)],[f267,f36]) ).
fof(f267,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f22,f261]) ).
fof(f271,plain,
multiply(greatest_lower_bound(identity,b),a) != a,
inference(forward_demodulation,[status(thm)],[f252,f266]) ).
fof(f272,plain,
multiply(identity,a) != a,
inference(forward_demodulation,[status(thm)],[f41,f271]) ).
fof(f273,plain,
a != a,
inference(forward_demodulation,[status(thm)],[f19,f272]) ).
fof(f274,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n017.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sun Sep 20 19:58:26 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.033897 seconds
% 0.12/0.40 % CPU time: 0.099069 seconds
% 0.12/0.40 % Total memory used: 3.799 MB
% 0.12/0.40 % Net memory used: 3.723 MB
%------------------------------------------------------------------------------