%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP166-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.10s 0.60s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 30 unt; 2 def)
% Number of atoms : 30 ( 29 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 : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] : least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : least_upper_bound(X,X) = X,
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(f17,hypothesis,
least_upper_bound(b,identity) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
least_upper_bound(a,multiply(b,a)) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f23,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f25,plain,
! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0] : least_upper_bound(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f32,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(f35,plain,
least_upper_bound(b,identity) = b,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f36,plain,
least_upper_bound(a,multiply(b,a)) != multiply(b,a),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f37,definition,
sF1_fnc = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f38,definition,
sF0_fnc = least_upper_bound(a,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f39,plain,
sF0_fnc != sF1_fnc,
inference(definition_folding,[],[f36,f38,f37]) ).
fof(f61,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X0,X1)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f26,f25]) ).
fof(f75,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f23,f61]) ).
fof(f98,plain,
least_upper_bound(sF1_fnc,sF0_fnc) = least_upper_bound(sF1_fnc,a),
inference(paramodulation,[status(thm)],[f38,f75]) ).
fof(f131,plain,
least_upper_bound(sF0_fnc,sF1_fnc) = least_upper_bound(sF1_fnc,a),
inference(paramodulation,[status(thm)],[f23,f98]) ).
fof(f141,plain,
least_upper_bound(sF0_fnc,sF1_fnc) = least_upper_bound(a,sF1_fnc),
inference(paramodulation,[status(thm)],[f23,f131]) ).
fof(f148,plain,
least_upper_bound(sF0_fnc,sF1_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f38,f141]) ).
fof(f188,plain,
! [X0] : multiply(least_upper_bound(b,X0),a) = least_upper_bound(sF1_fnc,multiply(X0,a)),
inference(paramodulation,[status(thm)],[f37,f32]) ).
fof(f259,plain,
sF0_fnc = least_upper_bound(sF1_fnc,a),
inference(backward_demodulation,[status(thm)],[f148,f131]) ).
fof(f2349,plain,
multiply(b,a) = least_upper_bound(sF1_fnc,multiply(identity,a)),
inference(paramodulation,[status(thm)],[f35,f188]) ).
fof(f2378,plain,
sF1_fnc = least_upper_bound(sF1_fnc,multiply(identity,a)),
inference(forward_demodulation,[status(thm)],[f37,f2349]) ).
fof(f2379,plain,
sF1_fnc = least_upper_bound(sF1_fnc,a),
inference(forward_demodulation,[status(thm)],[f19,f2378]) ).
fof(f2380,plain,
sF1_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f259,f2379]) ).
fof(f2381,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2380,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n018.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Sun Sep 20 20:05:14 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.58 % Drodi V4.1.1
% 0.10/0.60 % Refutation found
% 0.10/0.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.62 % Elapsed time: 0.038356 seconds
% 0.10/0.62 % CPU time: 0.152189 seconds
% 0.10/0.62 % Total memory used: 5.459 MB
% 0.10/0.62 % Net memory used: 5.366 MB
%------------------------------------------------------------------------------