%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP172-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.18s 0.53s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 49 unt; 2 def)
% Number of atoms : 49 ( 48 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 : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 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(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] : greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
greatest_lower_bound(identity,a) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
greatest_lower_bound(identity,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f29,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f30,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(f34,plain,
greatest_lower_bound(identity,a) = identity,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f35,plain,
greatest_lower_bound(identity,b) = identity,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f36,plain,
least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f37,definition,
sF1_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f38,definition,
sF0_fnc = least_upper_bound(identity,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(f40,plain,
greatest_lower_bound(a,identity) = identity,
inference(forward_demodulation,[status(thm)],[f22,f34]) ).
fof(f41,plain,
greatest_lower_bound(b,identity) = identity,
inference(forward_demodulation,[status(thm)],[f22,f35]) ).
fof(f48,plain,
least_upper_bound(b,identity) = b,
inference(paramodulation,[status(thm)],[f41,f28]) ).
fof(f127,plain,
! [X0] : multiply(a,least_upper_bound(b,X0)) = least_upper_bound(sF1_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f37,f30]) ).
fof(f153,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f20,f21]) ).
fof(f155,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f19,f153]) ).
fof(f156,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f155,f155]) ).
fof(f157,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f20,f155]) ).
fof(f165,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f156,f157]) ).
fof(f195,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f22,f28]) ).
fof(f412,plain,
! [X0,X1,X2] : least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f24,f195]) ).
fof(f661,plain,
multiply(a,b) = least_upper_bound(sF1_fnc,multiply(a,identity)),
inference(paramodulation,[status(thm)],[f48,f127]) ).
fof(f676,plain,
sF1_fnc = least_upper_bound(sF1_fnc,multiply(a,identity)),
inference(forward_demodulation,[status(thm)],[f37,f661]) ).
fof(f677,plain,
sF1_fnc = least_upper_bound(sF1_fnc,a),
inference(forward_demodulation,[status(thm)],[f165,f676]) ).
fof(f678,plain,
sF1_fnc = least_upper_bound(a,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f23,f677]) ).
fof(f699,plain,
greatest_lower_bound(a,sF1_fnc) = a,
inference(paramodulation,[status(thm)],[f678,f29]) ).
fof(f916,plain,
! [X0] : least_upper_bound(sF1_fnc,greatest_lower_bound(X0,a)) = sF1_fnc,
inference(paramodulation,[status(thm)],[f699,f412]) ).
fof(f954,plain,
! [X0] : least_upper_bound(sF1_fnc,greatest_lower_bound(a,X0)) = sF1_fnc,
inference(paramodulation,[status(thm)],[f22,f916]) ).
fof(f1013,plain,
least_upper_bound(sF1_fnc,identity) = sF1_fnc,
inference(paramodulation,[status(thm)],[f40,f954]) ).
fof(f1035,plain,
least_upper_bound(identity,sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f23,f1013]) ).
fof(f1036,plain,
sF0_fnc = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f38,f1035]) ).
fof(f1037,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1036,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP172-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n026.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 20 20:06:06 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.53 % Refutation found
% 0.18/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.58 % Elapsed time: 0.109154 seconds
% 0.18/0.58 % CPU time: 0.427141 seconds
% 0.18/0.58 % Total memory used: 10.509 MB
% 0.18/0.58 % Net memory used: 10.346 MB
%------------------------------------------------------------------------------