%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP172-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 12:32:57 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 41 ( 41 unt; 2 def)
% Number of atoms : 41 ( 40 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
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(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,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,
greatest_lower_bound(identity,multiply(a,b)) != identity,
file('/export/starexec/sandbox/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(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(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(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,
greatest_lower_bound(identity,multiply(a,b)) != identity,
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 = greatest_lower_bound(identity,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f39,plain,
sF0_fnc != identity,
inference(definition_folding,[],[f36,f38,f37]) ).
fof(f49,plain,
greatest_lower_bound(a,identity) = identity,
inference(paramodulation,[status(thm)],[f22,f34]) ).
fof(f65,plain,
! [X0] : greatest_lower_bound(identity,greatest_lower_bound(sF1_fnc,X0)) = greatest_lower_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f38,f24]) ).
fof(f134,plain,
! [X0] : multiply(greatest_lower_bound(a,X0),b) = greatest_lower_bound(sF1_fnc,multiply(X0,b)),
inference(paramodulation,[status(thm)],[f37,f33]) ).
fof(f169,plain,
least_upper_bound(identity,sF0_fnc) = identity,
inference(paramodulation,[status(thm)],[f38,f28]) ).
fof(f171,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f22,f28]) ).
fof(f176,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f23,f29]) ).
fof(f193,plain,
! [X0,X1,X2] : least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f24,f171]) ).
fof(f209,plain,
greatest_lower_bound(sF0_fnc,identity) = sF0_fnc,
inference(paramodulation,[status(thm)],[f169,f176]) ).
fof(f546,plain,
! [X0] : least_upper_bound(b,greatest_lower_bound(X0,identity)) = b,
inference(paramodulation,[status(thm)],[f35,f193]) ).
fof(f998,plain,
least_upper_bound(b,sF0_fnc) = b,
inference(paramodulation,[status(thm)],[f209,f546]) ).
fof(f1019,plain,
greatest_lower_bound(sF0_fnc,b) = sF0_fnc,
inference(paramodulation,[status(thm)],[f998,f176]) ).
fof(f1743,plain,
multiply(identity,b) = greatest_lower_bound(sF1_fnc,multiply(identity,b)),
inference(paramodulation,[status(thm)],[f49,f134]) ).
fof(f1767,plain,
b = greatest_lower_bound(sF1_fnc,multiply(identity,b)),
inference(forward_demodulation,[status(thm)],[f19,f1743]) ).
fof(f1768,plain,
b = greatest_lower_bound(sF1_fnc,b),
inference(forward_demodulation,[status(thm)],[f19,f1767]) ).
fof(f1784,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(sF0_fnc,b),
inference(paramodulation,[status(thm)],[f1768,f65]) ).
fof(f1799,plain,
identity = greatest_lower_bound(sF0_fnc,b),
inference(forward_demodulation,[status(thm)],[f35,f1784]) ).
fof(f1800,plain,
identity = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f1019,f1799]) ).
fof(f1801,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1800,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP172-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:01:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.44 % Refutation found
% 0.10/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.45 % Elapsed time: 0.068587 seconds
% 0.10/0.45 % CPU time: 0.415198 seconds
% 0.10/0.45 % Total memory used: 15.948 MB
% 0.10/0.45 % Net memory used: 15.708 MB
%------------------------------------------------------------------------------