%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP185-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 12:33:02 PM UTC 2026
% Result : Unsatisfiable 3.55s 0.91s
% Output : CNFRefutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 74 ( 74 unt; 7 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 65 ( 65 !; 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(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
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(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f23,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,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,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(f30,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(f32,plain,
greatest_lower_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != least_upper_bound(multiply(a,b),identity),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
sF2_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f34,definition,
sF1_fnc = least_upper_bound(sF2_fnc,identity),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f35,definition,
sF4_fnc = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f36,definition,
sF5_fnc = least_upper_bound(b,identity),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f37,definition,
sF3_fnc = multiply(sF4_fnc,sF5_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f38,definition,
sF0_fnc = greatest_lower_bound(sF1_fnc,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f39,definition,
sF6_fnc = least_upper_bound(sF2_fnc,identity),
introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition]) ).
fof(f40,plain,
sF0_fnc != sF6_fnc,
inference(definition_folding,[],[f32,f39,f38,f37,f36,f35,f34,f33]) ).
fof(f54,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f20,f26]) ).
fof(f58,plain,
greatest_lower_bound(a,sF4_fnc) = a,
inference(paramodulation,[status(thm)],[f35,f27]) ).
fof(f61,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f21,f27]) ).
fof(f65,plain,
sF0_fnc != sF1_fnc,
inference(backward_demodulation,[status(thm)],[f66,f40]) ).
fof(f66,plain,
sF6_fnc = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f34,f39]) ).
fof(f93,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f94,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f93]) ).
fof(f112,plain,
least_upper_bound(sF4_fnc,a) = sF4_fnc,
inference(paramodulation,[status(thm)],[f58,f54]) ).
fof(f126,plain,
greatest_lower_bound(identity,sF5_fnc) = identity,
inference(paramodulation,[status(thm)],[f36,f61]) ).
fof(f127,plain,
greatest_lower_bound(identity,sF4_fnc) = identity,
inference(paramodulation,[status(thm)],[f35,f61]) ).
fof(f158,plain,
least_upper_bound(a,sF4_fnc) = sF4_fnc,
inference(paramodulation,[status(thm)],[f21,f112]) ).
fof(f178,plain,
! [X0] : least_upper_bound(sF2_fnc,least_upper_bound(identity,X0)) = least_upper_bound(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f34,f23]) ).
fof(f186,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f23,f61]) ).
fof(f201,plain,
! [X0] : multiply(sF4_fnc,least_upper_bound(sF5_fnc,X0)) = least_upper_bound(sF3_fnc,multiply(sF4_fnc,X0)),
inference(paramodulation,[status(thm)],[f37,f28]) ).
fof(f202,plain,
! [X0] : multiply(a,least_upper_bound(b,X0)) = least_upper_bound(sF2_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f33,f28]) ).
fof(f275,plain,
least_upper_bound(sF5_fnc,identity) = sF5_fnc,
inference(paramodulation,[status(thm)],[f126,f54]) ).
fof(f278,plain,
least_upper_bound(sF4_fnc,identity) = sF4_fnc,
inference(paramodulation,[status(thm)],[f127,f54]) ).
fof(f311,plain,
! [X0] : multiply(least_upper_bound(X0,sF4_fnc),sF5_fnc) = least_upper_bound(multiply(X0,sF5_fnc),sF3_fnc),
inference(paramodulation,[status(thm)],[f37,f30]) ).
fof(f613,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f94,f94]) ).
fof(f614,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f18,f94]) ).
fof(f1240,plain,
! [X0] : greatest_lower_bound(identity,least_upper_bound(X0,sF4_fnc)) = identity,
inference(paramodulation,[status(thm)],[f278,f186]) ).
fof(f1241,plain,
! [X0] : greatest_lower_bound(a,least_upper_bound(X0,sF4_fnc)) = a,
inference(paramodulation,[status(thm)],[f112,f186]) ).
fof(f3421,plain,
multiply(sF4_fnc,sF5_fnc) = least_upper_bound(sF3_fnc,multiply(sF4_fnc,identity)),
inference(paramodulation,[status(thm)],[f275,f201]) ).
fof(f3450,plain,
sF3_fnc = least_upper_bound(sF3_fnc,multiply(sF4_fnc,identity)),
inference(forward_demodulation,[status(thm)],[f37,f3421]) ).
fof(f3963,plain,
! [X0] : X0 = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f613,f614]) ).
fof(f4434,plain,
multiply(a,sF5_fnc) = least_upper_bound(sF2_fnc,multiply(a,identity)),
inference(paramodulation,[status(thm)],[f36,f202]) ).
fof(f4460,plain,
multiply(a,sF5_fnc) = least_upper_bound(sF2_fnc,a),
inference(forward_demodulation,[status(thm)],[f3963,f4434]) ).
fof(f4738,plain,
sF3_fnc = least_upper_bound(sF3_fnc,sF4_fnc),
inference(forward_demodulation,[status(thm)],[f3963,f3450]) ).
fof(f4740,plain,
greatest_lower_bound(a,sF3_fnc) = a,
inference(paramodulation,[status(thm)],[f4738,f1241]) ).
fof(f4741,plain,
greatest_lower_bound(identity,sF3_fnc) = identity,
inference(paramodulation,[status(thm)],[f4738,f1240]) ).
fof(f4773,plain,
least_upper_bound(sF3_fnc,a) = sF3_fnc,
inference(paramodulation,[status(thm)],[f4740,f54]) ).
fof(f4794,plain,
least_upper_bound(sF3_fnc,identity) = sF3_fnc,
inference(paramodulation,[status(thm)],[f4741,f54]) ).
fof(f5143,plain,
least_upper_bound(a,sF3_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f21,f4773]) ).
fof(f5170,plain,
least_upper_bound(identity,sF3_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f21,f4794]) ).
fof(f5281,plain,
least_upper_bound(sF2_fnc,sF3_fnc) = least_upper_bound(sF1_fnc,sF3_fnc),
inference(paramodulation,[status(thm)],[f5170,f178]) ).
fof(f11218,plain,
multiply(sF4_fnc,sF5_fnc) = least_upper_bound(multiply(a,sF5_fnc),sF3_fnc),
inference(paramodulation,[status(thm)],[f158,f311]) ).
fof(f11261,plain,
sF3_fnc = least_upper_bound(multiply(a,sF5_fnc),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f37,f11218]) ).
fof(f11262,plain,
sF3_fnc = least_upper_bound(least_upper_bound(sF2_fnc,a),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f4460,f11261]) ).
fof(f11263,plain,
sF3_fnc = least_upper_bound(sF2_fnc,least_upper_bound(a,sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f23,f11262]) ).
fof(f11264,plain,
sF3_fnc = least_upper_bound(sF2_fnc,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f5143,f11263]) ).
fof(f11265,plain,
sF3_fnc = least_upper_bound(sF1_fnc,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f5281,f11264]) ).
fof(f11379,plain,
greatest_lower_bound(sF1_fnc,sF3_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f11265,f27]) ).
fof(f11384,plain,
sF0_fnc = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f38,f11379]) ).
fof(f11385,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f11384,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP185-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n016.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 20 20:10:09 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 3.55/0.91 % Refutation found
% 3.55/0.91 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.55/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 21.73/6.32 % Elapsed time: 5.930328 seconds
% 21.73/6.32 % CPU time: 33.585271 seconds
% 21.73/6.32 % Total memory used: 20.271 GB
% 21.73/6.32 % Net memory used: 20.270 GB
%------------------------------------------------------------------------------