%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP184-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:33:01 PM UTC 2026
% Result : Unsatisfiable 36.03s 10.00s
% Output : CNFRefutation 35.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 62 ( 62 unt; 6 def)
% Number of atoms : 62 ( 61 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 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 74 ( 74 !; 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(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(f13,axiom,
! [X,Y,Z] : multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
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(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,negated_conjecture,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
file('/export/starexec/sandbox/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(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(f29,plain,
! [X0,X1,X2] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f13]) ).
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(f31,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(f32,plain,
multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
sF1_fnc = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f34,definition,
sF3_fnc = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f35,definition,
sF2_fnc = inverse(sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f36,definition,
sF0_fnc = multiply(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f37,definition,
sF5_fnc = inverse(sF3_fnc),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f38,definition,
sF4_fnc = multiply(sF5_fnc,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f39,plain,
sF0_fnc != sF4_fnc,
inference(definition_folding,[],[f32,f38,f37,f36,f35,f34,f33]) ).
fof(f40,plain,
sF5_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f35,f37]) ).
fof(f41,plain,
sF4_fnc = multiply(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f40,f38]) ).
fof(f42,plain,
multiply(sF2_fnc,sF3_fnc) = identity,
inference(paramodulation,[status(thm)],[f35,f18]) ).
fof(f70,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f72,plain,
! [X0] : multiply(identity,X0) = multiply(sF2_fnc,multiply(sF3_fnc,X0)),
inference(paramodulation,[status(thm)],[f42,f19]) ).
fof(f77,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f70]) ).
fof(f78,plain,
! [X0] : X0 = multiply(sF2_fnc,multiply(sF3_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f17,f72]) ).
fof(f117,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f77,f77]) ).
fof(f118,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f18,f77]) ).
fof(f125,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f117,f118]) ).
fof(f240,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f125,f117]) ).
fof(f249,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f125,f240]) ).
fof(f257,plain,
sF3_fnc = inverse(sF2_fnc),
inference(paramodulation,[status(thm)],[f35,f249]) ).
fof(f353,plain,
! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X2),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f28]) ).
fof(f409,plain,
multiply(sF3_fnc,sF2_fnc) = identity,
inference(paramodulation,[status(thm)],[f257,f18]) ).
fof(f778,plain,
! [X0] : multiply(sF1_fnc,greatest_lower_bound(sF2_fnc,X0)) = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f36,f29]) ).
fof(f897,plain,
! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f17,f30]) ).
fof(f937,plain,
! [X0,X1] : multiply(least_upper_bound(X0,identity),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f21,f897]) ).
fof(f1613,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f17,f31]) ).
fof(f1656,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f1613]) ).
fof(f9378,plain,
! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = multiply(X0,least_upper_bound(X2,X1)),
inference(paramodulation,[status(thm)],[f28,f353]) ).
fof(f25593,plain,
! [X0] : multiply(sF1_fnc,X0) = least_upper_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f33,f937]) ).
fof(f38000,plain,
! [X0] : multiply(sF3_fnc,X0) = greatest_lower_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f34,f1656]) ).
fof(f48409,plain,
! [X0] : multiply(sF1_fnc,multiply(a,X0)) = multiply(a,least_upper_bound(multiply(a,X0),X0)),
inference(paramodulation,[status(thm)],[f353,f25593]) ).
fof(f48509,plain,
! [X0] : multiply(sF1_fnc,multiply(a,X0)) = multiply(a,least_upper_bound(X0,multiply(a,X0))),
inference(forward_demodulation,[status(thm)],[f9378,f48409]) ).
fof(f48510,plain,
! [X0] : multiply(sF1_fnc,multiply(a,X0)) = multiply(a,multiply(sF1_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f25593,f48509]) ).
fof(f54180,plain,
multiply(sF1_fnc,multiply(sF3_fnc,sF2_fnc)) = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc))),
inference(paramodulation,[status(thm)],[f38000,f778]) ).
fof(f54299,plain,
multiply(sF1_fnc,identity) = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f409,f54180]) ).
fof(f54300,plain,
sF1_fnc = greatest_lower_bound(sF0_fnc,multiply(sF1_fnc,multiply(a,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f125,f54299]) ).
fof(f54301,plain,
sF1_fnc = greatest_lower_bound(sF0_fnc,multiply(a,multiply(sF1_fnc,sF2_fnc))),
inference(forward_demodulation,[status(thm)],[f48510,f54300]) ).
fof(f54302,plain,
sF1_fnc = greatest_lower_bound(sF0_fnc,multiply(a,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f36,f54301]) ).
fof(f54308,plain,
sF1_fnc = multiply(sF3_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f38000,f54302]) ).
fof(f54409,plain,
sF0_fnc = multiply(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f54308,f78]) ).
fof(f54462,plain,
sF4_fnc = sF0_fnc,
inference(backward_demodulation,[status(thm)],[f54409,f41]) ).
fof(f54699,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f54462,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP184-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/5.33 % Computer : n012.cluster.edu
% 0.05/5.33 % Model : x86_64 x86_64
% 0.05/5.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/5.33 % Memory : 8046.5625MB
% 0.05/5.33 % OS : Linux 6.8.0-71-generic
% 0.05/5.33 % CPULimit : 300
% 0.05/5.33 % WCLimit : 300
% 0.05/5.33 % DateTime : Sun Sep 20 20:04:58 UTC 2026
% 0.05/5.34 % CPUTime :
% 0.05/5.34 % Drodi V4.1.1
% 36.03/10.00 % Refutation found
% 36.03/10.00 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 36.03/10.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.53/10.22 % Elapsed time: 4.878872 seconds
% 1.53/10.22 % CPU time: 37.628885 seconds
% 1.53/10.22 % Total memory used: 505.308 MB
% 1.53/10.22 % Net memory used: 491.702 MB
%------------------------------------------------------------------------------