%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP185-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 4.10s 0.93s
% Output : CNFRefutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 68 ( 68 unt; 7 def)
% Number of atoms : 68 ( 67 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 : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 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(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(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(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(f16,negated_conjecture,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
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(f24,plain,
! [X0] : least_upper_bound(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
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,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(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 = least_upper_bound(sF1_fnc,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f39,definition,
sF6_fnc = multiply(sF4_fnc,sF5_fnc),
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(f49,plain,
sF0_fnc != sF3_fnc,
inference(backward_demodulation,[status(thm)],[f50,f40]) ).
fof(f50,plain,
sF6_fnc = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f37,f39]) ).
fof(f65,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(f68,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X0,X1)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f24,f23]) ).
fof(f80,plain,
least_upper_bound(b,sF5_fnc) = least_upper_bound(b,identity),
inference(paramodulation,[status(thm)],[f36,f68]) ).
fof(f95,plain,
least_upper_bound(b,sF5_fnc) = sF5_fnc,
inference(forward_demodulation,[status(thm)],[f36,f80]) ).
fof(f111,plain,
! [X0] : multiply(sF4_fnc,least_upper_bound(X0,sF5_fnc)) = least_upper_bound(multiply(sF4_fnc,X0),sF3_fnc),
inference(paramodulation,[status(thm)],[f37,f28]) ).
fof(f138,plain,
! [X0] : multiply(least_upper_bound(sF4_fnc,X0),sF5_fnc) = least_upper_bound(sF3_fnc,multiply(X0,sF5_fnc)),
inference(paramodulation,[status(thm)],[f37,f30]) ).
fof(f139,plain,
! [X0] : multiply(least_upper_bound(a,X0),b) = least_upper_bound(sF2_fnc,multiply(X0,b)),
inference(paramodulation,[status(thm)],[f33,f30]) ).
fof(f169,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f20,f26]) ).
fof(f181,plain,
greatest_lower_bound(b,sF5_fnc) = b,
inference(paramodulation,[status(thm)],[f36,f27]) ).
fof(f186,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f21,f27]) ).
fof(f234,plain,
least_upper_bound(sF5_fnc,b) = sF5_fnc,
inference(paramodulation,[status(thm)],[f181,f169]) ).
fof(f247,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f23,f186]) ).
fof(f253,plain,
greatest_lower_bound(identity,sF5_fnc) = identity,
inference(paramodulation,[status(thm)],[f36,f186]) ).
fof(f255,plain,
greatest_lower_bound(identity,sF4_fnc) = identity,
inference(paramodulation,[status(thm)],[f35,f186]) ).
fof(f539,plain,
least_upper_bound(sF5_fnc,identity) = sF5_fnc,
inference(paramodulation,[status(thm)],[f253,f169]) ).
fof(f542,plain,
least_upper_bound(sF4_fnc,identity) = sF4_fnc,
inference(paramodulation,[status(thm)],[f255,f169]) ).
fof(f1160,plain,
! [X0] : greatest_lower_bound(identity,least_upper_bound(X0,sF5_fnc)) = identity,
inference(paramodulation,[status(thm)],[f539,f247]) ).
fof(f1161,plain,
! [X0] : greatest_lower_bound(b,least_upper_bound(X0,sF5_fnc)) = b,
inference(paramodulation,[status(thm)],[f234,f247]) ).
fof(f2424,plain,
multiply(sF4_fnc,sF5_fnc) = least_upper_bound(multiply(sF4_fnc,b),sF3_fnc),
inference(paramodulation,[status(thm)],[f95,f111]) ).
fof(f2447,plain,
sF3_fnc = least_upper_bound(multiply(sF4_fnc,b),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f37,f2424]) ).
fof(f3144,plain,
multiply(sF4_fnc,sF5_fnc) = least_upper_bound(sF3_fnc,multiply(identity,sF5_fnc)),
inference(paramodulation,[status(thm)],[f542,f138]) ).
fof(f3176,plain,
sF3_fnc = least_upper_bound(sF3_fnc,multiply(identity,sF5_fnc)),
inference(forward_demodulation,[status(thm)],[f37,f3144]) ).
fof(f3177,plain,
sF3_fnc = least_upper_bound(sF3_fnc,sF5_fnc),
inference(forward_demodulation,[status(thm)],[f17,f3176]) ).
fof(f3196,plain,
greatest_lower_bound(b,sF3_fnc) = b,
inference(paramodulation,[status(thm)],[f3177,f1161]) ).
fof(f3197,plain,
greatest_lower_bound(identity,sF3_fnc) = identity,
inference(paramodulation,[status(thm)],[f3177,f1160]) ).
fof(f3234,plain,
least_upper_bound(sF3_fnc,b) = sF3_fnc,
inference(paramodulation,[status(thm)],[f3196,f169]) ).
fof(f3246,plain,
least_upper_bound(sF3_fnc,identity) = sF3_fnc,
inference(paramodulation,[status(thm)],[f3197,f169]) ).
fof(f3305,plain,
least_upper_bound(b,sF3_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f21,f3234]) ).
fof(f3328,plain,
least_upper_bound(identity,sF3_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f21,f3246]) ).
fof(f3485,plain,
least_upper_bound(sF2_fnc,sF3_fnc) = least_upper_bound(sF1_fnc,sF3_fnc),
inference(paramodulation,[status(thm)],[f3328,f65]) ).
fof(f3499,plain,
least_upper_bound(sF2_fnc,sF3_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f38,f3485]) ).
fof(f3614,plain,
multiply(sF4_fnc,b) = least_upper_bound(sF2_fnc,multiply(identity,b)),
inference(paramodulation,[status(thm)],[f35,f139]) ).
fof(f3644,plain,
multiply(sF4_fnc,b) = least_upper_bound(sF2_fnc,b),
inference(forward_demodulation,[status(thm)],[f17,f3614]) ).
fof(f11947,plain,
sF3_fnc = least_upper_bound(least_upper_bound(sF2_fnc,b),sF3_fnc),
inference(backward_demodulation,[status(thm)],[f3644,f2447]) ).
fof(f11972,plain,
sF3_fnc = least_upper_bound(sF2_fnc,least_upper_bound(b,sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f23,f11947]) ).
fof(f11973,plain,
sF3_fnc = least_upper_bound(sF2_fnc,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f3305,f11972]) ).
fof(f11974,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f3499,f11973]) ).
fof(f11975,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f11974,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP185-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:06:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 4.10/0.93 % Refutation found
% 4.10/0.93 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.10/0.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 50.95/9.39 % Elapsed time: 8.814109 seconds
% 50.95/9.39 % CPU time: 11.033856 seconds
% 50.95/9.39 % Total memory used: 8.219 GB
% 50.95/9.39 % Net memory used: 8.218 GB
%------------------------------------------------------------------------------