%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP179-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:32:59 PM UTC 2026
% Result : Unsatisfiable 4.85s 1.10s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 17
% Syntax : Number of formulae : 106 ( 106 unt; 4 def)
% Number of atoms : 106 ( 105 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 96 ( 96 !; 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(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/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(f13,axiom,
! [X,Y,Z] : multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,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(f22,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(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(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(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,
least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,identity)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
sF1_fnc = inverse(a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f34,definition,
sF0_fnc = least_upper_bound(sF1_fnc,identity),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f35,definition,
sF3_fnc = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f36,definition,
sF2_fnc = inverse(sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f37,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f32,f36,f35,f34,f33]) ).
fof(f38,plain,
multiply(sF2_fnc,sF3_fnc) = identity,
inference(paramodulation,[status(thm)],[f36,f18]) ).
fof(f39,plain,
multiply(sF1_fnc,a) = identity,
inference(paramodulation,[status(thm)],[f33,f18]) ).
fof(f44,plain,
sF0_fnc = least_upper_bound(identity,sF1_fnc),
inference(paramodulation,[status(thm)],[f34,f21]) ).
fof(f52,plain,
least_upper_bound(a,sF3_fnc) = a,
inference(paramodulation,[status(thm)],[f35,f26]) ).
fof(f53,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f20,f26]) ).
fof(f58,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f21,f27]) ).
fof(f62,plain,
greatest_lower_bound(identity,sF0_fnc) = identity,
inference(paramodulation,[status(thm)],[f44,f27]) ).
fof(f88,plain,
! [X0] : least_upper_bound(sF1_fnc,least_upper_bound(identity,X0)) = least_upper_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f34,f23]) ).
fof(f107,plain,
least_upper_bound(identity,sF3_fnc) = identity,
inference(paramodulation,[status(thm)],[f35,f53]) ).
fof(f108,plain,
! [X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X0) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f27,f53]) ).
fof(f116,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f23,f108]) ).
fof(f126,plain,
greatest_lower_bound(sF3_fnc,a) = sF3_fnc,
inference(paramodulation,[status(thm)],[f52,f58]) ).
fof(f131,plain,
! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,X1),X0) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f26,f58]) ).
fof(f141,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) = greatest_lower_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f22,f131]) ).
fof(f144,plain,
! [X0] : greatest_lower_bound(identity,greatest_lower_bound(sF0_fnc,X0)) = greatest_lower_bound(identity,X0),
inference(paramodulation,[status(thm)],[f62,f22]) ).
fof(f146,plain,
greatest_lower_bound(sF3_fnc,identity) = sF3_fnc,
inference(paramodulation,[status(thm)],[f107,f58]) ).
fof(f169,plain,
greatest_lower_bound(identity,sF3_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f20,f146]) ).
fof(f177,plain,
! [X0] : multiply(identity,X0) = multiply(sF1_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f39,f19]) ).
fof(f178,plain,
! [X0] : multiply(identity,X0) = multiply(sF2_fnc,multiply(sF3_fnc,X0)),
inference(paramodulation,[status(thm)],[f38,f19]) ).
fof(f179,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f183,plain,
! [X0] : X0 = multiply(sF1_fnc,multiply(a,X0)),
inference(forward_demodulation,[status(thm)],[f17,f177]) ).
fof(f184,plain,
! [X0] : X0 = multiply(sF2_fnc,multiply(sF3_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f17,f178]) ).
fof(f185,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f179]) ).
fof(f192,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f18,f28]) ).
fof(f197,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(multiply(inverse(X0),X1),identity),
inference(paramodulation,[status(thm)],[f18,f28]) ).
fof(f223,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f18,f29]) ).
fof(f324,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X0),X1) = greatest_lower_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f17,f31]) ).
fof(f368,plain,
! [X0] : multiply(a,X0) = multiply(inverse(sF1_fnc),X0),
inference(paramodulation,[status(thm)],[f183,f185]) ).
fof(f370,plain,
! [X0] : multiply(sF3_fnc,X0) = multiply(inverse(sF2_fnc),X0),
inference(paramodulation,[status(thm)],[f184,f185]) ).
fof(f372,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f185,f185]) ).
fof(f373,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f18,f185]) ).
fof(f718,plain,
greatest_lower_bound(identity,sF3_fnc) = greatest_lower_bound(identity,a),
inference(paramodulation,[status(thm)],[f35,f141]) ).
fof(f750,plain,
sF3_fnc = greatest_lower_bound(identity,a),
inference(forward_demodulation,[status(thm)],[f169,f718]) ).
fof(f2322,plain,
multiply(a,sF1_fnc) = identity,
inference(paramodulation,[status(thm)],[f18,f368]) ).
fof(f2681,plain,
! [X0] : X0 = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f372,f373]) ).
fof(f2721,plain,
inverse(sF2_fnc) = multiply(sF3_fnc,identity),
inference(paramodulation,[status(thm)],[f370,f2681]) ).
fof(f2722,plain,
inverse(sF1_fnc) = multiply(a,identity),
inference(paramodulation,[status(thm)],[f368,f2681]) ).
fof(f2746,plain,
inverse(sF2_fnc) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f2681,f2721]) ).
fof(f2747,plain,
inverse(sF1_fnc) = a,
inference(forward_demodulation,[status(thm)],[f2681,f2722]) ).
fof(f5635,plain,
multiply(inverse(sF1_fnc),sF0_fnc) = least_upper_bound(identity,multiply(inverse(sF1_fnc),identity)),
inference(paramodulation,[status(thm)],[f34,f192]) ).
fof(f5733,plain,
multiply(a,sF0_fnc) = least_upper_bound(identity,multiply(inverse(sF1_fnc),identity)),
inference(forward_demodulation,[status(thm)],[f2747,f5635]) ).
fof(f5734,plain,
multiply(a,sF0_fnc) = least_upper_bound(identity,inverse(sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f2681,f5733]) ).
fof(f5735,plain,
multiply(a,sF0_fnc) = least_upper_bound(identity,a),
inference(forward_demodulation,[status(thm)],[f2747,f5734]) ).
fof(f5790,plain,
multiply(inverse(sF3_fnc),identity) = least_upper_bound(multiply(inverse(sF3_fnc),identity),identity),
inference(paramodulation,[status(thm)],[f107,f197]) ).
fof(f5859,plain,
inverse(sF3_fnc) = least_upper_bound(multiply(inverse(sF3_fnc),identity),identity),
inference(forward_demodulation,[status(thm)],[f2681,f5790]) ).
fof(f5860,plain,
sF2_fnc = least_upper_bound(multiply(inverse(sF3_fnc),identity),identity),
inference(forward_demodulation,[status(thm)],[f36,f5859]) ).
fof(f5861,plain,
sF2_fnc = least_upper_bound(inverse(sF3_fnc),identity),
inference(forward_demodulation,[status(thm)],[f2681,f5860]) ).
fof(f5862,plain,
sF2_fnc = least_upper_bound(sF2_fnc,identity),
inference(forward_demodulation,[status(thm)],[f36,f5861]) ).
fof(f6086,plain,
sF2_fnc = least_upper_bound(identity,sF2_fnc),
inference(paramodulation,[status(thm)],[f21,f5862]) ).
fof(f6122,plain,
least_upper_bound(sF1_fnc,sF2_fnc) = least_upper_bound(sF0_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f6086,f88]) ).
fof(f6446,plain,
multiply(inverse(sF3_fnc),sF3_fnc) = greatest_lower_bound(identity,multiply(inverse(sF3_fnc),a)),
inference(paramodulation,[status(thm)],[f126,f223]) ).
fof(f6538,plain,
identity = greatest_lower_bound(identity,multiply(inverse(sF3_fnc),a)),
inference(forward_demodulation,[status(thm)],[f18,f6446]) ).
fof(f6539,plain,
identity = greatest_lower_bound(identity,multiply(sF2_fnc,a)),
inference(forward_demodulation,[status(thm)],[f36,f6538]) ).
fof(f7638,plain,
least_upper_bound(sF2_fnc,least_upper_bound(sF0_fnc,sF2_fnc)) = least_upper_bound(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f6122,f116]) ).
fof(f7650,plain,
least_upper_bound(sF2_fnc,sF0_fnc) = least_upper_bound(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f116,f7638]) ).
fof(f13308,plain,
! [X0] : multiply(identity,X0) = greatest_lower_bound(X0,multiply(multiply(sF2_fnc,a),X0)),
inference(paramodulation,[status(thm)],[f6539,f324]) ).
fof(f13318,plain,
! [X0] : multiply(sF3_fnc,X0) = greatest_lower_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f750,f324]) ).
fof(f13458,plain,
! [X0] : X0 = greatest_lower_bound(X0,multiply(multiply(sF2_fnc,a),X0)),
inference(forward_demodulation,[status(thm)],[f17,f13308]) ).
fof(f13459,plain,
! [X0] : X0 = greatest_lower_bound(X0,multiply(sF2_fnc,multiply(a,X0))),
inference(forward_demodulation,[status(thm)],[f19,f13458]) ).
fof(f18619,plain,
sF1_fnc = greatest_lower_bound(sF1_fnc,multiply(sF2_fnc,identity)),
inference(paramodulation,[status(thm)],[f2322,f13459]) ).
fof(f18683,plain,
sF1_fnc = greatest_lower_bound(sF1_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f2681,f18619]) ).
fof(f18750,plain,
least_upper_bound(sF2_fnc,sF1_fnc) = sF2_fnc,
inference(paramodulation,[status(thm)],[f18683,f53]) ).
fof(f18762,plain,
least_upper_bound(sF2_fnc,sF0_fnc) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f7650,f18750]) ).
fof(f18764,plain,
least_upper_bound(sF0_fnc,sF2_fnc) = sF2_fnc,
inference(paramodulation,[status(thm)],[f21,f18762]) ).
fof(f18873,plain,
multiply(inverse(sF2_fnc),sF2_fnc) = least_upper_bound(multiply(inverse(sF2_fnc),sF0_fnc),identity),
inference(paramodulation,[status(thm)],[f18764,f197]) ).
fof(f18893,plain,
identity = least_upper_bound(multiply(inverse(sF2_fnc),sF0_fnc),identity),
inference(forward_demodulation,[status(thm)],[f18,f18873]) ).
fof(f18894,plain,
identity = least_upper_bound(multiply(sF3_fnc,sF0_fnc),identity),
inference(forward_demodulation,[status(thm)],[f2746,f18893]) ).
fof(f21807,plain,
greatest_lower_bound(identity,multiply(sF3_fnc,sF0_fnc)) = greatest_lower_bound(identity,multiply(a,sF0_fnc)),
inference(paramodulation,[status(thm)],[f13318,f144]) ).
fof(f21878,plain,
greatest_lower_bound(identity,multiply(sF3_fnc,sF0_fnc)) = greatest_lower_bound(identity,least_upper_bound(identity,a)),
inference(forward_demodulation,[status(thm)],[f5735,f21807]) ).
fof(f21879,plain,
greatest_lower_bound(identity,multiply(sF3_fnc,sF0_fnc)) = identity,
inference(forward_demodulation,[status(thm)],[f27,f21878]) ).
fof(f22137,plain,
least_upper_bound(multiply(sF3_fnc,sF0_fnc),identity) = multiply(sF3_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f21879,f53]) ).
fof(f22156,plain,
identity = multiply(sF3_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f18894,f22137]) ).
fof(f22168,plain,
sF0_fnc = multiply(sF2_fnc,identity),
inference(paramodulation,[status(thm)],[f22156,f184]) ).
fof(f22197,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f2681,f22168]) ).
fof(f22198,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f22197,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP179-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:04:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 4.85/1.10 % Refutation found
% 4.85/1.10 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.85/1.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.99/1.12 % Elapsed time: 0.744357 seconds
% 0.99/1.12 % CPU time: 5.717889 seconds
% 0.99/1.12 % Total memory used: 94.821 MB
% 0.99/1.12 % Net memory used: 93.039 MB
%------------------------------------------------------------------------------