%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP183-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 9.64s 1.69s
% Output : CNFRefutation 10.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 16
% Syntax : Number of formulae : 95 ( 95 unt; 4 def)
% Number of atoms : 95 ( 94 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 : 87 ( 87 !; 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(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(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(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,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != 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(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(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(a,identity),least_upper_bound(inverse(a),identity)) != 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 = inverse(a),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f35,definition,
sF2_fnc = least_upper_bound(sF3_fnc,identity),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f36,definition,
sF0_fnc = greatest_lower_bound(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f37,plain,
sF0_fnc != identity,
inference(definition_folding,[],[f32,f36,f35,f34,f33]) ).
fof(f38,plain,
multiply(sF3_fnc,a) = identity,
inference(paramodulation,[status(thm)],[f34,f18]) ).
fof(f43,plain,
sF2_fnc = least_upper_bound(identity,sF3_fnc),
inference(paramodulation,[status(thm)],[f35,f21]) ).
fof(f51,plain,
least_upper_bound(sF1_fnc,sF0_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f36,f26]) ).
fof(f52,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f20,f26]) ).
fof(f56,plain,
greatest_lower_bound(a,sF1_fnc) = a,
inference(paramodulation,[status(thm)],[f33,f27]) ).
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,sF2_fnc) = identity,
inference(paramodulation,[status(thm)],[f43,f27]) ).
fof(f92,plain,
! [X0] : least_upper_bound(sF1_fnc,least_upper_bound(sF0_fnc,X0)) = least_upper_bound(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f51,f23]) ).
fof(f94,plain,
! [X0] : least_upper_bound(sF3_fnc,least_upper_bound(identity,X0)) = least_upper_bound(sF2_fnc,X0),
inference(paramodulation,[status(thm)],[f35,f23]) ).
fof(f95,plain,
! [X0] : least_upper_bound(a,least_upper_bound(identity,X0)) = least_upper_bound(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f33,f23]) ).
fof(f112,plain,
least_upper_bound(sF2_fnc,sF0_fnc) = sF2_fnc,
inference(paramodulation,[status(thm)],[f36,f52]) ).
fof(f113,plain,
! [X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X0) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f27,f52]) ).
fof(f121,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f23,f113]) ).
fof(f129,plain,
least_upper_bound(sF1_fnc,a) = sF1_fnc,
inference(paramodulation,[status(thm)],[f56,f52]) ).
fof(f138,plain,
greatest_lower_bound(identity,sF1_fnc) = identity,
inference(paramodulation,[status(thm)],[f33,f58]) ).
fof(f140,plain,
! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,X1),X0) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f26,f58]) ).
fof(f150,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) = greatest_lower_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f22,f140]) ).
fof(f153,plain,
! [X0] : greatest_lower_bound(identity,greatest_lower_bound(sF2_fnc,X0)) = greatest_lower_bound(identity,X0),
inference(paramodulation,[status(thm)],[f62,f22]) ).
fof(f171,plain,
least_upper_bound(a,sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f21,f129]) ).
fof(f179,plain,
! [X0] : multiply(identity,X0) = multiply(sF3_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f38,f19]) ).
fof(f180,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f184,plain,
! [X0] : X0 = multiply(sF3_fnc,multiply(a,X0)),
inference(forward_demodulation,[status(thm)],[f17,f179]) ).
fof(f185,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f180]) ).
fof(f190,plain,
! [X0] : multiply(sF3_fnc,least_upper_bound(a,X0)) = least_upper_bound(identity,multiply(sF3_fnc,X0)),
inference(paramodulation,[status(thm)],[f38,f28]) ).
fof(f191,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(f249,plain,
least_upper_bound(sF1_fnc,identity) = sF1_fnc,
inference(paramodulation,[status(thm)],[f138,f52]) ).
fof(f282,plain,
least_upper_bound(identity,sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f21,f249]) ).
fof(f299,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f17,f30]) ).
fof(f359,plain,
! [X0] : multiply(a,X0) = multiply(inverse(sF3_fnc),X0),
inference(paramodulation,[status(thm)],[f184,f185]) ).
fof(f361,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f185,f185]) ).
fof(f362,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f18,f185]) ).
fof(f370,plain,
! [X0,X1,X2] : multiply(inverse(X0),least_upper_bound(X1,multiply(X0,X2))) = least_upper_bound(multiply(inverse(X0),X1),X2),
inference(paramodulation,[status(thm)],[f185,f28]) ).
fof(f935,plain,
least_upper_bound(identity,sF1_fnc) = least_upper_bound(identity,a),
inference(paramodulation,[status(thm)],[f33,f121]) ).
fof(f971,plain,
sF1_fnc = least_upper_bound(identity,a),
inference(forward_demodulation,[status(thm)],[f282,f935]) ).
fof(f1086,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f36,f150]) ).
fof(f2681,plain,
! [X0] : multiply(a,multiply(sF3_fnc,X0)) = X0,
inference(paramodulation,[status(thm)],[f185,f359]) ).
fof(f2758,plain,
! [X0] : X0 = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f361,f362]) ).
fof(f2795,plain,
inverse(sF3_fnc) = multiply(a,identity),
inference(paramodulation,[status(thm)],[f359,f2758]) ).
fof(f2816,plain,
inverse(sF3_fnc) = a,
inference(forward_demodulation,[status(thm)],[f2758,f2795]) ).
fof(f3541,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = greatest_lower_bound(sF1_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f20,f1086]) ).
fof(f3561,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f36,f3541]) ).
fof(f3573,plain,
sF0_fnc = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f3561,f1086]) ).
fof(f4414,plain,
greatest_lower_bound(identity,sF0_fnc) = greatest_lower_bound(identity,sF1_fnc),
inference(paramodulation,[status(thm)],[f3573,f153]) ).
fof(f4461,plain,
greatest_lower_bound(identity,sF0_fnc) = identity,
inference(forward_demodulation,[status(thm)],[f138,f4414]) ).
fof(f4507,plain,
least_upper_bound(sF0_fnc,identity) = sF0_fnc,
inference(paramodulation,[status(thm)],[f4461,f52]) ).
fof(f4907,plain,
least_upper_bound(identity,sF0_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f21,f4507]) ).
fof(f4935,plain,
least_upper_bound(sF3_fnc,sF0_fnc) = least_upper_bound(sF2_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f4907,f94]) ).
fof(f4953,plain,
least_upper_bound(sF3_fnc,sF0_fnc) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f112,f4935]) ).
fof(f4981,plain,
multiply(sF3_fnc,sF1_fnc) = least_upper_bound(identity,multiply(sF3_fnc,identity)),
inference(paramodulation,[status(thm)],[f33,f190]) ).
fof(f5011,plain,
multiply(sF3_fnc,sF1_fnc) = least_upper_bound(identity,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f2758,f4981]) ).
fof(f5012,plain,
multiply(sF3_fnc,sF1_fnc) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f43,f5011]) ).
fof(f5086,plain,
multiply(a,sF2_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f5012,f2681]) ).
fof(f5249,plain,
multiply(inverse(sF3_fnc),sF2_fnc) = least_upper_bound(identity,multiply(inverse(sF3_fnc),sF0_fnc)),
inference(paramodulation,[status(thm)],[f4953,f191]) ).
fof(f5342,plain,
multiply(a,sF2_fnc) = least_upper_bound(identity,multiply(inverse(sF3_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f2816,f5249]) ).
fof(f5343,plain,
sF1_fnc = least_upper_bound(identity,multiply(inverse(sF3_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f5086,f5342]) ).
fof(f5344,plain,
sF1_fnc = least_upper_bound(identity,multiply(a,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f2816,f5343]) ).
fof(f6036,plain,
least_upper_bound(a,sF1_fnc) = least_upper_bound(sF1_fnc,multiply(a,sF0_fnc)),
inference(paramodulation,[status(thm)],[f5344,f95]) ).
fof(f6056,plain,
sF1_fnc = least_upper_bound(sF1_fnc,multiply(a,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f171,f6036]) ).
fof(f9525,plain,
! [X0] : multiply(sF1_fnc,X0) = least_upper_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f971,f299]) ).
fof(f25805,plain,
least_upper_bound(sF1_fnc,multiply(sF1_fnc,sF0_fnc)) = least_upper_bound(sF1_fnc,multiply(a,sF0_fnc)),
inference(paramodulation,[status(thm)],[f9525,f92]) ).
fof(f25875,plain,
least_upper_bound(sF1_fnc,multiply(sF1_fnc,sF0_fnc)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f6056,f25805]) ).
fof(f26639,plain,
multiply(inverse(sF1_fnc),sF1_fnc) = least_upper_bound(multiply(inverse(sF1_fnc),sF1_fnc),sF0_fnc),
inference(paramodulation,[status(thm)],[f25875,f370]) ).
fof(f26665,plain,
identity = least_upper_bound(multiply(inverse(sF1_fnc),sF1_fnc),sF0_fnc),
inference(forward_demodulation,[status(thm)],[f18,f26639]) ).
fof(f26666,plain,
identity = least_upper_bound(identity,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f18,f26665]) ).
fof(f26667,plain,
identity = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f4907,f26666]) ).
fof(f26668,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f26667,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP183-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:04:21 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 9.64/1.69 % Refutation found
% 9.64/1.69 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.64/1.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.46/1.78 % Elapsed time: 1.412586 seconds
% 10.46/1.78 % CPU time: 10.897040 seconds
% 10.46/1.78 % Total memory used: 158.745 MB
% 10.46/1.78 % Net memory used: 156.220 MB
%------------------------------------------------------------------------------