%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP184-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 8.33s 1.47s
% Output : CNFRefutation 8.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 21
% Syntax : Number of formulae : 102 ( 102 unt; 6 def)
% Number of atoms : 102 ( 101 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 : 5 ( 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 : 89 ( 89 !; 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(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,hypothesis,
inverse(identity) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
! [X] : inverse(inverse(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
! [X,Y] : inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
! [X,Y] : inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,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(f22,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f23,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f25,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,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] : 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(f31,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f32,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f33,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(f35,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(f37,plain,
inverse(identity) = identity,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f38,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f39,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f40,plain,
! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X0),inverse(X1)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f42,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)],[f21]) ).
fof(f43,definition,
sF1_fnc = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f44,definition,
sF3_fnc = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f45,definition,
sF2_fnc = inverse(sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f46,definition,
sF0_fnc = multiply(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f47,definition,
sF5_fnc = inverse(sF3_fnc),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f48,definition,
sF4_fnc = multiply(sF5_fnc,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f49,plain,
sF0_fnc != sF4_fnc,
inference(definition_folding,[],[f42,f48,f47,f46,f45,f44,f43]) ).
fof(f50,plain,
sF5_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f45,f47]) ).
fof(f51,plain,
sF4_fnc = multiply(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f50,f48]) ).
fof(f55,plain,
inverse(sF2_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f45,f38]) ).
fof(f57,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f38,f23]) ).
fof(f59,plain,
multiply(sF3_fnc,sF2_fnc) = identity,
inference(paramodulation,[status(thm)],[f55,f23]) ).
fof(f61,plain,
! [X0] : multiply(sF0_fnc,X0) = multiply(sF1_fnc,multiply(sF2_fnc,X0)),
inference(paramodulation,[status(thm)],[f46,f24]) ).
fof(f67,plain,
! [X0] : multiply(sF4_fnc,X0) = multiply(sF2_fnc,multiply(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f51,f24]) ).
fof(f70,plain,
least_upper_bound(a,sF3_fnc) = a,
inference(paramodulation,[status(thm)],[f44,f31]) ).
fof(f72,plain,
! [X0] : multiply(identity,X0) = multiply(sF3_fnc,multiply(sF2_fnc,X0)),
inference(paramodulation,[status(thm)],[f59,f24]) ).
fof(f73,plain,
! [X0] : X0 = multiply(sF3_fnc,multiply(sF2_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f22,f72]) ).
fof(f86,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f25,f31]) ).
fof(f100,plain,
! [X0,X1] : multiply(identity,X0) = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f57,f24]) ).
fof(f101,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f22,f100]) ).
fof(f106,plain,
! [X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X0) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f32,f86]) ).
fof(f112,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f28,f106]) ).
fof(f115,plain,
sF1_fnc = least_upper_bound(identity,a),
inference(paramodulation,[status(thm)],[f43,f26]) ).
fof(f124,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f26,f32]) ).
fof(f145,plain,
greatest_lower_bound(sF3_fnc,a) = sF3_fnc,
inference(paramodulation,[status(thm)],[f70,f124]) ).
fof(f259,plain,
! [X0] : X0 = multiply(X0,identity),
inference(paramodulation,[status(thm)],[f23,f101]) ).
fof(f328,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f23,f33]) ).
fof(f330,plain,
! [X0,X1] : multiply(X0,least_upper_bound(identity,X1)) = least_upper_bound(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f259,f33]) ).
fof(f724,plain,
! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f23,f35]) ).
fof(f725,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f35]) ).
fof(f983,plain,
! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = least_upper_bound(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f26,f40]) ).
fof(f989,plain,
! [X0] : inverse(greatest_lower_bound(identity,X0)) = least_upper_bound(identity,inverse(X0)),
inference(paramodulation,[status(thm)],[f37,f40]) ).
fof(f992,plain,
! [X0] : inverse(greatest_lower_bound(X0,sF3_fnc)) = least_upper_bound(inverse(X0),sF2_fnc),
inference(paramodulation,[status(thm)],[f45,f40]) ).
fof(f1002,plain,
! [X0,X1] : inverse(greatest_lower_bound(X0,X1)) = inverse(greatest_lower_bound(X1,X0)),
inference(forward_demodulation,[status(thm)],[f40,f983]) ).
fof(f1142,plain,
! [X0] : inverse(multiply(sF2_fnc,X0)) = multiply(inverse(X0),sF3_fnc),
inference(paramodulation,[status(thm)],[f55,f39]) ).
fof(f1146,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f39,f101]) ).
fof(f1201,plain,
multiply(sF4_fnc,inverse(sF1_fnc)) = multiply(sF2_fnc,identity),
inference(paramodulation,[status(thm)],[f57,f67]) ).
fof(f1215,plain,
multiply(sF4_fnc,inverse(sF1_fnc)) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f259,f1201]) ).
fof(f1387,plain,
inverse(sF4_fnc) = multiply(inverse(sF1_fnc),inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f1215,f1146]) ).
fof(f1432,plain,
inverse(sF4_fnc) = inverse(multiply(sF2_fnc,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f39,f1387]) ).
fof(f1433,plain,
inverse(sF4_fnc) = multiply(inverse(sF1_fnc),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f1142,f1432]) ).
fof(f6008,plain,
inverse(sF3_fnc) = inverse(greatest_lower_bound(a,sF3_fnc)),
inference(paramodulation,[status(thm)],[f145,f1002]) ).
fof(f6011,plain,
inverse(sF3_fnc) = inverse(greatest_lower_bound(identity,a)),
inference(paramodulation,[status(thm)],[f44,f1002]) ).
fof(f6079,plain,
sF2_fnc = inverse(greatest_lower_bound(a,sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f45,f6008]) ).
fof(f6080,plain,
sF2_fnc = least_upper_bound(inverse(a),sF2_fnc),
inference(forward_demodulation,[status(thm)],[f992,f6079]) ).
fof(f6084,plain,
sF2_fnc = inverse(greatest_lower_bound(identity,a)),
inference(forward_demodulation,[status(thm)],[f45,f6011]) ).
fof(f6085,plain,
sF2_fnc = least_upper_bound(identity,inverse(a)),
inference(forward_demodulation,[status(thm)],[f989,f6084]) ).
fof(f6213,plain,
least_upper_bound(inverse(a),sF2_fnc) = least_upper_bound(inverse(a),identity),
inference(paramodulation,[status(thm)],[f6085,f112]) ).
fof(f6220,plain,
sF2_fnc = least_upper_bound(inverse(a),identity),
inference(forward_demodulation,[status(thm)],[f6080,f6213]) ).
fof(f7570,plain,
multiply(inverse(inverse(a)),sF2_fnc) = least_upper_bound(identity,multiply(inverse(inverse(a)),identity)),
inference(paramodulation,[status(thm)],[f6220,f328]) ).
fof(f7681,plain,
multiply(a,sF2_fnc) = least_upper_bound(identity,multiply(inverse(inverse(a)),identity)),
inference(forward_demodulation,[status(thm)],[f38,f7570]) ).
fof(f7682,plain,
multiply(a,sF2_fnc) = multiply(least_upper_bound(identity,inverse(inverse(a))),identity),
inference(forward_demodulation,[status(thm)],[f725,f7681]) ).
fof(f7683,plain,
multiply(a,sF2_fnc) = least_upper_bound(identity,inverse(inverse(a))),
inference(forward_demodulation,[status(thm)],[f259,f7682]) ).
fof(f7684,plain,
multiply(a,sF2_fnc) = least_upper_bound(identity,a),
inference(forward_demodulation,[status(thm)],[f38,f7683]) ).
fof(f7685,plain,
multiply(a,sF2_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f115,f7684]) ).
fof(f7890,plain,
inverse(a) = multiply(sF2_fnc,inverse(sF1_fnc)),
inference(paramodulation,[status(thm)],[f7685,f1146]) ).
fof(f14957,plain,
multiply(sF2_fnc,a) = least_upper_bound(identity,multiply(identity,a)),
inference(paramodulation,[status(thm)],[f6220,f724]) ).
fof(f15023,plain,
multiply(sF2_fnc,a) = multiply(identity,least_upper_bound(identity,a)),
inference(forward_demodulation,[status(thm)],[f330,f14957]) ).
fof(f15024,plain,
multiply(sF2_fnc,a) = least_upper_bound(identity,a),
inference(forward_demodulation,[status(thm)],[f22,f15023]) ).
fof(f15026,plain,
multiply(sF2_fnc,a) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f115,f15024]) ).
fof(f15100,plain,
a = multiply(sF3_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f15026,f73]) ).
fof(f15145,plain,
inverse(sF3_fnc) = multiply(sF1_fnc,inverse(a)),
inference(paramodulation,[status(thm)],[f15100,f1146]) ).
fof(f15158,plain,
sF2_fnc = multiply(sF1_fnc,inverse(a)),
inference(forward_demodulation,[status(thm)],[f45,f15145]) ).
fof(f17231,plain,
multiply(sF0_fnc,inverse(sF1_fnc)) = multiply(sF1_fnc,inverse(a)),
inference(paramodulation,[status(thm)],[f7890,f61]) ).
fof(f17262,plain,
multiply(sF0_fnc,inverse(sF1_fnc)) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f15158,f17231]) ).
fof(f17283,plain,
inverse(sF0_fnc) = multiply(inverse(sF1_fnc),inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f17262,f1146]) ).
fof(f17305,plain,
inverse(sF0_fnc) = inverse(multiply(sF2_fnc,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f39,f17283]) ).
fof(f17306,plain,
inverse(sF0_fnc) = multiply(inverse(sF1_fnc),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f1142,f17305]) ).
fof(f17392,plain,
inverse(sF0_fnc) = inverse(sF4_fnc),
inference(forward_demodulation,[status(thm)],[f1433,f17306]) ).
fof(f17470,plain,
inverse(inverse(sF0_fnc)) = sF4_fnc,
inference(paramodulation,[status(thm)],[f17392,f38]) ).
fof(f17493,plain,
sF0_fnc = sF4_fnc,
inference(forward_demodulation,[status(thm)],[f38,f17470]) ).
fof(f17494,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f17493,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP184-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:02:51 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 8.33/1.47 % Refutation found
% 8.33/1.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.33/1.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.67/1.53 % Elapsed time: 1.155813 seconds
% 0.67/1.53 % CPU time: 8.836933 seconds
% 0.67/1.53 % Total memory used: 155.922 MB
% 0.67/1.53 % Net memory used: 150.908 MB
%------------------------------------------------------------------------------