%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP183-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 8.70s 1.55s
% Output : CNFRefutation 8.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 18
% Syntax : Number of formulae : 97 ( 97 unt; 4 def)
% Number of atoms : 97 ( 96 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 : 83 ( 83 !; 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(f9,axiom,
! [X] : greatest_lower_bound(X,X) = X,
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(f14,axiom,
! [Y,Z,X] : multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
! [X] : inverse(inverse(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f25,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(f26,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(f28,plain,
! [X0] : greatest_lower_bound(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f29,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f30,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f31,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(f33,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(f36,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f38,plain,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f39,definition,
sF1_fnc = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f40,definition,
sF3_fnc = inverse(a),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f41,definition,
sF2_fnc = least_upper_bound(sF3_fnc,identity),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f42,definition,
sF0_fnc = greatest_lower_bound(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f43,plain,
sF0_fnc != identity,
inference(definition_folding,[],[f38,f42,f41,f40,f39]) ).
fof(f46,plain,
inverse(sF3_fnc) = a,
inference(paramodulation,[status(thm)],[f40,f36]) ).
fof(f48,plain,
multiply(a,sF3_fnc) = identity,
inference(paramodulation,[status(thm)],[f46,f21]) ).
fof(f51,plain,
multiply(sF3_fnc,a) = identity,
inference(paramodulation,[status(thm)],[f40,f21]) ).
fof(f56,plain,
sF2_fnc = least_upper_bound(identity,sF3_fnc),
inference(paramodulation,[status(thm)],[f41,f24]) ).
fof(f64,plain,
least_upper_bound(sF1_fnc,sF0_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f42,f29]) ).
fof(f65,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f23,f29]) ).
fof(f69,plain,
greatest_lower_bound(a,sF1_fnc) = a,
inference(paramodulation,[status(thm)],[f39,f30]) ).
fof(f71,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f24,f30]) ).
fof(f84,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X1))) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f28,f25]) ).
fof(f86,plain,
! [X0] : greatest_lower_bound(sF1_fnc,greatest_lower_bound(sF2_fnc,X0)) = greatest_lower_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f42,f25]) ).
fof(f105,plain,
! [X0] : least_upper_bound(sF3_fnc,least_upper_bound(identity,X0)) = least_upper_bound(sF2_fnc,X0),
inference(paramodulation,[status(thm)],[f41,f26]) ).
fof(f106,plain,
! [X0] : least_upper_bound(a,least_upper_bound(identity,X0)) = least_upper_bound(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f39,f26]) ).
fof(f121,plain,
greatest_lower_bound(identity,sF2_fnc) = identity,
inference(paramodulation,[status(thm)],[f56,f30]) ).
fof(f124,plain,
! [X0] : least_upper_bound(sF1_fnc,least_upper_bound(sF0_fnc,X0)) = least_upper_bound(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f64,f26]) ).
fof(f131,plain,
least_upper_bound(sF2_fnc,sF0_fnc) = sF2_fnc,
inference(paramodulation,[status(thm)],[f42,f65]) ).
fof(f132,plain,
! [X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X0) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f30,f65]) ).
fof(f140,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f26,f132]) ).
fof(f148,plain,
least_upper_bound(sF1_fnc,a) = sF1_fnc,
inference(paramodulation,[status(thm)],[f69,f65]) ).
fof(f153,plain,
greatest_lower_bound(sF0_fnc,sF1_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f64,f71]) ).
fof(f157,plain,
greatest_lower_bound(identity,sF1_fnc) = identity,
inference(paramodulation,[status(thm)],[f39,f71]) ).
fof(f172,plain,
! [X0] : greatest_lower_bound(identity,greatest_lower_bound(sF2_fnc,X0)) = greatest_lower_bound(identity,X0),
inference(paramodulation,[status(thm)],[f121,f25]) ).
fof(f187,plain,
! [X0] : multiply(identity,X0) = multiply(a,multiply(sF3_fnc,X0)),
inference(paramodulation,[status(thm)],[f48,f22]) ).
fof(f188,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f195,plain,
! [X0] : X0 = multiply(a,multiply(sF3_fnc,X0)),
inference(forward_demodulation,[status(thm)],[f20,f187]) ).
fof(f196,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f20,f188]) ).
fof(f202,plain,
! [X0] : multiply(sF3_fnc,least_upper_bound(a,X0)) = least_upper_bound(identity,multiply(sF3_fnc,X0)),
inference(paramodulation,[status(thm)],[f51,f31]) ).
fof(f204,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f21,f31]) ).
fof(f272,plain,
least_upper_bound(a,sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f24,f148]) ).
fof(f296,plain,
least_upper_bound(sF1_fnc,identity) = sF1_fnc,
inference(paramodulation,[status(thm)],[f157,f65]) ).
fof(f323,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f20,f33]) ).
fof(f375,plain,
least_upper_bound(identity,sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f24,f296]) ).
fof(f723,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f21,f196]) ).
fof(f741,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f36,f723]) ).
fof(f892,plain,
greatest_lower_bound(sF2_fnc,greatest_lower_bound(sF0_fnc,sF1_fnc)) = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f86,f84]) ).
fof(f940,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f153,f892]) ).
fof(f1140,plain,
least_upper_bound(identity,sF1_fnc) = least_upper_bound(identity,a),
inference(paramodulation,[status(thm)],[f39,f140]) ).
fof(f1176,plain,
sF1_fnc = least_upper_bound(identity,a),
inference(forward_demodulation,[status(thm)],[f375,f1140]) ).
fof(f3251,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = greatest_lower_bound(sF1_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f23,f940]) ).
fof(f3271,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f42,f3251]) ).
fof(f3283,plain,
sF0_fnc = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f3271,f940]) ).
fof(f4549,plain,
multiply(sF3_fnc,sF1_fnc) = least_upper_bound(identity,multiply(sF3_fnc,identity)),
inference(paramodulation,[status(thm)],[f39,f202]) ).
fof(f4578,plain,
multiply(sF3_fnc,sF1_fnc) = least_upper_bound(identity,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f741,f4549]) ).
fof(f4579,plain,
multiply(sF3_fnc,sF1_fnc) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f56,f4578]) ).
fof(f4598,plain,
sF1_fnc = multiply(a,sF2_fnc),
inference(paramodulation,[status(thm)],[f4579,f195]) ).
fof(f5301,plain,
greatest_lower_bound(identity,sF0_fnc) = greatest_lower_bound(identity,sF1_fnc),
inference(paramodulation,[status(thm)],[f3283,f172]) ).
fof(f5348,plain,
greatest_lower_bound(identity,sF0_fnc) = identity,
inference(forward_demodulation,[status(thm)],[f157,f5301]) ).
fof(f5394,plain,
least_upper_bound(sF0_fnc,identity) = sF0_fnc,
inference(paramodulation,[status(thm)],[f5348,f65]) ).
fof(f5400,plain,
least_upper_bound(identity,sF0_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f24,f5394]) ).
fof(f5430,plain,
least_upper_bound(sF3_fnc,sF0_fnc) = least_upper_bound(sF2_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f5400,f105]) ).
fof(f5448,plain,
least_upper_bound(sF3_fnc,sF0_fnc) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f131,f5430]) ).
fof(f5633,plain,
multiply(inverse(sF3_fnc),sF2_fnc) = least_upper_bound(identity,multiply(inverse(sF3_fnc),sF0_fnc)),
inference(paramodulation,[status(thm)],[f5448,f204]) ).
fof(f5736,plain,
multiply(a,sF2_fnc) = least_upper_bound(identity,multiply(inverse(sF3_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f46,f5633]) ).
fof(f5737,plain,
sF1_fnc = least_upper_bound(identity,multiply(inverse(sF3_fnc),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f4598,f5736]) ).
fof(f5738,plain,
sF1_fnc = least_upper_bound(identity,multiply(a,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f46,f5737]) ).
fof(f6801,plain,
least_upper_bound(a,sF1_fnc) = least_upper_bound(sF1_fnc,multiply(a,sF0_fnc)),
inference(paramodulation,[status(thm)],[f5738,f106]) ).
fof(f6821,plain,
sF1_fnc = least_upper_bound(sF1_fnc,multiply(a,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f272,f6801]) ).
fof(f9508,plain,
! [X0] : multiply(sF1_fnc,X0) = least_upper_bound(X0,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f1176,f323]) ).
fof(f22720,plain,
least_upper_bound(sF1_fnc,multiply(sF1_fnc,sF0_fnc)) = least_upper_bound(sF1_fnc,multiply(a,sF0_fnc)),
inference(paramodulation,[status(thm)],[f9508,f124]) ).
fof(f22784,plain,
least_upper_bound(sF1_fnc,multiply(sF1_fnc,sF0_fnc)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f6821,f22720]) ).
fof(f23408,plain,
multiply(inverse(sF1_fnc),sF1_fnc) = least_upper_bound(identity,multiply(inverse(sF1_fnc),multiply(sF1_fnc,sF0_fnc))),
inference(paramodulation,[status(thm)],[f22784,f204]) ).
fof(f23430,plain,
identity = least_upper_bound(identity,multiply(inverse(sF1_fnc),multiply(sF1_fnc,sF0_fnc))),
inference(forward_demodulation,[status(thm)],[f21,f23408]) ).
fof(f23431,plain,
identity = least_upper_bound(identity,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f196,f23430]) ).
fof(f23432,plain,
identity = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f5400,f23431]) ).
fof(f23433,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f23432,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP183-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:05:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 8.70/1.55 % Refutation found
% 8.70/1.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.70/1.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.70/1.59 % Elapsed time: 1.216259 seconds
% 8.70/1.59 % CPU time: 9.429368 seconds
% 8.70/1.59 % Total memory used: 154.925 MB
% 8.70/1.59 % Net memory used: 152.307 MB
%------------------------------------------------------------------------------