%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP193-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:33:04 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 60 ( 60 unt; 3 def)
% Number of atoms : 60 ( 59 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 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 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(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(f9,axiom,
! [X] : greatest_lower_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(f15,axiom,
! [Y,Z,X] : multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
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(f27,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(f30,plain,
! [X0] : greatest_lower_bound(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f9]) ).
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(f36,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(f40,plain,
greatest_lower_bound(a,b) = identity,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f42,plain,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f43,definition,
sF1_fnc = multiply(b,c),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f44,definition,
sF0_fnc = greatest_lower_bound(a,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f45,definition,
sF2_fnc = greatest_lower_bound(a,c),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f46,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f42,f45,f44,f43]) ).
fof(f47,plain,
sF2_fnc = greatest_lower_bound(c,a),
inference(paramodulation,[status(thm)],[f45,f25]) ).
fof(f65,plain,
! [X0] : greatest_lower_bound(a,greatest_lower_bound(sF1_fnc,X0)) = greatest_lower_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f44,f27]) ).
fof(f68,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f30,f27]) ).
fof(f78,plain,
greatest_lower_bound(c,sF2_fnc) = greatest_lower_bound(c,a),
inference(paramodulation,[status(thm)],[f47,f68]) ).
fof(f82,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f25,f68]) ).
fof(f91,plain,
greatest_lower_bound(c,sF2_fnc) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f47,f78]) ).
fof(f107,plain,
greatest_lower_bound(sF2_fnc,sF2_fnc) = greatest_lower_bound(sF2_fnc,c),
inference(paramodulation,[status(thm)],[f91,f82]) ).
fof(f123,plain,
sF2_fnc = greatest_lower_bound(sF2_fnc,c),
inference(forward_demodulation,[status(thm)],[f30,f107]) ).
fof(f188,plain,
! [X0] : multiply(greatest_lower_bound(b,X0),c) = greatest_lower_bound(sF1_fnc,multiply(X0,c)),
inference(paramodulation,[status(thm)],[f43,f36]) ).
fof(f238,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f25,f31]) ).
fof(f243,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f26,f32]) ).
fof(f255,plain,
greatest_lower_bound(b,a) = identity,
inference(paramodulation,[status(thm)],[f25,f40]) ).
fof(f282,plain,
! [X0,X1,X2] : least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f27,f238]) ).
fof(f407,plain,
greatest_lower_bound(b,identity) = greatest_lower_bound(b,a),
inference(paramodulation,[status(thm)],[f255,f68]) ).
fof(f410,plain,
greatest_lower_bound(b,identity) = identity,
inference(forward_demodulation,[status(thm)],[f255,f407]) ).
fof(f449,plain,
least_upper_bound(greatest_lower_bound(a,sF1_fnc),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(forward_demodulation,[status(thm)],[f43,f41]) ).
fof(f450,plain,
least_upper_bound(sF0_fnc,multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(forward_demodulation,[status(thm)],[f44,f449]) ).
fof(f451,plain,
least_upper_bound(sF0_fnc,multiply(identity,greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(forward_demodulation,[status(thm)],[f40,f450]) ).
fof(f452,plain,
least_upper_bound(sF0_fnc,greatest_lower_bound(a,c)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(forward_demodulation,[status(thm)],[f22,f451]) ).
fof(f453,plain,
least_upper_bound(sF0_fnc,sF2_fnc) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(forward_demodulation,[status(thm)],[f45,f452]) ).
fof(f454,plain,
least_upper_bound(sF0_fnc,sF2_fnc) = multiply(identity,greatest_lower_bound(a,c)),
inference(forward_demodulation,[status(thm)],[f40,f453]) ).
fof(f455,plain,
least_upper_bound(sF0_fnc,sF2_fnc) = greatest_lower_bound(a,c),
inference(forward_demodulation,[status(thm)],[f22,f454]) ).
fof(f456,plain,
least_upper_bound(sF0_fnc,sF2_fnc) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f45,f455]) ).
fof(f458,plain,
greatest_lower_bound(sF0_fnc,sF2_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f456,f32]) ).
fof(f911,plain,
! [X0] : least_upper_bound(c,greatest_lower_bound(X0,sF2_fnc)) = c,
inference(paramodulation,[status(thm)],[f123,f282]) ).
fof(f1582,plain,
least_upper_bound(c,sF0_fnc) = c,
inference(paramodulation,[status(thm)],[f458,f911]) ).
fof(f1604,plain,
greatest_lower_bound(sF0_fnc,c) = sF0_fnc,
inference(paramodulation,[status(thm)],[f1582,f243]) ).
fof(f2310,plain,
multiply(identity,c) = greatest_lower_bound(sF1_fnc,multiply(identity,c)),
inference(paramodulation,[status(thm)],[f410,f188]) ).
fof(f2337,plain,
c = greatest_lower_bound(sF1_fnc,multiply(identity,c)),
inference(forward_demodulation,[status(thm)],[f22,f2310]) ).
fof(f2338,plain,
c = greatest_lower_bound(sF1_fnc,c),
inference(forward_demodulation,[status(thm)],[f22,f2337]) ).
fof(f2357,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(sF0_fnc,c),
inference(paramodulation,[status(thm)],[f2338,f65]) ).
fof(f2374,plain,
sF2_fnc = greatest_lower_bound(sF0_fnc,c),
inference(forward_demodulation,[status(thm)],[f45,f2357]) ).
fof(f2375,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f1604,f2374]) ).
fof(f2376,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2375,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP193-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n026.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 20:08:22 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.11/0.45 % Refutation found
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.47 % Elapsed time: 0.109978 seconds
% 0.11/0.47 % CPU time: 0.719136 seconds
% 0.11/0.47 % Total memory used: 21.802 MB
% 0.11/0.47 % Net memory used: 21.512 MB
%------------------------------------------------------------------------------