%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP178-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 121.69s 20.75s
% Output : CNFRefutation 121.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 17
% Syntax : Number of formulae : 78 ( 78 unt; 3 def)
% Number of atoms : 78 ( 77 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 : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 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(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(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,hypothesis,
greatest_lower_bound(identity,a) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
greatest_lower_bound(identity,c) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,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,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f31,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,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f35,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(f36,plain,
greatest_lower_bound(identity,a) = identity,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f38,plain,
greatest_lower_bound(identity,c) = identity,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f39,plain,
greatest_lower_bound(a,b) = identity,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f40,plain,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f41,definition,
sF1_fnc = multiply(b,c),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f42,definition,
sF0_fnc = greatest_lower_bound(a,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f43,definition,
sF2_fnc = greatest_lower_bound(a,c),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f44,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f40,f43,f42,f41]) ).
fof(f47,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f21,f35]) ).
fof(f61,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f22,f33]) ).
fof(f67,plain,
! [X0] : multiply(greatest_lower_bound(b,X0),c) = greatest_lower_bound(sF1_fnc,multiply(X0,c)),
inference(paramodulation,[status(thm)],[f41,f35]) ).
fof(f72,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f25,f31]) ).
fof(f81,plain,
least_upper_bound(a,sF0_fnc) = a,
inference(paramodulation,[status(thm)],[f42,f30]) ).
fof(f90,plain,
! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,X1),X0) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f30,f72]) ).
fof(f92,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) = greatest_lower_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f26,f90]) ).
fof(f95,plain,
greatest_lower_bound(sF0_fnc,a) = sF0_fnc,
inference(paramodulation,[status(thm)],[f81,f72]) ).
fof(f111,plain,
greatest_lower_bound(b,identity) = greatest_lower_bound(b,a),
inference(paramodulation,[status(thm)],[f39,f92]) ).
fof(f112,plain,
greatest_lower_bound(c,sF2_fnc) = greatest_lower_bound(c,a),
inference(paramodulation,[status(thm)],[f43,f92]) ).
fof(f140,plain,
! [X0] : greatest_lower_bound(sF0_fnc,greatest_lower_bound(a,X0)) = greatest_lower_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f95,f26]) ).
fof(f143,plain,
! [X0] : greatest_lower_bound(a,greatest_lower_bound(sF1_fnc,X0)) = greatest_lower_bound(sF0_fnc,X0),
inference(paramodulation,[status(thm)],[f42,f26]) ).
fof(f146,plain,
! [X0] : greatest_lower_bound(identity,greatest_lower_bound(c,X0)) = greatest_lower_bound(identity,X0),
inference(paramodulation,[status(thm)],[f38,f26]) ).
fof(f257,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f22,f23]) ).
fof(f263,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f21,f257]) ).
fof(f274,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f263,f263]) ).
fof(f275,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f22,f263]) ).
fof(f283,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f274,f275]) ).
fof(f339,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f274,f263]) ).
fof(f888,plain,
greatest_lower_bound(sF0_fnc,identity) = greatest_lower_bound(sF0_fnc,b),
inference(paramodulation,[status(thm)],[f39,f140]) ).
fof(f985,plain,
greatest_lower_bound(identity,greatest_lower_bound(c,a)) = greatest_lower_bound(identity,sF2_fnc),
inference(paramodulation,[status(thm)],[f112,f146]) ).
fof(f1008,plain,
greatest_lower_bound(identity,a) = greatest_lower_bound(identity,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f146,f985]) ).
fof(f1009,plain,
identity = greatest_lower_bound(identity,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f36,f1008]) ).
fof(f1168,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(b,identity),
inference(paramodulation,[status(thm)],[f111,f24]) ).
fof(f1190,plain,
greatest_lower_bound(sF0_fnc,identity) = greatest_lower_bound(b,sF0_fnc),
inference(paramodulation,[status(thm)],[f24,f888]) ).
fof(f1226,plain,
identity = greatest_lower_bound(b,identity),
inference(forward_demodulation,[status(thm)],[f39,f1168]) ).
fof(f1408,plain,
! [X0] : multiply(identity,X0) = greatest_lower_bound(multiply(b,X0),X0),
inference(paramodulation,[status(thm)],[f1226,f47]) ).
fof(f1467,plain,
! [X0] : X0 = greatest_lower_bound(multiply(b,X0),X0),
inference(forward_demodulation,[status(thm)],[f21,f1408]) ).
fof(f1741,plain,
c = greatest_lower_bound(sF1_fnc,c),
inference(paramodulation,[status(thm)],[f41,f1467]) ).
fof(f1764,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(sF0_fnc,c),
inference(paramodulation,[status(thm)],[f1741,f143]) ).
fof(f1773,plain,
sF2_fnc = greatest_lower_bound(sF0_fnc,c),
inference(forward_demodulation,[status(thm)],[f43,f1764]) ).
fof(f1840,plain,
sF2_fnc = greatest_lower_bound(c,sF0_fnc),
inference(paramodulation,[status(thm)],[f24,f1773]) ).
fof(f1895,plain,
greatest_lower_bound(identity,sF2_fnc) = greatest_lower_bound(identity,sF0_fnc),
inference(paramodulation,[status(thm)],[f1840,f146]) ).
fof(f1902,plain,
identity = greatest_lower_bound(identity,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f1009,f1895]) ).
fof(f2882,plain,
greatest_lower_bound(identity,sF0_fnc) = greatest_lower_bound(b,sF0_fnc),
inference(paramodulation,[status(thm)],[f1190,f24]) ).
fof(f2890,plain,
identity = greatest_lower_bound(b,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f1902,f2882]) ).
fof(f3305,plain,
multiply(identity,c) = greatest_lower_bound(sF1_fnc,multiply(sF0_fnc,c)),
inference(paramodulation,[status(thm)],[f2890,f67]) ).
fof(f3324,plain,
c = greatest_lower_bound(sF1_fnc,multiply(sF0_fnc,c)),
inference(forward_demodulation,[status(thm)],[f21,f3305]) ).
fof(f5804,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(sF0_fnc,multiply(sF0_fnc,c)),
inference(paramodulation,[status(thm)],[f3324,f143]) ).
fof(f5819,plain,
sF2_fnc = greatest_lower_bound(sF0_fnc,multiply(sF0_fnc,c)),
inference(forward_demodulation,[status(thm)],[f43,f5804]) ).
fof(f7333,plain,
multiply(inverse(sF0_fnc),sF2_fnc) = greatest_lower_bound(identity,multiply(inverse(sF0_fnc),multiply(sF0_fnc,c))),
inference(paramodulation,[status(thm)],[f5819,f61]) ).
fof(f7343,plain,
multiply(inverse(sF0_fnc),sF2_fnc) = greatest_lower_bound(identity,c),
inference(forward_demodulation,[status(thm)],[f263,f7333]) ).
fof(f7347,plain,
multiply(inverse(sF0_fnc),sF2_fnc) = identity,
inference(forward_demodulation,[status(thm)],[f38,f7343]) ).
fof(f7349,plain,
sF2_fnc = multiply(sF0_fnc,identity),
inference(paramodulation,[status(thm)],[f7347,f339]) ).
fof(f7372,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f283,f7349]) ).
fof(f7373,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f7372,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP178-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/5.35 % Computer : n016.cluster.edu
% 0.07/5.35 % Model : x86_64 x86_64
% 0.07/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.35 % Memory : 8046.5625MB
% 0.07/5.35 % OS : Linux 6.8.0-71-generic
% 0.07/5.36 % CPULimit : 300
% 0.07/5.36 % WCLimit : 300
% 0.07/5.36 % DateTime : Sun Sep 20 20:09:00 UTC 2026
% 0.07/5.36 % CPUTime :
% 0.07/5.37 % Drodi V4.1.1
% 121.69/20.75 % Refutation found
% 121.69/20.75 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 121.69/20.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.93/20.93 % Elapsed time: 15.547274 seconds
% 7.93/20.93 % CPU time: 123.062873 seconds
% 7.93/20.93 % Total memory used: 769.022 MB
% 7.93/20.93 % Net memory used: 753.995 MB
%------------------------------------------------------------------------------