%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP169-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:32:56 PM UTC 2026
% Result : Unsatisfiable 1.60s 0.74s
% Output : CNFRefutation 1.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 44 unt; 1 def)
% Number of atoms : 44 ( 43 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 55 !; 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(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(f13,axiom,
! [X,Y,Z] : multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
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(f16,hypothesis,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
greatest_lower_bound(a,b) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,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] : greatest_lower_bound(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f30,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(f32,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(f33,plain,
greatest_lower_bound(inverse(a),inverse(b)) = inverse(a),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
greatest_lower_bound(a,b) != b,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f35,definition,
sF0_fnc = greatest_lower_bound(a,b),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f36,plain,
sF0_fnc != b,
inference(definition_folding,[],[f34,f35]) ).
fof(f42,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f23]) ).
fof(f47,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f26,f23]) ).
fof(f58,plain,
greatest_lower_bound(a,sF0_fnc) = greatest_lower_bound(a,b),
inference(paramodulation,[status(thm)],[f35,f47]) ).
fof(f70,plain,
greatest_lower_bound(a,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f35,f58]) ).
fof(f107,plain,
! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f32]) ).
fof(f109,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f19,f30]) ).
fof(f125,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f133,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f18,f125]) ).
fof(f280,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X1,X0),
inference(paramodulation,[status(thm)],[f26,f42]) ).
fof(f400,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f133,f133]) ).
fof(f401,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f19,f133]) ).
fof(f408,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f400,f401]) ).
fof(f732,plain,
greatest_lower_bound(a,sF0_fnc) = greatest_lower_bound(b,a),
inference(paramodulation,[status(thm)],[f35,f280]) ).
fof(f789,plain,
sF0_fnc = greatest_lower_bound(b,a),
inference(forward_demodulation,[status(thm)],[f70,f732]) ).
fof(f1849,plain,
multiply(inverse(a),a) = greatest_lower_bound(identity,multiply(inverse(b),a)),
inference(paramodulation,[status(thm)],[f33,f107]) ).
fof(f1887,plain,
identity = greatest_lower_bound(identity,multiply(inverse(b),a)),
inference(forward_demodulation,[status(thm)],[f19,f1849]) ).
fof(f2004,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f133,f400]) ).
fof(f2219,plain,
multiply(inverse(b),sF0_fnc) = greatest_lower_bound(identity,multiply(inverse(b),a)),
inference(paramodulation,[status(thm)],[f789,f109]) ).
fof(f2280,plain,
multiply(inverse(b),sF0_fnc) = identity,
inference(forward_demodulation,[status(thm)],[f1887,f2219]) ).
fof(f2699,plain,
multiply(b,identity) = sF0_fnc,
inference(paramodulation,[status(thm)],[f2280,f2004]) ).
fof(f2718,plain,
b = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f408,f2699]) ).
fof(f2719,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2718,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP169-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:09:15 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 1.60/0.74 % Refutation found
% 1.60/0.74 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.60/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.60/0.78 % Elapsed time: 0.398753 seconds
% 1.60/0.78 % CPU time: 3.011458 seconds
% 1.60/0.78 % Total memory used: 57.470 MB
% 1.60/0.78 % Net memory used: 56.273 MB
%------------------------------------------------------------------------------