%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 3.42s 0.90s
% Output : CNFRefutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 42 unt; 1 def)
% Number of atoms : 42 ( 41 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 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(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(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,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
least_upper_bound(a,b) != a,
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(f22,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,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(f31,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(f33,plain,
least_upper_bound(inverse(a),inverse(b)) = inverse(b),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
least_upper_bound(a,b) != a,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f35,definition,
sF0_fnc = least_upper_bound(a,b),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f36,plain,
sF0_fnc != a,
inference(definition_folding,[],[f34,f35]) ).
fof(f312,plain,
! [X0,X1,X2] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X1,X2),multiply(X0,X2)),
inference(paramodulation,[status(thm)],[f22,f31]) ).
fof(f323,plain,
! [X0,X1,X2] : multiply(least_upper_bound(X0,X1),X2) = multiply(least_upper_bound(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f31,f312]) ).
fof(f343,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f19,f29]) ).
fof(f515,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f523,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f18,f515]) ).
fof(f1831,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f523,f523]) ).
fof(f1832,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f19,f523]) ).
fof(f1841,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f1831,f1832]) ).
fof(f1876,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f523,f1831]) ).
fof(f1877,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f19,f1831]) ).
fof(f1878,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f1841,f1831]) ).
fof(f1892,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f1841,f1878]) ).
fof(f1912,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(least_upper_bound(X1,X0))) = identity,
inference(paramodulation,[status(thm)],[f323,f1877]) ).
fof(f1926,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(X1)) = least_upper_bound(multiply(X0,inverse(X1)),identity),
inference(paramodulation,[status(thm)],[f1877,f31]) ).
fof(f1932,plain,
! [X0,X1] : multiply(least_upper_bound(X0,X1),inverse(X1)) = least_upper_bound(identity,multiply(X0,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f22,f1926]) ).
fof(f4433,plain,
multiply(least_upper_bound(inverse(b),inverse(a)),inverse(inverse(b))) = identity,
inference(paramodulation,[status(thm)],[f33,f1912]) ).
fof(f4572,plain,
multiply(least_upper_bound(inverse(a),inverse(b)),inverse(inverse(b))) = identity,
inference(forward_demodulation,[status(thm)],[f323,f4433]) ).
fof(f4573,plain,
least_upper_bound(identity,multiply(inverse(a),inverse(inverse(b)))) = identity,
inference(forward_demodulation,[status(thm)],[f1932,f4572]) ).
fof(f4574,plain,
multiply(inverse(a),least_upper_bound(a,inverse(inverse(b)))) = identity,
inference(forward_demodulation,[status(thm)],[f343,f4573]) ).
fof(f4575,plain,
multiply(inverse(a),least_upper_bound(a,b)) = identity,
inference(forward_demodulation,[status(thm)],[f1892,f4574]) ).
fof(f4576,plain,
multiply(inverse(a),sF0_fnc) = identity,
inference(forward_demodulation,[status(thm)],[f35,f4575]) ).
fof(f4621,plain,
multiply(a,identity) = sF0_fnc,
inference(paramodulation,[status(thm)],[f4576,f1876]) ).
fof(f4632,plain,
a = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f1841,f4621]) ).
fof(f4633,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4632,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP169-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:03:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 3.42/0.90 % Refutation found
% 3.42/0.90 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.42/0.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.04/0.94 % Elapsed time: 0.571073 seconds
% 4.04/0.94 % CPU time: 4.314294 seconds
% 4.04/0.94 % Total memory used: 59.877 MB
% 4.04/0.94 % Net memory used: 58.745 MB
%------------------------------------------------------------------------------