%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP192-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 61 unt; 2 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 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(f16,hypothesis,
! [X] : least_upper_bound(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
multiply(a,b) != multiply(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(f33,plain,
! [X0] : least_upper_bound(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
multiply(a,b) != multiply(b,a),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f35,definition,
sF0_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f36,definition,
sF1_fnc = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f37,plain,
sF0_fnc != sF1_fnc,
inference(definition_folding,[],[f34,f36,f35]) ).
fof(f39,plain,
! [X0] : multiply(sF1_fnc,X0) = multiply(b,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f36,f20]) ).
fof(f40,plain,
! [X0] : multiply(sF0_fnc,X0) = multiply(a,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f35,f20]) ).
fof(f50,plain,
multiply(sF0_fnc,a) = multiply(a,sF1_fnc),
inference(paramodulation,[status(thm)],[f36,f40]) ).
fof(f76,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f77,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f18,f76]) ).
fof(f78,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f77,f77]) ).
fof(f79,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f19,f77]) ).
fof(f82,plain,
a = multiply(inverse(sF0_fnc),multiply(a,sF1_fnc)),
inference(paramodulation,[status(thm)],[f50,f77]) ).
fof(f89,plain,
b = multiply(inverse(a),sF0_fnc),
inference(paramodulation,[status(thm)],[f35,f77]) ).
fof(f93,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f19,f78]) ).
fof(f100,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f78,f79]) ).
fof(f133,plain,
! [X0] : X0 = least_upper_bound(X0,identity),
inference(paramodulation,[status(thm)],[f33,f22]) ).
fof(f240,plain,
! [X0] : multiply(b,least_upper_bound(a,X0)) = least_upper_bound(sF1_fnc,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f36,f29]) ).
fof(f242,plain,
! [X0] : multiply(a,least_upper_bound(b,X0)) = least_upper_bound(sF0_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f35,f29]) ).
fof(f243,plain,
! [X0,X1] : multiply(X0,least_upper_bound(identity,X1)) = least_upper_bound(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f100,f29]) ).
fof(f269,plain,
! [X0,X1] : multiply(X0,X1) = least_upper_bound(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f33,f243]) ).
fof(f327,plain,
multiply(b,a) = least_upper_bound(sF1_fnc,multiply(b,identity)),
inference(paramodulation,[status(thm)],[f133,f240]) ).
fof(f338,plain,
sF1_fnc = least_upper_bound(sF1_fnc,multiply(b,identity)),
inference(forward_demodulation,[status(thm)],[f36,f327]) ).
fof(f339,plain,
sF1_fnc = least_upper_bound(sF1_fnc,b),
inference(forward_demodulation,[status(thm)],[f100,f338]) ).
fof(f355,plain,
multiply(sF0_fnc,inverse(b)) = multiply(a,identity),
inference(paramodulation,[status(thm)],[f93,f40]) ).
fof(f357,plain,
multiply(sF1_fnc,inverse(a)) = multiply(b,identity),
inference(paramodulation,[status(thm)],[f93,f39]) ).
fof(f365,plain,
multiply(sF0_fnc,inverse(b)) = a,
inference(forward_demodulation,[status(thm)],[f100,f355]) ).
fof(f367,plain,
multiply(sF1_fnc,inverse(a)) = b,
inference(forward_demodulation,[status(thm)],[f100,f357]) ).
fof(f415,plain,
multiply(a,b) = least_upper_bound(sF0_fnc,multiply(a,identity)),
inference(paramodulation,[status(thm)],[f133,f242]) ).
fof(f426,plain,
sF0_fnc = least_upper_bound(sF0_fnc,multiply(a,identity)),
inference(forward_demodulation,[status(thm)],[f35,f415]) ).
fof(f427,plain,
sF0_fnc = least_upper_bound(sF0_fnc,a),
inference(forward_demodulation,[status(thm)],[f100,f426]) ).
fof(f615,plain,
multiply(sF0_fnc,inverse(b)) = least_upper_bound(sF0_fnc,a),
inference(paramodulation,[status(thm)],[f365,f269]) ).
fof(f618,plain,
multiply(sF1_fnc,inverse(a)) = least_upper_bound(sF1_fnc,b),
inference(paramodulation,[status(thm)],[f367,f269]) ).
fof(f630,plain,
! [X0] : multiply(X0,inverse(X0)) = least_upper_bound(X0,identity),
inference(paramodulation,[status(thm)],[f93,f269]) ).
fof(f650,plain,
a = least_upper_bound(sF0_fnc,a),
inference(forward_demodulation,[status(thm)],[f365,f615]) ).
fof(f651,plain,
a = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f427,f650]) ).
fof(f654,plain,
b = least_upper_bound(sF1_fnc,b),
inference(forward_demodulation,[status(thm)],[f367,f618]) ).
fof(f655,plain,
b = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f339,f654]) ).
fof(f668,plain,
! [X0] : identity = least_upper_bound(X0,identity),
inference(forward_demodulation,[status(thm)],[f93,f630]) ).
fof(f669,plain,
! [X0] : identity = X0,
inference(forward_demodulation,[status(thm)],[f133,f668]) ).
fof(f939,plain,
a = multiply(inverse(a),multiply(a,sF1_fnc)),
inference(backward_demodulation,[status(thm)],[f651,f82]) ).
fof(f940,plain,
b = multiply(inverse(a),a),
inference(backward_demodulation,[status(thm)],[f651,f89]) ).
fof(f947,plain,
a != sF1_fnc,
inference(backward_demodulation,[status(thm)],[f651,f37]) ).
fof(f954,plain,
a = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f77,f939]) ).
fof(f955,plain,
b = identity,
inference(forward_demodulation,[status(thm)],[f19,f940]) ).
fof(f987,plain,
a = b,
inference(forward_demodulation,[status(thm)],[f655,f954]) ).
fof(f988,plain,
a = identity,
inference(forward_demodulation,[status(thm)],[f987,f955]) ).
fof(f1004,plain,
! [X0] : a = X0,
inference(forward_demodulation,[status(thm)],[f988,f669]) ).
fof(f1005,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f947,f1004]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP192-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n007.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 20 20:03:35 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.17/0.46 % Refutation found
% 0.17/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.51 % Elapsed time: 0.067978 seconds
% 0.17/0.51 % CPU time: 0.108882 seconds
% 0.17/0.51 % Total memory used: 2.529 MB
% 0.17/0.51 % Net memory used: 2.453 MB
%------------------------------------------------------------------------------