%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP191-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 3.31s 0.83s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 55 ( 55 unt; 3 def)
% Number of atoms : 55 ( 54 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 60 ( 60 !; 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(f7,axiom,
! [X,Y,Z] : least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : least_upper_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(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,
greatest_lower_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
least_upper_bound(inverse(a),inverse(b)) != inverse(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(f22,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0] : least_upper_bound(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
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,
greatest_lower_bound(a,b) = b,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
least_upper_bound(inverse(a),inverse(b)) != inverse(b),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f35,definition,
sF1_fnc = inverse(a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f36,definition,
sF2_fnc = inverse(b),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f37,definition,
sF0_fnc = least_upper_bound(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f38,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f34,f37,f36,f35]) ).
fof(f50,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X0,X1)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f25,f24]) ).
fof(f69,plain,
least_upper_bound(a,b) = a,
inference(paramodulation,[status(thm)],[f33,f27]) ).
fof(f91,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f22,f50]) ).
fof(f146,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f18,f31]) ).
fof(f151,plain,
multiply(sF2_fnc,b) = identity,
inference(paramodulation,[status(thm)],[f36,f19]) ).
fof(f156,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(f222,plain,
! [X0] : multiply(identity,X0) = multiply(sF2_fnc,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f151,f20]) ).
fof(f223,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f232,plain,
! [X0] : X0 = multiply(sF2_fnc,multiply(b,X0)),
inference(forward_demodulation,[status(thm)],[f18,f222]) ).
fof(f233,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f18,f223]) ).
fof(f417,plain,
least_upper_bound(sF2_fnc,sF0_fnc) = least_upper_bound(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f37,f91]) ).
fof(f705,plain,
! [X0] : multiply(b,X0) = multiply(inverse(sF2_fnc),X0),
inference(paramodulation,[status(thm)],[f232,f233]) ).
fof(f707,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f233,f233]) ).
fof(f708,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f19,f233]) ).
fof(f1404,plain,
least_upper_bound(sF2_fnc,sF0_fnc) = least_upper_bound(sF1_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f22,f417]) ).
fof(f1420,plain,
least_upper_bound(sF2_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f37,f1404]) ).
fof(f1430,plain,
sF0_fnc = least_upper_bound(sF2_fnc,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f1420,f417]) ).
fof(f1740,plain,
multiply(b,sF2_fnc) = identity,
inference(paramodulation,[status(thm)],[f19,f705]) ).
fof(f1934,plain,
! [X0] : X0 = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f707,f708]) ).
fof(f7414,plain,
multiply(inverse(a),a) = least_upper_bound(identity,multiply(inverse(a),b)),
inference(paramodulation,[status(thm)],[f69,f156]) ).
fof(f7501,plain,
identity = least_upper_bound(identity,multiply(inverse(a),b)),
inference(forward_demodulation,[status(thm)],[f19,f7414]) ).
fof(f7502,plain,
identity = least_upper_bound(identity,multiply(sF1_fnc,b)),
inference(forward_demodulation,[status(thm)],[f35,f7501]) ).
fof(f7553,plain,
! [X0] : multiply(identity,X0) = least_upper_bound(X0,multiply(multiply(sF1_fnc,b),X0)),
inference(paramodulation,[status(thm)],[f7502,f146]) ).
fof(f7577,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(multiply(sF1_fnc,b),X0)),
inference(forward_demodulation,[status(thm)],[f18,f7553]) ).
fof(f7578,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(sF1_fnc,multiply(b,X0))),
inference(forward_demodulation,[status(thm)],[f20,f7577]) ).
fof(f7592,plain,
sF2_fnc = least_upper_bound(sF2_fnc,multiply(sF1_fnc,identity)),
inference(paramodulation,[status(thm)],[f1740,f7578]) ).
fof(f7643,plain,
sF2_fnc = least_upper_bound(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f1934,f7592]) ).
fof(f7644,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f1430,f7643]) ).
fof(f7645,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f7644,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP191-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:06:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 3.31/0.83 % Refutation found
% 3.31/0.83 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.31/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.31/0.86 % Elapsed time: 0.482322 seconds
% 3.31/0.86 % CPU time: 3.629917 seconds
% 3.31/0.86 % Total memory used: 59.494 MB
% 3.31/0.86 % Net memory used: 58.404 MB
%------------------------------------------------------------------------------