%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP191-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.16s 0.62s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 52 unt; 3 def)
% Number of atoms : 52 ( 51 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 : 9 ( 9 usr; 6 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(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(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(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(a,b) = b,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
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 = greatest_lower_bound(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f38,plain,
sF0_fnc != sF1_fnc,
inference(definition_folding,[],[f34,f37,f36,f35]) ).
fof(f50,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f26,f23]) ).
fof(f64,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f21,f50]) ).
fof(f93,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f37,f64]) ).
fof(f126,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = greatest_lower_bound(sF1_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f21,f93]) ).
fof(f133,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f37,f126]) ).
fof(f140,plain,
sF0_fnc = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f133,f93]) ).
fof(f187,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,identity),X1) = greatest_lower_bound(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f18,f32]) ).
fof(f193,plain,
multiply(sF2_fnc,b) = identity,
inference(paramodulation,[status(thm)],[f36,f19]) ).
fof(f194,plain,
multiply(sF1_fnc,a) = identity,
inference(paramodulation,[status(thm)],[f35,f19]) ).
fof(f245,plain,
! [X0] : multiply(sF2_fnc,greatest_lower_bound(X0,b)) = greatest_lower_bound(multiply(sF2_fnc,X0),identity),
inference(paramodulation,[status(thm)],[f193,f30]) ).
fof(f257,plain,
! [X0] : multiply(identity,X0) = multiply(sF1_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f194,f20]) ).
fof(f259,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f267,plain,
! [X0] : X0 = multiply(sF1_fnc,multiply(a,X0)),
inference(forward_demodulation,[status(thm)],[f18,f257]) ).
fof(f269,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f18,f259]) ).
fof(f606,plain,
! [X0] : multiply(a,X0) = multiply(inverse(sF1_fnc),X0),
inference(paramodulation,[status(thm)],[f267,f269]) ).
fof(f610,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f269,f269]) ).
fof(f611,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f19,f269]) ).
fof(f1467,plain,
multiply(a,sF1_fnc) = identity,
inference(paramodulation,[status(thm)],[f19,f606]) ).
fof(f1873,plain,
! [X0] : X0 = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f610,f611]) ).
fof(f2543,plain,
multiply(sF2_fnc,b) = greatest_lower_bound(multiply(sF2_fnc,a),identity),
inference(paramodulation,[status(thm)],[f33,f245]) ).
fof(f2563,plain,
identity = greatest_lower_bound(multiply(sF2_fnc,a),identity),
inference(forward_demodulation,[status(thm)],[f193,f2543]) ).
fof(f3082,plain,
! [X0] : multiply(identity,X0) = greatest_lower_bound(multiply(multiply(sF2_fnc,a),X0),X0),
inference(paramodulation,[status(thm)],[f2563,f187]) ).
fof(f3158,plain,
! [X0] : X0 = greatest_lower_bound(multiply(multiply(sF2_fnc,a),X0),X0),
inference(forward_demodulation,[status(thm)],[f18,f3082]) ).
fof(f3159,plain,
! [X0] : X0 = greatest_lower_bound(multiply(sF2_fnc,multiply(a,X0)),X0),
inference(forward_demodulation,[status(thm)],[f20,f3158]) ).
fof(f3288,plain,
sF1_fnc = greatest_lower_bound(multiply(sF2_fnc,identity),sF1_fnc),
inference(paramodulation,[status(thm)],[f1467,f3159]) ).
fof(f3330,plain,
sF1_fnc = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f1873,f3288]) ).
fof(f3331,plain,
sF1_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f140,f3330]) ).
fof(f3332,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3331,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP191-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.47 % Computer : n018.cluster.edu
% 0.16/0.47 % Model : x86_64 x86_64
% 0.16/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.47 % Memory : 8046.5625MB
% 0.16/0.47 % OS : Linux 6.8.0-71-generic
% 0.16/0.47 % CPULimit : 300
% 0.16/0.47 % WCLimit : 300
% 0.16/0.47 % DateTime : Sun Sep 20 20:07:43 UTC 2026
% 0.16/0.47 % CPUTime :
% 0.16/0.49 % Drodi V4.1.1
% 0.16/0.62 % Refutation found
% 0.16/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.67 % Elapsed time: 0.172967 seconds
% 0.21/0.67 % CPU time: 0.940619 seconds
% 0.21/0.67 % Total memory used: 19.680 MB
% 0.21/0.67 % Net memory used: 19.353 MB
%------------------------------------------------------------------------------