%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP190-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 1.36s 0.59s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 57 unt; 3 def)
% Number of atoms : 57 ( 56 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 : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
least_upper_bound(a,b) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
file('/export/starexec/sandbox2/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(f22,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
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(f27,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
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,
least_upper_bound(a,b) = a,
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(f131,plain,
multiply(sF2_fnc,b) = identity,
inference(paramodulation,[status(thm)],[f36,f19]) ).
fof(f132,plain,
multiply(sF1_fnc,a) = identity,
inference(paramodulation,[status(thm)],[f35,f19]) ).
fof(f151,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f22,f28]) ).
fof(f159,plain,
! [X0] : multiply(sF2_fnc,greatest_lower_bound(X0,b)) = greatest_lower_bound(multiply(sF2_fnc,X0),identity),
inference(paramodulation,[status(thm)],[f131,f30]) ).
fof(f161,plain,
! [X0] : multiply(greatest_lower_bound(X0,sF1_fnc),a) = greatest_lower_bound(multiply(X0,a),identity),
inference(paramodulation,[status(thm)],[f132,f32]) ).
fof(f178,plain,
greatest_lower_bound(b,a) = b,
inference(paramodulation,[status(thm)],[f33,f151]) ).
fof(f180,plain,
! [X0,X1] : greatest_lower_bound(greatest_lower_bound(X0,X1),X0) = greatest_lower_bound(X0,X1),
inference(paramodulation,[status(thm)],[f27,f151]) ).
fof(f190,plain,
! [X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X0)) = greatest_lower_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f23,f180]) ).
fof(f194,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f204,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f18,f194]) ).
fof(f299,plain,
greatest_lower_bound(a,b) = b,
inference(paramodulation,[status(thm)],[f21,f178]) ).
fof(f601,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f204,f204]) ).
fof(f602,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f19,f204]) ).
fof(f736,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(paramodulation,[status(thm)],[f37,f190]) ).
fof(f2234,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = greatest_lower_bound(sF1_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f21,f736]) ).
fof(f2255,plain,
greatest_lower_bound(sF2_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f37,f2234]) ).
fof(f2269,plain,
sF0_fnc = greatest_lower_bound(sF2_fnc,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f2255,f736]) ).
fof(f2495,plain,
! [X0] : X0 = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f601,f602]) ).
fof(f2554,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(paramodulation,[status(thm)],[f601,f2495]) ).
fof(f2578,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f2495,f2554]) ).
fof(f5100,plain,
multiply(greatest_lower_bound(sF2_fnc,sF1_fnc),a) = multiply(sF2_fnc,greatest_lower_bound(a,b)),
inference(paramodulation,[status(thm)],[f159,f161]) ).
fof(f5135,plain,
multiply(sF0_fnc,a) = multiply(sF2_fnc,greatest_lower_bound(a,b)),
inference(forward_demodulation,[status(thm)],[f2269,f5100]) ).
fof(f5136,plain,
multiply(sF0_fnc,a) = multiply(sF2_fnc,b),
inference(forward_demodulation,[status(thm)],[f299,f5135]) ).
fof(f5137,plain,
multiply(sF0_fnc,a) = identity,
inference(forward_demodulation,[status(thm)],[f131,f5136]) ).
fof(f5175,plain,
a = multiply(inverse(sF0_fnc),identity),
inference(paramodulation,[status(thm)],[f5137,f204]) ).
fof(f5185,plain,
a = inverse(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f2495,f5175]) ).
fof(f5191,plain,
inverse(a) = sF0_fnc,
inference(paramodulation,[status(thm)],[f5185,f2578]) ).
fof(f5194,plain,
sF1_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f35,f5191]) ).
fof(f5195,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5194,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP190-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.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
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:05:57 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 1.36/0.59 % Refutation found
% 1.36/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.36/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.36/0.61 % Elapsed time: 0.248157 seconds
% 1.36/0.61 % CPU time: 1.836941 seconds
% 1.36/0.61 % Total memory used: 43.832 MB
% 1.36/0.61 % Net memory used: 43.126 MB
%------------------------------------------------------------------------------