%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP568-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:34:41 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 5
% Syntax : Number of formulae : 57 ( 57 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 77 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(identity,identity)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = double_divide(X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : identity = double_divide(X0,inverse(X0)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
multiply(a,b) != multiply(b,a),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1] : multiply(identity,double_divide(X0,X1)) = double_divide(multiply(X1,X0),identity),
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = double_divide(identity,identity),
inference(paramodulation,[status(thm)],[f9,f7]) ).
fof(f23,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,identity),double_divide(identity,inverse(X0)))),double_divide(identity,identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f24,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,inverse(identity))),identity)),double_divide(identity,identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f27,plain,
! [X0,X1] : double_divide(double_divide(X0,multiply(double_divide(X0,inverse(identity)),X1)),double_divide(identity,identity)) = X1,
inference(forward_demodulation,[status(thm)],[f7,f24]) ).
fof(f28,plain,
! [X0] : double_divide(double_divide(identity,multiply(identity,X0)),double_divide(identity,identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f27]) ).
fof(f33,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(multiply(X0,X1),identity)),double_divide(identity,identity)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f14,f28]) ).
fof(f52,plain,
! [X0,X1] : double_divide(double_divide(multiply(X0,X1),double_divide(X1,X0)),double_divide(identity,identity)) = identity,
inference(paramodulation,[status(thm)],[f33,f6]) ).
fof(f65,plain,
! [X0] : double_divide(double_divide(double_divide(identity,identity),double_divide(X0,inverse(X0))),double_divide(identity,identity)) = identity,
inference(paramodulation,[status(thm)],[f18,f52]) ).
fof(f80,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = identity,
inference(forward_demodulation,[status(thm)],[f9,f65]) ).
fof(f81,plain,
double_divide(multiply(identity,identity),double_divide(identity,identity)) = identity,
inference(forward_demodulation,[status(thm)],[f7,f80]) ).
fof(f88,plain,
double_divide(identity,double_divide(identity,identity)) = identity,
inference(paramodulation,[status(thm)],[f81,f52]) ).
fof(f95,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)) = identity,
inference(paramodulation,[status(thm)],[f88,f6]) ).
fof(f101,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(forward_demodulation,[status(thm)],[f88,f95]) ).
fof(f113,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramodulation,[status(thm)],[f101,f6]) ).
fof(f118,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(forward_demodulation,[status(thm)],[f88,f113]) ).
fof(f119,plain,
identity = double_divide(identity,identity),
inference(forward_demodulation,[status(thm)],[f101,f118]) ).
fof(f130,plain,
! [X0] : double_divide(double_divide(identity,multiply(identity,X0)),identity) = X0,
inference(backward_demodulation,[status(thm)],[f119,f28]) ).
fof(f132,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),identity) = X1,
inference(backward_demodulation,[status(thm)],[f119,f6]) ).
fof(f133,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(backward_demodulation,[status(thm)],[f119,f18]) ).
fof(f142,plain,
! [X0] : multiply(multiply(identity,X0),identity) = X0,
inference(forward_demodulation,[status(thm)],[f7,f130]) ).
fof(f144,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f7,f132]) ).
fof(f149,plain,
! [X0,X1] : multiply(double_divide(double_divide(X0,double_divide(X1,identity)),identity),X1) = X0,
inference(paramodulation,[status(thm)],[f119,f144]) ).
fof(f155,plain,
! [X0,X1] : multiply(multiply(double_divide(X0,identity),X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f7,f149]) ).
fof(f175,plain,
identity = inverse(identity),
inference(backward_demodulation,[status(thm)],[f8,f119]) ).
fof(f177,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f195,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f177]) ).
fof(f208,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f8,f155]) ).
fof(f209,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f133,f208]) ).
fof(f217,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f209,f195]) ).
fof(f218,plain,
! [X0] : multiply(X0,identity) = X0,
inference(backward_demodulation,[status(thm)],[f209,f142]) ).
fof(f229,plain,
! [X0] : identity = double_divide(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f217,f9]) ).
fof(f323,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),double_divide(identity,inverse(X0)))),double_divide(identity,identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f23]) ).
fof(f324,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),double_divide(identity,inverse(X0)))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f323]) ).
fof(f325,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),double_divide(identity,inverse(X0)))),identity) = X1,
inference(forward_demodulation,[status(thm)],[f175,f324]) ).
fof(f326,plain,
! [X0,X1] : inverse(double_divide(X0,double_divide(inverse(X1),double_divide(identity,inverse(X0))))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f325]) ).
fof(f327,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),double_divide(identity,inverse(X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f177,f326]) ).
fof(f329,plain,
! [X0] : multiply(identity,X0) = double_divide(identity,inverse(X0)),
inference(paramodulation,[status(thm)],[f229,f327]) ).
fof(f342,plain,
! [X0] : X0 = double_divide(identity,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f209,f329]) ).
fof(f352,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),X1),X1) = X0,
inference(backward_demodulation,[status(thm)],[f342,f327]) ).
fof(f363,plain,
! [X0,X1] : multiply(double_divide(double_divide(X0,X1),double_divide(identity,inverse(X1))),identity) = X0,
inference(paramodulation,[status(thm)],[f342,f144]) ).
fof(f367,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),double_divide(identity,inverse(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f218,f363]) ).
fof(f368,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f342,f367]) ).
fof(f468,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f217,f352]) ).
fof(f535,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f368,f468]) ).
fof(f547,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f177,f535]) ).
fof(f689,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f10,f547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP568-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.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 20:20:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.42/1.61 % Elapsed time: 1.031149 seconds
% 1.42/1.61 % CPU time: 0.078880 seconds
% 1.42/1.61 % Total memory used: 3.575 MB
% 1.42/1.61 % Net memory used: 3.396 MB
%------------------------------------------------------------------------------