%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP582-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 12:34:43 PM UTC 2026
% Result : Unsatisfiable 0.12s 10.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 83 ( 83 unt; 0 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 119 ( 119 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),double_divide(identity,identity)) = X2,
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(identity,a2) != a2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),inverse(identity)) = X2,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f14,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0))))),double_divide(X3,X2))),inverse(identity)) = X3,
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f40,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f14]) ).
fof(f41,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),double_divide(X1,inverse(X0)))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f8,f13]) ).
fof(f42,plain,
inverse(inverse(a2)) != a2,
inference(backward_demodulation,[status(thm)],[f40,f10]) ).
fof(f53,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f14]) ).
fof(f54,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X0),double_divide(X1,identity))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f13]) ).
fof(f62,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f54]) ).
fof(f76,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X0)),inverse(identity)) = double_divide(identity,double_divide(double_divide(identity,X1),double_divide(X0,inverse(X1)))),
inference(paramodulation,[status(thm)],[f41,f41]) ).
fof(f77,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X0)),inverse(identity)) = double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1))))),double_divide(X0,X3))),
inference(paramodulation,[status(thm)],[f15,f41]) ).
fof(f79,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X0)),inverse(identity)) = double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X0,double_divide(X2,X1)))),
inference(paramodulation,[status(thm)],[f13,f41]) ).
fof(f80,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),identity)),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f41]) ).
fof(f89,plain,
! [X0] : double_divide(double_divide(double_divide(identity,double_divide(inverse(identity),X0)),inverse(identity)),inverse(identity)) = X0,
inference(backward_demodulation,[status(thm)],[f93,f41]) ).
fof(f93,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(inverse(identity),X0)),inverse(identity)) = double_divide(identity,double_divide(double_divide(identity,X1),double_divide(X0,inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f8,f76]) ).
fof(f101,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(inverse(identity),X0)),inverse(identity)) = double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X3,double_divide(X2,X1))))),double_divide(X0,X3))),
inference(forward_demodulation,[status(thm)],[f8,f77]) ).
fof(f120,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(inverse(identity),X0)),inverse(identity)) = double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(inverse(identity),X1)),inverse(identity))),double_divide(X0,X1))),
inference(backward_demodulation,[status(thm)],[f121,f101]) ).
fof(f121,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(inverse(identity),X0)),inverse(identity)) = double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X0,double_divide(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f8,f79]) ).
fof(f122,plain,
! [X0] : double_divide(double_divide(identity,inverse(double_divide(identity,X0))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f80]) ).
fof(f123,plain,
! [X0] : double_divide(double_divide(identity,multiply(X0,identity)),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f14,f122]) ).
fof(f166,plain,
double_divide(double_divide(identity,inverse(identity)),inverse(identity)) = inverse(identity),
inference(paramodulation,[status(thm)],[f53,f123]) ).
fof(f171,plain,
double_divide(identity,inverse(identity)) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f9,f166]) ).
fof(f172,plain,
! [X0] : double_divide(double_divide(identity,multiply(X0,identity)),identity) = X0,
inference(backward_demodulation,[status(thm)],[f202,f123]) ).
fof(f175,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(inverse(identity),X0)),inverse(identity)) = double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(inverse(identity),X1)),identity)),double_divide(X0,X1))),
inference(backward_demodulation,[status(thm)],[f202,f120]) ).
fof(f184,plain,
! [X0] : double_divide(double_divide(double_divide(identity,double_divide(inverse(identity),X0)),inverse(identity)),identity) = X0,
inference(backward_demodulation,[status(thm)],[f202,f89]) ).
fof(f194,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1))),identity) = X1,
inference(backward_demodulation,[status(thm)],[f202,f62]) ).
fof(f202,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f9,f171]) ).
fof(f217,plain,
! [X0] : inverse(double_divide(identity,multiply(X0,identity))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f172]) ).
fof(f219,plain,
! [X0] : multiply(multiply(X0,identity),identity) = X0,
inference(forward_demodulation,[status(thm)],[f14,f217]) ).
fof(f222,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),inverse(identity)) = double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(inverse(identity),X1)),identity)),double_divide(X0,X1))),
inference(forward_demodulation,[status(thm)],[f202,f175]) ).
fof(f223,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,X0)),identity) = double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(inverse(identity),X1)),identity)),double_divide(X0,X1))),
inference(forward_demodulation,[status(thm)],[f202,f222]) ).
fof(f224,plain,
! [X0,X1] : inverse(double_divide(identity,double_divide(identity,X0))) = double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(inverse(identity),X1)),identity)),double_divide(X0,X1))),
inference(forward_demodulation,[status(thm)],[f8,f223]) ).
fof(f225,plain,
! [X0,X1] : multiply(double_divide(identity,X0),identity) = double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(inverse(identity),X1)),identity)),double_divide(X0,X1))),
inference(forward_demodulation,[status(thm)],[f14,f224]) ).
fof(f226,plain,
! [X0,X1] : multiply(double_divide(identity,X0),identity) = double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(inverse(identity),X1)),identity)),double_divide(X0,X1))),
inference(forward_demodulation,[status(thm)],[f202,f225]) ).
fof(f227,plain,
! [X0,X1] : multiply(double_divide(identity,X0),identity) = double_divide(identity,double_divide(double_divide(identity,inverse(double_divide(identity,double_divide(inverse(identity),X1)))),double_divide(X0,X1))),
inference(forward_demodulation,[status(thm)],[f8,f226]) ).
fof(f228,plain,
! [X0,X1] : multiply(double_divide(identity,X0),identity) = double_divide(identity,double_divide(double_divide(identity,multiply(double_divide(inverse(identity),X1),identity)),double_divide(X0,X1))),
inference(forward_demodulation,[status(thm)],[f14,f227]) ).
fof(f229,plain,
! [X0,X1] : multiply(double_divide(identity,X0),identity) = double_divide(identity,double_divide(double_divide(identity,multiply(double_divide(identity,X1),identity)),double_divide(X0,X1))),
inference(forward_demodulation,[status(thm)],[f202,f228]) ).
fof(f306,plain,
! [X0] : inverse(double_divide(double_divide(identity,double_divide(inverse(identity),X0)),inverse(identity))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f184]) ).
fof(f307,plain,
! [X0] : multiply(inverse(identity),double_divide(identity,double_divide(inverse(identity),X0))) = X0,
inference(forward_demodulation,[status(thm)],[f14,f306]) ).
fof(f308,plain,
! [X0] : multiply(identity,double_divide(identity,double_divide(inverse(identity),X0))) = X0,
inference(forward_demodulation,[status(thm)],[f202,f307]) ).
fof(f309,plain,
! [X0] : inverse(inverse(double_divide(identity,double_divide(inverse(identity),X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f40,f308]) ).
fof(f310,plain,
! [X0] : inverse(multiply(double_divide(inverse(identity),X0),identity)) = X0,
inference(forward_demodulation,[status(thm)],[f14,f309]) ).
fof(f315,plain,
! [X0] : inverse(multiply(double_divide(identity,X0),identity)) = X0,
inference(forward_demodulation,[status(thm)],[f202,f310]) ).
fof(f368,plain,
! [X0,X1] : inverse(double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f194]) ).
fof(f369,plain,
! [X0,X1] : multiply(double_divide(double_divide(identity,X0),inverse(X1)),inverse(X0)) = X1,
inference(forward_demodulation,[status(thm)],[f14,f368]) ).
fof(f411,plain,
! [X0] : multiply(identity,inverse(X0)) = double_divide(identity,X0),
inference(paramodulation,[status(thm)],[f9,f369]) ).
fof(f414,plain,
! [X0,X1] : multiply(double_divide(double_divide(identity,X0),X1),inverse(X0)) = multiply(double_divide(identity,X1),identity),
inference(paramodulation,[status(thm)],[f315,f369]) ).
fof(f419,plain,
! [X0] : inverse(inverse(inverse(X0))) = double_divide(identity,X0),
inference(forward_demodulation,[status(thm)],[f40,f411]) ).
fof(f435,plain,
! [X0] : inverse(double_divide(identity,X0)) = double_divide(identity,inverse(X0)),
inference(paramodulation,[status(thm)],[f419,f419]) ).
fof(f436,plain,
! [X0] : inverse(inverse(double_divide(identity,X0))) = double_divide(identity,inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f419,f419]) ).
fof(f438,plain,
! [X0] : inverse(inverse(X0)) = double_divide(identity,multiply(double_divide(identity,X0),identity)),
inference(paramodulation,[status(thm)],[f315,f419]) ).
fof(f439,plain,
! [X0,X1] : inverse(inverse(multiply(X0,X1))) = double_divide(identity,double_divide(X1,X0)),
inference(paramodulation,[status(thm)],[f14,f419]) ).
fof(f442,plain,
! [X0] : multiply(X0,identity) = double_divide(identity,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f14,f435]) ).
fof(f443,plain,
! [X0] : inverse(multiply(X0,identity)) = double_divide(identity,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f14,f436]) ).
fof(f444,plain,
! [X0] : inverse(multiply(X0,identity)) = multiply(inverse(X0),identity),
inference(forward_demodulation,[status(thm)],[f442,f443]) ).
fof(f449,plain,
! [X0,X1] : multiply(double_divide(identity,X0),identity) = double_divide(identity,double_divide(inverse(inverse(X1)),double_divide(X0,X1))),
inference(backward_demodulation,[status(thm)],[f438,f229]) ).
fof(f454,plain,
! [X0,X1] : multiply(double_divide(identity,X0),identity) = inverse(inverse(multiply(double_divide(X0,X1),inverse(inverse(X1))))),
inference(forward_demodulation,[status(thm)],[f439,f449]) ).
fof(f548,plain,
! [X0] : multiply(double_divide(identity,double_divide(identity,inverse(X0))),identity) = inverse(inverse(multiply(double_divide(identity,X0),identity))),
inference(paramodulation,[status(thm)],[f414,f454]) ).
fof(f565,plain,
! [X0] : multiply(inverse(inverse(multiply(inverse(X0),identity))),identity) = inverse(inverse(multiply(double_divide(identity,X0),identity))),
inference(forward_demodulation,[status(thm)],[f439,f548]) ).
fof(f566,plain,
! [X0] : inverse(multiply(inverse(multiply(inverse(X0),identity)),identity)) = inverse(inverse(multiply(double_divide(identity,X0),identity))),
inference(forward_demodulation,[status(thm)],[f444,f565]) ).
fof(f567,plain,
! [X0] : inverse(inverse(multiply(multiply(inverse(X0),identity),identity))) = inverse(inverse(multiply(double_divide(identity,X0),identity))),
inference(forward_demodulation,[status(thm)],[f444,f566]) ).
fof(f568,plain,
! [X0] : inverse(inverse(inverse(X0))) = inverse(inverse(multiply(double_divide(identity,X0),identity))),
inference(forward_demodulation,[status(thm)],[f219,f567]) ).
fof(f569,plain,
! [X0] : double_divide(identity,X0) = inverse(inverse(multiply(double_divide(identity,X0),identity))),
inference(forward_demodulation,[status(thm)],[f419,f568]) ).
fof(f574,plain,
! [X0] : inverse(multiply(inverse(X0),identity)) = X0,
inference(backward_demodulation,[status(thm)],[f588,f315]) ).
fof(f576,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f588,f442]) ).
fof(f588,plain,
! [X0] : double_divide(identity,X0) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f315,f569]) ).
fof(f672,plain,
! [X0] : inverse(inverse(multiply(X0,identity))) = X0,
inference(forward_demodulation,[status(thm)],[f444,f574]) ).
fof(f680,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(backward_demodulation,[status(thm)],[f576,f672]) ).
fof(f732,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f419,f680]) ).
fof(f733,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f442,f732]) ).
fof(f734,plain,
a2 != a2,
inference(backward_demodulation,[status(thm)],[f740,f42]) ).
fof(f740,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f576,f733]) ).
fof(f783,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP582-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n006.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Sun Sep 20 20:17:08 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.38 % Drodi V4.1.1
% 0.12/10.41 % Refutation found
% 0.12/10.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/10.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/10.44 % Elapsed time: 0.067163 seconds
% 0.12/10.44 % CPU time: 0.257713 seconds
% 0.12/10.44 % Total memory used: 36.720 MB
% 0.12/10.44 % Net memory used: 36.509 MB
%------------------------------------------------------------------------------