%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP490-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:34:31 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 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 : 6 ( 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 : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C,
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(inverse(a1),a1) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(double_divide(double_divide(X0,X1),identity),double_divide(X2,X1)))) = 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(inverse(a1),a1) != identity,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(X1,X0),double_divide(X2,X1)))) = X2,
inference(backward_demodulation,[status(thm)],[f7,f6]) ).
fof(f15,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f16,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f15]) ).
fof(f19,plain,
inverse(identity) != identity,
inference(backward_demodulation,[status(thm)],[f16,f10]) ).
fof(f23,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(inverse(X1),X0),identity))) = X1,
inference(paramodulation,[status(thm)],[f9,f14]) ).
fof(f26,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,inverse(multiply(inverse(X1),X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f23]) ).
fof(f66,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,inverse(inverse(identity)))) = X0,
inference(paramodulation,[status(thm)],[f16,f26]) ).
fof(f74,plain,
double_divide(identity,double_divide(identity,inverse(inverse(identity)))) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f66]) ).
fof(f75,plain,
double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = identity,
inference(paramodulation,[status(thm)],[f8,f66]) ).
fof(f89,plain,
double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))),
inference(paramodulation,[status(thm)],[f74,f66]) ).
fof(f97,plain,
double_divide(inverse(identity),identity) = identity,
inference(backward_demodulation,[status(thm)],[f102,f75]) ).
fof(f102,plain,
identity = double_divide(identity,inverse(inverse(identity))),
inference(forward_demodulation,[status(thm)],[f75,f89]) ).
fof(f111,plain,
identity = double_divide(identity,identity),
inference(backward_demodulation,[status(thm)],[f112,f102]) ).
fof(f112,plain,
inverse(inverse(identity)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f97]) ).
fof(f122,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f8,f111]) ).
fof(f123,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f122,f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP490-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:16:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.40 % Elapsed time: 0.022271 seconds
% 0.11/0.40 % CPU time: 0.033652 seconds
% 0.11/0.40 % Total memory used: 1.054 MB
% 0.11/0.40 % Net memory used: 1.027 MB
%------------------------------------------------------------------------------