%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP569-1 : 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 12:34:41 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.36s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 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 : 61 ( 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(C,identity))),double_divide(identity,identity)) = B,
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(inverse(a1),a1) != identity,
file('/export/starexec/sandbox/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(X2,identity))),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(inverse(a1),a1) != identity,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),inverse(identity)) = X1,
inference(backward_demodulation,[status(thm)],[f8,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,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f14]) ).
fof(f17,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f15]) ).
fof(f20,plain,
inverse(identity) != identity,
inference(backward_demodulation,[status(thm)],[f17,f10]) ).
fof(f21,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2))),double_divide(double_divide(X3,X1),inverse(inverse(identity)))),inverse(identity)) = X3,
inference(paramodulation,[status(thm)],[f16,f16]) ).
fof(f22,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,identity),inverse(inverse(X0)))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f16]) ).
fof(f23,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,inverse(X0)),inverse(identity))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f8,f16]) ).
fof(f26,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),inverse(inverse(X0)))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f22]) ).
fof(f59,plain,
! [X0] : double_divide(double_divide(X0,identity),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f26]) ).
fof(f66,plain,
! [X0] : double_divide(inverse(X0),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f59]) ).
fof(f132,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(inverse(identity),double_divide(X0,X1)),inverse(X1))),double_divide(X2,inverse(inverse(identity)))),inverse(identity)) = inverse(X2),
inference(paramodulation,[status(thm)],[f66,f21]) ).
fof(f135,plain,
! [X0,X1,X2,X3,X4] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(inverse(identity),double_divide(X0,X1)),inverse(X1))),double_divide(X2,inverse(inverse(identity)))),inverse(identity)) = double_divide(X3,double_divide(double_divide(X2,double_divide(X3,X4)),inverse(X4))),
inference(paramodulation,[status(thm)],[f16,f21]) ).
fof(f138,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(identity,double_divide(X0,X1)),inverse(X1))),double_divide(inverse(X2),inverse(inverse(identity)))),inverse(identity)) = X2,
inference(paramodulation,[status(thm)],[f8,f21]) ).
fof(f156,plain,
! [X0] : double_divide(double_divide(inverse(inverse(identity)),double_divide(X0,inverse(inverse(identity)))),inverse(identity)) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f159,f132]) ).
fof(f159,plain,
! [X0,X1,X2] : inverse(X0) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X2))),
inference(forward_demodulation,[status(thm)],[f132,f135]) ).
fof(f162,plain,
! [X0] : double_divide(double_divide(inverse(identity),double_divide(inverse(X0),inverse(inverse(identity)))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f159,f138]) ).
fof(f171,plain,
! [X0] : double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)) = inverse(X0),
inference(paramodulation,[status(thm)],[f66,f23]) ).
fof(f172,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)) = double_divide(X1,double_divide(double_divide(X0,inverse(X1)),inverse(identity))),
inference(paramodulation,[status(thm)],[f23,f23]) ).
fof(f181,plain,
! [X0,X1] : inverse(X0) = double_divide(X1,double_divide(double_divide(X0,inverse(X1)),inverse(identity))),
inference(forward_demodulation,[status(thm)],[f171,f172]) ).
fof(f206,plain,
! [X0] : inverse(inverse(X0)) = double_divide(identity,double_divide(X0,inverse(identity))),
inference(paramodulation,[status(thm)],[f66,f181]) ).
fof(f221,plain,
inverse(inverse(identity)) = double_divide(identity,identity),
inference(paramodulation,[status(thm)],[f9,f206]) ).
fof(f228,plain,
! [X0] : double_divide(double_divide(inverse(inverse(identity)),double_divide(X0,inverse(identity))),inverse(identity)) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f235,f156]) ).
fof(f229,plain,
! [X0] : double_divide(double_divide(inverse(identity),double_divide(inverse(X0),inverse(identity))),inverse(identity)) = X0,
inference(backward_demodulation,[status(thm)],[f235,f162]) ).
fof(f235,plain,
inverse(inverse(identity)) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f8,f221]) ).
fof(f240,plain,
! [X0] : double_divide(double_divide(inverse(identity),double_divide(X0,inverse(identity))),inverse(identity)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f235,f228]) ).
fof(f246,plain,
identity = inverse(identity),
inference(backward_demodulation,[status(thm)],[f250,f235]) ).
fof(f250,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f240,f229]) ).
fof(f268,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f246,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP569-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:16:42 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.36 % Refutation found
% 0.09/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.030810 seconds
% 0.13/0.39 % CPU time: 0.057809 seconds
% 0.13/0.39 % Total memory used: 2.954 MB
% 0.13/0.39 % Net memory used: 2.911 MB
%------------------------------------------------------------------------------