%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP570-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 44 ( 44 unt; 0 def)
% Number of atoms : 44 ( 43 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 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 : 72 ( 72 !; 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(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(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(identity,a2) != a2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(X2,identity))),
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),double_divide(double_divide(X3,X1),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = X3,
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),double_divide(double_divide(X3,X1),multiply(identity,identity))),double_divide(identity,identity)) = X3,
inference(forward_demodulation,[status(thm)],[f7,f17]) ).
fof(f64,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(X1,double_divide(identity,identity))),
inference(paramodulation,[status(thm)],[f16,f6]) ).
fof(f88,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = double_divide(identity,double_divide(X0,double_divide(identity,identity))),
inference(forward_demodulation,[status(thm)],[f6,f64]) ).
fof(f106,plain,
! [X0,X1,X2] : double_divide(identity,double_divide(double_divide(X0,double_divide(identity,identity)),double_divide(identity,identity))) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(X2,identity))),
inference(backward_demodulation,[status(thm)],[f88,f16]) ).
fof(f669,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,identity),double_divide(inverse(X0),identity))),double_divide(identity,identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f675,plain,
! [X0,X1,X2] : double_divide(identity,double_divide(double_divide(X0,double_divide(identity,identity)),inverse(identity))) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(X2,identity))),
inference(backward_demodulation,[status(thm)],[f8,f106]) ).
fof(f676,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),double_divide(double_divide(X3,X1),multiply(identity,identity))),inverse(identity)) = X3,
inference(backward_demodulation,[status(thm)],[f8,f22]) ).
fof(f690,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f691,plain,
! [X0,X1,X2] : double_divide(identity,double_divide(double_divide(X0,inverse(identity)),inverse(identity))) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(X2,identity))),
inference(forward_demodulation,[status(thm)],[f8,f675]) ).
fof(f692,plain,
! [X0,X1,X2] : double_divide(identity,double_divide(double_divide(X0,inverse(identity)),inverse(identity))) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X2))),
inference(forward_demodulation,[status(thm)],[f8,f691]) ).
fof(f693,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),multiply(identity,identity))),inverse(identity)) = X3,
inference(forward_demodulation,[status(thm)],[f8,f676]) ).
fof(f706,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f690]) ).
fof(f708,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f690,f9]) ).
fof(f713,plain,
! [X0] : identity = double_divide(inverse(X0),multiply(identity,X0)),
inference(paramodulation,[status(thm)],[f706,f9]) ).
fof(f805,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),double_divide(inverse(X0),identity))),double_divide(identity,identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f669]) ).
fof(f806,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),inverse(inverse(X0)))),double_divide(identity,identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f805]) ).
fof(f807,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),multiply(identity,X0))),double_divide(identity,identity)) = X1,
inference(forward_demodulation,[status(thm)],[f706,f806]) ).
fof(f808,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),multiply(identity,X0))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f807]) ).
fof(f809,plain,
! [X0] : double_divide(double_divide(X0,identity),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f713,f808]) ).
fof(f819,plain,
! [X0] : double_divide(inverse(X0),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f809]) ).
fof(f947,plain,
! [X0,X1] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,inverse(identity)),inverse(identity))),double_divide(double_divide(X1,X0),multiply(identity,identity))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f692,f693]) ).
fof(f954,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,inverse(identity)),inverse(identity))),identity),inverse(identity)) = identity,
inference(paramodulation,[status(thm)],[f708,f947]) ).
fof(f975,plain,
double_divide(inverse(double_divide(identity,double_divide(double_divide(identity,inverse(identity)),inverse(identity)))),inverse(identity)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f954]) ).
fof(f976,plain,
double_divide(identity,double_divide(double_divide(identity,inverse(identity)),inverse(identity))) = identity,
inference(forward_demodulation,[status(thm)],[f819,f975]) ).
fof(f977,plain,
double_divide(identity,double_divide(identity,inverse(identity))) = identity,
inference(forward_demodulation,[status(thm)],[f9,f976]) ).
fof(f978,plain,
double_divide(identity,identity) = identity,
inference(forward_demodulation,[status(thm)],[f9,f977]) ).
fof(f979,plain,
inverse(identity) = identity,
inference(forward_demodulation,[status(thm)],[f8,f978]) ).
fof(f1071,plain,
! [X0] : double_divide(inverse(X0),identity) = X0,
inference(backward_demodulation,[status(thm)],[f979,f819]) ).
fof(f1101,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f1071]) ).
fof(f1102,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f706,f1101]) ).
fof(f1113,plain,
a2 != a2,
inference(backward_demodulation,[status(thm)],[f1102,f10]) ).
fof(f1118,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP570-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n016.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 20:21:36 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.033445 seconds
% 0.12/0.39 % CPU time: 0.097859 seconds
% 0.12/0.39 % Total memory used: 5.343 MB
% 0.12/0.39 % Net memory used: 5.226 MB
%------------------------------------------------------------------------------