%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP572-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 12:34:42 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 5
% Syntax : Number of formulae : 80 ( 80 unt; 0 def)
% Number of atoms : 80 ( 79 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 145 ( 145 !; 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/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(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(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(f20,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(f21,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(f23,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(f26,plain,
! [X0,X1,X2] : multiply(double_divide(identity,identity),double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity)))) = double_divide(X1,identity),
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f27,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,f21]) ).
fof(f283,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,f27]) ).
fof(f288,plain,
! [X0,X1,X2] : multiply(inverse(identity),double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity)))) = double_divide(X1,identity),
inference(backward_demodulation,[status(thm)],[f8,f26]) ).
fof(f290,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(f291,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(backward_demodulation,[status(thm)],[f8,f18]) ).
fof(f292,plain,
! [X0,X1] : multiply(identity,double_divide(X0,X1)) = inverse(multiply(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f14]) ).
fof(f293,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f298,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,f283]) ).
fof(f305,plain,
! [X0,X1,X2] : multiply(inverse(identity),double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2)))) = double_divide(X1,identity),
inference(forward_demodulation,[status(thm)],[f8,f288]) ).
fof(f306,plain,
! [X0,X1,X2] : multiply(inverse(identity),double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2)))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f8,f305]) ).
fof(f307,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,f290]) ).
fof(f308,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f293]) ).
fof(f315,plain,
! [X0] : identity = double_divide(inverse(X0),multiply(identity,X0)),
inference(paramodulation,[status(thm)],[f308,f9]) ).
fof(f389,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,f307]) ).
fof(f404,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),inverse(inverse(X0)))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f389]) ).
fof(f405,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),multiply(identity,X0))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f308,f404]) ).
fof(f406,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,inverse(identity))),double_divide(identity,identity)) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(X2,identity))),
inference(forward_demodulation,[status(thm)],[f8,f20]) ).
fof(f407,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,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,f406]) ).
fof(f408,plain,
! [X0] : double_divide(double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)),inverse(identity)) = X0,
inference(backward_demodulation,[status(thm)],[f409,f307]) ).
fof(f409,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,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,f407]) ).
fof(f473,plain,
! [X0,X1] : double_divide(double_divide(double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)),double_divide(double_divide(X1,X0),multiply(identity,identity))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f409,f298]) ).
fof(f521,plain,
! [X0] : double_divide(double_divide(X0,identity),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f315,f405]) ).
fof(f534,plain,
! [X0] : double_divide(inverse(X0),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f521]) ).
fof(f537,plain,
! [X0] : double_divide(multiply(identity,X0),inverse(identity)) = inverse(X0),
inference(paramodulation,[status(thm)],[f308,f534]) ).
fof(f546,plain,
! [X0] : multiply(inverse(identity),inverse(X0)) = inverse(X0),
inference(paramodulation,[status(thm)],[f534,f293]) ).
fof(f555,plain,
! [X0,X1] : multiply(inverse(identity),multiply(X0,X1)) = inverse(double_divide(X1,X0)),
inference(paramodulation,[status(thm)],[f293,f546]) ).
fof(f560,plain,
! [X0,X1] : multiply(inverse(identity),multiply(X0,X1)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f293,f555]) ).
fof(f580,plain,
! [X0] : double_divide(double_divide(double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),inverse(identity)),double_divide(inverse(X0),multiply(identity,identity))),inverse(identity)) = multiply(identity,X0),
inference(paramodulation,[status(thm)],[f537,f473]) ).
fof(f587,plain,
! [X0] : double_divide(double_divide(double_divide(double_divide(identity,identity),inverse(identity)),double_divide(inverse(X0),multiply(identity,identity))),inverse(identity)) = multiply(identity,X0),
inference(forward_demodulation,[status(thm)],[f534,f580]) ).
fof(f588,plain,
! [X0] : double_divide(double_divide(double_divide(inverse(identity),inverse(identity)),double_divide(inverse(X0),multiply(identity,identity))),inverse(identity)) = multiply(identity,X0),
inference(forward_demodulation,[status(thm)],[f8,f587]) ).
fof(f589,plain,
! [X0] : double_divide(double_divide(identity,double_divide(inverse(X0),multiply(identity,identity))),inverse(identity)) = multiply(identity,X0),
inference(forward_demodulation,[status(thm)],[f534,f588]) ).
fof(f590,plain,
! [X0] : X0 = multiply(identity,X0),
inference(forward_demodulation,[status(thm)],[f405,f589]) ).
fof(f598,plain,
! [X0,X1] : double_divide(X0,X1) = inverse(multiply(X1,X0)),
inference(backward_demodulation,[status(thm)],[f590,f292]) ).
fof(f606,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f590,f308]) ).
fof(f607,plain,
! [X0] : multiply(inverse(identity),X0) = multiply(identity,X0),
inference(paramodulation,[status(thm)],[f590,f560]) ).
fof(f616,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(forward_demodulation,[status(thm)],[f590,f607]) ).
fof(f629,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f291,f616]) ).
fof(f635,plain,
! [X0] : double_divide(double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)),identity) = X0,
inference(backward_demodulation,[status(thm)],[f629,f408]) ).
fof(f642,plain,
! [X0] : inverse(double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f635]) ).
fof(f643,plain,
! [X0] : multiply(inverse(identity),double_divide(identity,double_divide(X0,inverse(identity)))) = X0,
inference(forward_demodulation,[status(thm)],[f293,f642]) ).
fof(f644,plain,
! [X0] : multiply(identity,double_divide(identity,double_divide(X0,inverse(identity)))) = X0,
inference(forward_demodulation,[status(thm)],[f629,f643]) ).
fof(f645,plain,
! [X0] : double_divide(identity,double_divide(X0,inverse(identity))) = X0,
inference(forward_demodulation,[status(thm)],[f590,f644]) ).
fof(f646,plain,
! [X0] : double_divide(identity,double_divide(X0,identity)) = X0,
inference(forward_demodulation,[status(thm)],[f629,f645]) ).
fof(f647,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f646]) ).
fof(f655,plain,
! [X0] : double_divide(identity,X0) = inverse(X0),
inference(paramodulation,[status(thm)],[f606,f647]) ).
fof(f746,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,f23]) ).
fof(f747,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,f746]) ).
fof(f748,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),X0)),double_divide(identity,identity)) = X1,
inference(forward_demodulation,[status(thm)],[f606,f747]) ).
fof(f749,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),X0)),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f655,f748]) ).
fof(f750,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),X0)),identity) = X1,
inference(forward_demodulation,[status(thm)],[f629,f749]) ).
fof(f751,plain,
! [X0,X1] : inverse(double_divide(X0,double_divide(inverse(X1),X0))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f750]) ).
fof(f752,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f293,f751]) ).
fof(f759,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f606,f752]) ).
fof(f770,plain,
! [X0,X1,X2] : multiply(identity,double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2)))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f629,f306]) ).
fof(f771,plain,
! [X0,X1,X2] : double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f590,f770]) ).
fof(f911,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f759,f598]) ).
fof(f920,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f606,f911]) ).
fof(f927,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f920,f920]) ).
fof(f962,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f927,f771]) ).
fof(f978,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f606,f962]) ).
fof(f993,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X1) = X0,
inference(paramodulation,[status(thm)],[f927,f978]) ).
fof(f1040,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f993,f759]) ).
fof(f1052,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f293,f1040]) ).
fof(f1054,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f10,f1052]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP572-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:19:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.43/1.61 % Elapsed time: 1.027824 seconds
% 1.43/1.61 % CPU time: 0.077712 seconds
% 1.43/1.61 % Total memory used: 3.547 MB
% 1.43/1.61 % Net memory used: 3.356 MB
%------------------------------------------------------------------------------