%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP606-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:34:47 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 3
% Syntax : Number of formulae : 70 ( 70 unt; 0 def)
% Number of atoms : 70 ( 69 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 156 ( 156 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(X0,inverse(double_divide(inverse(X1),double_divide(X0,X2))))),X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(X0,multiply(double_divide(X0,X1),inverse(X2)))),X1) = X2,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f12,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(double_divide(X0,X1),inverse(X2)),X0),X1) = X2,
inference(forward_demodulation,[status(thm)],[f5,f11]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(X0,inverse(X1)),multiply(multiply(double_divide(X2,X3),inverse(X0)),X2)),X3) = X1,
inference(paramodulation,[status(thm)],[f12,f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(double_divide(X0,X1),multiply(X2,X3)),X0),X1) = double_divide(X3,X2),
inference(paramodulation,[status(thm)],[f5,f12]) ).
fof(f15,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(double_divide(X1,X0),inverse(X2)),X1)) = inverse(X2),
inference(paramodulation,[status(thm)],[f12,f5]) ).
fof(f26,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(X0,inverse(X1))) = X1,
inference(paramodulation,[status(thm)],[f15,f13]) ).
fof(f41,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),inverse(X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f26,f5]) ).
fof(f45,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,inverse(X1))),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f41,f26]) ).
fof(f50,plain,
! [X0,X1] : double_divide(inverse(inverse(X0)),inverse(X1)) = multiply(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f41,f45]) ).
fof(f60,plain,
! [X0,X1,X2] : double_divide(inverse(multiply(X0,X1)),inverse(X2)) = multiply(X2,inverse(double_divide(X1,X0))),
inference(paramodulation,[status(thm)],[f5,f50]) ).
fof(f67,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f68,f45]) ).
fof(f68,plain,
! [X0,X1,X2] : double_divide(inverse(multiply(X0,X1)),inverse(X2)) = multiply(X2,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f5,f60]) ).
fof(f70,plain,
! [X0,X1] : inverse(X0) = multiply(double_divide(inverse(X1),X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f15,f67]) ).
fof(f72,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X2,multiply(X1,X0))) = X2,
inference(paramodulation,[status(thm)],[f5,f67]) ).
fof(f88,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),X1),X1) = X0,
inference(paramodulation,[status(thm)],[f67,f72]) ).
fof(f100,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(X0,inverse(X1)),multiply(X2,inverse(X2))),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f88,f13]) ).
fof(f101,plain,
! [X0,X1] : double_divide(multiply(X0,inverse(X0)),inverse(X1)) = X1,
inference(paramodulation,[status(thm)],[f88,f12]) ).
fof(f102,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f88,f67]) ).
fof(f104,plain,
! [X0,X1] : double_divide(inverse(double_divide(inverse(X0),inverse(X1))),X0) = X1,
inference(paramodulation,[status(thm)],[f88,f26]) ).
fof(f106,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),X2) = double_divide(inverse(X2),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f88,f72]) ).
fof(f111,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),inverse(X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f5,f104]) ).
fof(f118,plain,
! [X0,X1,X2] : double_divide(multiply(X0,inverse(X0)),multiply(X1,X2)) = double_divide(X2,X1),
inference(paramodulation,[status(thm)],[f5,f101]) ).
fof(f125,plain,
! [X0,X1,X2] : multiply(X0,double_divide(X1,X2)) = double_divide(multiply(X2,X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f5,f102]) ).
fof(f127,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f102,f88]) ).
fof(f131,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f102,f5]) ).
fof(f132,plain,
! [X0,X1] : multiply(X0,double_divide(inverse(X1),X1)) = X0,
inference(backward_demodulation,[status(thm)],[f125,f101]) ).
fof(f138,plain,
! [X0,X1,X2] : multiply(X0,double_divide(multiply(X1,inverse(X1)),multiply(X0,inverse(X2)))) = X2,
inference(backward_demodulation,[status(thm)],[f125,f100]) ).
fof(f150,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,X1)),X1) = X0,
inference(backward_demodulation,[status(thm)],[f131,f111]) ).
fof(f155,plain,
! [X0,X1] : multiply(X0,double_divide(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f118,f138]) ).
fof(f159,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(inverse(X0),X1),X1),multiply(X2,X0)) = X2,
inference(paramodulation,[status(thm)],[f155,f72]) ).
fof(f162,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),X2) = double_divide(multiply(X2,X1),X0),
inference(paramodulation,[status(thm)],[f72,f14]) ).
fof(f170,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(double_divide(X0,X1),X2),X0),X1) = double_divide(double_divide(inverse(X2),X3),X3),
inference(paramodulation,[status(thm)],[f155,f14]) ).
fof(f176,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),multiply(double_divide(X1,X0),multiply(X2,X3))) = double_divide(X3,X2),
inference(backward_demodulation,[status(thm)],[f162,f14]) ).
fof(f185,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),multiply(double_divide(X1,X0),X2)) = double_divide(double_divide(inverse(X2),X3),X3),
inference(forward_demodulation,[status(thm)],[f162,f170]) ).
fof(f219,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(inverse(X0),X1),
inference(paramodulation,[status(thm)],[f155,f127]) ).
fof(f224,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),multiply(double_divide(X1,X0),X2)) = double_divide(inverse(X3),multiply(X3,X2)),
inference(paramodulation,[status(thm)],[f127,f176]) ).
fof(f229,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,X1)),X0) = X1,
inference(backward_demodulation,[status(thm)],[f219,f127]) ).
fof(f233,plain,
! [X0,X1] : inverse(X0) = double_divide(inverse(double_divide(inverse(X1),X1)),X0),
inference(backward_demodulation,[status(thm)],[f219,f70]) ).
fof(f265,plain,
! [X0,X1,X2] : double_divide(double_divide(inverse(X0),X0),multiply(X1,X2)) = double_divide(X2,X1),
inference(backward_demodulation,[status(thm)],[f219,f118]) ).
fof(f268,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),multiply(double_divide(X1,X0),X2)) = multiply(double_divide(X2,X3),X3),
inference(forward_demodulation,[status(thm)],[f106,f224]) ).
fof(f275,plain,
! [X0,X1] : inverse(X0) = double_divide(multiply(X1,inverse(X1)),X0),
inference(forward_demodulation,[status(thm)],[f5,f233]) ).
fof(f276,plain,
! [X0,X1] : inverse(X0) = double_divide(double_divide(inverse(X1),X1),X0),
inference(forward_demodulation,[status(thm)],[f219,f275]) ).
fof(f353,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X1) = X0,
inference(backward_demodulation,[status(thm)],[f355,f229]) ).
fof(f354,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(backward_demodulation,[status(thm)],[f355,f150]) ).
fof(f355,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f276,f265]) ).
fof(f359,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),multiply(double_divide(X1,X0),X2)) = inverse(X2),
inference(backward_demodulation,[status(thm)],[f353,f185]) ).
fof(f360,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(backward_demodulation,[status(thm)],[f353,f159]) ).
fof(f362,plain,
! [X0,X1] : inverse(X0) = multiply(double_divide(X0,X1),X1),
inference(backward_demodulation,[status(thm)],[f359,f268]) ).
fof(f365,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f362,f88]) ).
fof(f376,plain,
! [X0,X1] : multiply(inverse(X0),X1) = double_divide(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f365,f102]) ).
fof(f377,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f365,f102]) ).
fof(f380,plain,
multiply(double_divide(inverse(b2),b2),a2) != a2,
inference(backward_demodulation,[status(thm)],[f376,f6]) ).
fof(f383,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,X1)),X1) = X0,
inference(backward_demodulation,[status(thm)],[f376,f360]) ).
fof(f388,plain,
! [X0,X1] : multiply(X0,double_divide(X1,inverse(X1))) = X0,
inference(backward_demodulation,[status(thm)],[f390,f132]) ).
fof(f390,plain,
! [X0,X1] : double_divide(inverse(X0),X1) = double_divide(X1,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f219,f377]) ).
fof(f391,plain,
multiply(double_divide(b2,inverse(b2)),a2) != a2,
inference(forward_demodulation,[status(thm)],[f390,f380]) ).
fof(f397,plain,
! [X0,X1] : double_divide(X0,inverse(multiply(X1,X0))) = X1,
inference(forward_demodulation,[status(thm)],[f390,f383]) ).
fof(f399,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f355,f397]) ).
fof(f425,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f399,f354]) ).
fof(f466,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(inverse(X0),inverse(X1)),
inference(paramodulation,[status(thm)],[f102,f425]) ).
fof(f482,plain,
multiply(a2,double_divide(b2,inverse(b2))) != a2,
inference(backward_demodulation,[status(thm)],[f501,f391]) ).
fof(f501,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f102,f466]) ).
fof(f507,plain,
a2 != a2,
inference(forward_demodulation,[status(thm)],[f388,f482]) ).
fof(f508,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP606-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.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 20:18:04 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.37 % Refutation found
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.039830 seconds
% 0.12/0.40 % CPU time: 0.092491 seconds
% 0.12/0.40 % Total memory used: 4.602 MB
% 0.12/0.40 % Net memory used: 4.453 MB
%------------------------------------------------------------------------------