%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP594-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:34:45 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 3
% Syntax : Number of formulae : 90 ( 90 unt; 0 def)
% Number of atoms : 90 ( 89 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 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 : 267 ( 267 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B)))))) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(X2,X1)))))) = X2,
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] : multiply(inverse(double_divide(X0,inverse(double_divide(X1,X2)))),double_divide(X0,X2)) = X1,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f12,plain,
! [X0,X1,X2] : multiply(multiply(inverse(double_divide(X0,X1)),X2),double_divide(X2,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f5,f11]) ).
fof(f13,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),X2),double_divide(X2,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f14,plain,
! [X0,X1,X2] : multiply(X0,double_divide(double_divide(X1,X2),multiply(X2,X0))) = X1,
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(X1,multiply(multiply(X2,X0),X3))) = double_divide(X3,X2),
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : multiply(double_divide(double_divide(X0,X1),multiply(X1,X2)),double_divide(double_divide(X3,X2),X0)) = X3,
inference(paramodulation,[status(thm)],[f14,f14]) ).
fof(f18,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(double_divide(double_divide(X0,X1),multiply(X1,multiply(X2,X3))),X2)) = X3,
inference(paramodulation,[status(thm)],[f14,f13]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(X1,X2)) = double_divide(double_divide(X0,X3),multiply(X3,X2)),
inference(paramodulation,[status(thm)],[f14,f13]) ).
fof(f24,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,X1),double_divide(X1,double_divide(double_divide(X2,X3),multiply(X3,X4)))) = double_divide(double_divide(X0,X4),X2),
inference(paramodulation,[status(thm)],[f17,f13]) ).
fof(f25,plain,
! [X0,X1,X2] : X0 = double_divide(multiply(X1,double_divide(X0,multiply(X2,X1))),X2),
inference(paramodulation,[status(thm)],[f14,f15]) ).
fof(f34,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(double_divide(X0,X1),X2),double_divide(X2,multiply(X3,X4))) = double_divide(X4,multiply(multiply(X1,X3),X0)),
inference(paramodulation,[status(thm)],[f13,f15]) ).
fof(f47,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(X1,multiply(multiply(X2,X3),X0))) = double_divide(multiply(X3,X1),X2),
inference(paramodulation,[status(thm)],[f25,f25]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4] : X0 = double_divide(multiply(double_divide(double_divide(X1,X2),X3),double_divide(X0,X1)),double_divide(double_divide(X3,X4),multiply(X4,X2))),
inference(paramodulation,[status(thm)],[f17,f25]) ).
fof(f57,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,double_divide(X2,multiply(X0,X1)))) = inverse(X2),
inference(paramodulation,[status(thm)],[f25,f5]) ).
fof(f88,plain,
! [X0,X1,X2,X3] : multiply(inverse(X0),double_divide(multiply(X1,double_divide(X0,multiply(multiply(X2,X3),X1))),X2)) = X3,
inference(paramodulation,[status(thm)],[f57,f13]) ).
fof(f99,plain,
! [X0,X1,X2] : multiply(inverse(X0),double_divide(double_divide(multiply(X1,X0),X2),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f47,f88]) ).
fof(f100,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(double_divide(multiply(X2,double_divide(X1,X0)),X3),X3)) = X2,
inference(paramodulation,[status(thm)],[f5,f99]) ).
fof(f104,plain,
! [X0,X1,X2,X3] : multiply(inverse(double_divide(X0,X1)),double_divide(double_divide(X2,X3),X3)) = multiply(multiply(X1,X2),X0),
inference(paramodulation,[status(thm)],[f13,f99]) ).
fof(f109,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),multiply(X2,inverse(X1))) = double_divide(X0,X2),
inference(paramodulation,[status(thm)],[f99,f25]) ).
fof(f113,plain,
! [X0,X1,X2,X3] : X0 = double_divide(multiply(double_divide(double_divide(multiply(X1,X2),X3),X3),double_divide(X0,X1)),inverse(X2)),
inference(paramodulation,[status(thm)],[f99,f25]) ).
fof(f124,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(X1,double_divide(X2,X0))),X2) = X1,
inference(backward_demodulation,[status(thm)],[f125,f100]) ).
fof(f125,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(double_divide(X2,X3),X3)) = multiply(multiply(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f5,f104]) ).
fof(f142,plain,
! [X0,X1,X2,X3] : multiply(inverse(X0),double_divide(double_divide(X1,X2),X2)) = multiply(X3,multiply(X1,double_divide(X0,X3))),
inference(paramodulation,[status(thm)],[f124,f99]) ).
fof(f147,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,X1),double_divide(X1,multiply(X2,X3))) = double_divide(X3,multiply(X4,multiply(X2,double_divide(X0,X4)))),
inference(paramodulation,[status(thm)],[f124,f15]) ).
fof(f154,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,inverse(double_divide(X2,X3)))) = double_divide(multiply(multiply(X3,X0),X2),X1),
inference(paramodulation,[status(thm)],[f13,f109]) ).
fof(f158,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,inverse(double_divide(double_divide(X0,X2),multiply(X2,X3))))) = double_divide(X3,X1),
inference(paramodulation,[status(thm)],[f14,f109]) ).
fof(f159,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),X2) = double_divide(X0,multiply(X3,multiply(X2,double_divide(inverse(X1),X3)))),
inference(paramodulation,[status(thm)],[f124,f109]) ).
fof(f165,plain,
! [X0,X1,X2] : multiply(X0,X1) = double_divide(multiply(inverse(X1),double_divide(X0,X2)),X2),
inference(paramodulation,[status(thm)],[f109,f25]) ).
fof(f176,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,multiply(X2,X3))) = double_divide(multiply(multiply(X2,X0),X3),X1),
inference(forward_demodulation,[status(thm)],[f5,f154]) ).
fof(f178,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,multiply(multiply(X2,X3),double_divide(X0,X2)))) = double_divide(X3,X1),
inference(forward_demodulation,[status(thm)],[f5,f158]) ).
fof(f182,plain,
! [X0,X1,X2] : multiply(double_divide(multiply(X0,X1),X2),X1) = double_divide(X0,X2),
inference(paramodulation,[status(thm)],[f99,f165]) ).
fof(f183,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),X2) = double_divide(X0,multiply(X1,inverse(X2))),
inference(paramodulation,[status(thm)],[f14,f165]) ).
fof(f184,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(X1,X2)) = double_divide(multiply(multiply(X2,X1),double_divide(X0,X3)),X3),
inference(paramodulation,[status(thm)],[f5,f165]) ).
fof(f206,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),X2) = multiply(inverse(X1),double_divide(X0,X2)),
inference(backward_demodulation,[status(thm)],[f211,f159]) ).
fof(f210,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(X1,multiply(X2,X3))) = multiply(X0,double_divide(X3,X2)),
inference(backward_demodulation,[status(thm)],[f211,f147]) ).
fof(f211,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(X1,X2)) = double_divide(X1,multiply(X3,multiply(X2,double_divide(X0,X3)))),
inference(forward_demodulation,[status(thm)],[f176,f184]) ).
fof(f222,plain,
! [X0,X1,X2] : double_divide(multiply(double_divide(multiply(X0,X1),X2),X1),X2) = X0,
inference(backward_demodulation,[status(thm)],[f206,f99]) ).
fof(f225,plain,
! [X0,X1,X2,X3] : double_divide(multiply(double_divide(X0,X1),X2),X1) = multiply(X3,multiply(X0,double_divide(X2,X3))),
inference(backward_demodulation,[status(thm)],[f206,f142]) ).
fof(f234,plain,
! [X0,X1,X2] : multiply(X0,double_divide(X1,multiply(X2,X0))) = double_divide(X1,X2),
inference(backward_demodulation,[status(thm)],[f210,f15]) ).
fof(f235,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),double_divide(X2,X3)) = double_divide(X2,multiply(multiply(X1,X3),X0)),
inference(backward_demodulation,[status(thm)],[f210,f34]) ).
fof(f245,plain,
! [X0,X1,X2] : X0 = double_divide(multiply(multiply(X1,X2),double_divide(X0,X1)),inverse(X2)),
inference(backward_demodulation,[status(thm)],[f250,f113]) ).
fof(f249,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X2),X1),
inference(backward_demodulation,[status(thm)],[f250,f125]) ).
fof(f250,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f182,f222]) ).
fof(f258,plain,
! [X0,X1] : multiply(X0,double_divide(X1,X0)) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f234,f57]) ).
fof(f260,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,X2)) = double_divide(multiply(X2,X0),X1),
inference(backward_demodulation,[status(thm)],[f234,f47]) ).
fof(f284,plain,
! [X0,X1,X2,X3,X4] : X0 = double_divide(double_divide(X0,multiply(multiply(X1,X2),double_divide(X2,X3))),double_divide(double_divide(X1,X4),multiply(X4,X3))),
inference(backward_demodulation,[status(thm)],[f235,f48]) ).
fof(f294,plain,
! [X0,X1,X2] : X0 = double_divide(X1,multiply(inverse(X1),multiply(X2,double_divide(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f176,f245]) ).
fof(f302,plain,
! [X0,X1] : X0 = double_divide(X1,multiply(inverse(X1),inverse(X0))),
inference(backward_demodulation,[status(thm)],[f258,f294]) ).
fof(f311,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,double_divide(X2,X1))) = multiply(X3,multiply(X2,double_divide(X0,X3))),
inference(backward_demodulation,[status(thm)],[f260,f225]) ).
fof(f349,plain,
! [X0,X1] : X0 = multiply(double_divide(X1,inverse(X1)),X0),
inference(forward_demodulation,[status(thm)],[f183,f302]) ).
fof(f359,plain,
! [X0,X1,X2] : multiply(X0,double_divide(X1,X2)) = double_divide(X1,double_divide(X0,inverse(X2))),
inference(backward_demodulation,[status(thm)],[f363,f211]) ).
fof(f363,plain,
! [X0,X1,X2] : double_divide(X0,inverse(X1)) = multiply(X2,multiply(X1,double_divide(X0,X2))),
inference(forward_demodulation,[status(thm)],[f258,f311]) ).
fof(f388,plain,
! [X0,X1,X2] : multiply(X0,X1) = double_divide(double_divide(X1,multiply(X2,X0)),X2),
inference(paramodulation,[status(thm)],[f250,f234]) ).
fof(f409,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(double_divide(double_divide(X0,double_divide(X1,inverse(X1))),multiply(X2,X3)),X2)) = X3,
inference(paramodulation,[status(thm)],[f349,f18]) ).
fof(f425,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,double_divide(X0,double_divide(X2,inverse(X2))))) = X1,
inference(forward_demodulation,[status(thm)],[f388,f409]) ).
fof(f426,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,multiply(X2,double_divide(X0,X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f359,f425]) ).
fof(f427,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f258,f426]) ).
fof(f446,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(double_divide(double_divide(X0,X1),multiply(X1,X2)),X3)) = multiply(X2,inverse(X3)),
inference(paramodulation,[status(thm)],[f427,f18]) ).
fof(f448,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),double_divide(X1,X2)) = multiply(X0,inverse(X2)),
inference(paramodulation,[status(thm)],[f427,f13]) ).
fof(f465,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(double_divide(double_divide(X1,X2),multiply(X2,X3)))) = double_divide(double_divide(X0,X3),X1),
inference(backward_demodulation,[status(thm)],[f448,f24]) ).
fof(f467,plain,
! [X0,X1,X2,X3] : X0 = double_divide(double_divide(X0,multiply(X1,inverse(X2))),double_divide(double_divide(X1,X3),multiply(X3,X2))),
inference(backward_demodulation,[status(thm)],[f448,f284]) ).
fof(f472,plain,
! [X0,X1,X2] : multiply(X0,inverse(X1)) = double_divide(double_divide(X0,X2),multiply(X2,X1)),
inference(backward_demodulation,[status(thm)],[f448,f19]) ).
fof(f476,plain,
! [X0,X1,X2] : double_divide(X0,double_divide(double_divide(X1,X2),X0)) = double_divide(X2,X1),
inference(backward_demodulation,[status(thm)],[f477,f178]) ).
fof(f477,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(X1,X2),double_divide(X3,X1))) = double_divide(double_divide(X0,X2),X3),
inference(forward_demodulation,[status(thm)],[f5,f465]) ).
fof(f480,plain,
! [X0,X1,X2,X3] : X0 = double_divide(multiply(double_divide(X0,X1),X2),double_divide(double_divide(X1,X3),multiply(X3,X2))),
inference(forward_demodulation,[status(thm)],[f183,f467]) ).
fof(f481,plain,
! [X0,X1,X2,X3] : X0 = double_divide(X1,multiply(double_divide(double_divide(X2,X3),multiply(X3,X1)),double_divide(X0,X2))),
inference(forward_demodulation,[status(thm)],[f260,f480]) ).
fof(f482,plain,
! [X0,X1,X2,X3] : X0 = double_divide(X1,double_divide(X0,multiply(multiply(multiply(X2,X1),X3),double_divide(X3,X2)))),
inference(forward_demodulation,[status(thm)],[f235,f481]) ).
fof(f483,plain,
! [X0,X1] : X0 = double_divide(X1,double_divide(X0,X1)),
inference(forward_demodulation,[status(thm)],[f13,f482]) ).
fof(f494,plain,
! [X0,X1,X2] : multiply(X0,double_divide(multiply(X0,inverse(X1)),X2)) = multiply(X1,inverse(X2)),
inference(backward_demodulation,[status(thm)],[f472,f446]) ).
fof(f508,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f483,f476]) ).
fof(f517,plain,
! [X0,X1,X2] : multiply(X0,double_divide(inverse(X1),multiply(X2,X0))) = multiply(X1,inverse(X2)),
inference(forward_demodulation,[status(thm)],[f260,f494]) ).
fof(f518,plain,
! [X0,X1] : multiply(X0,double_divide(inverse(X1),X0)) = X1,
inference(backward_demodulation,[status(thm)],[f535,f427]) ).
fof(f535,plain,
! [X0,X1] : double_divide(inverse(X0),X1) = multiply(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f234,f517]) ).
fof(f545,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f258,f518]) ).
fof(f562,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f5,f545]) ).
fof(f588,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f508,f5]) ).
fof(f597,plain,
multiply(multiply(b2,inverse(b2)),a2) != a2,
inference(backward_demodulation,[status(thm)],[f607,f6]) ).
fof(f607,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f5,f588]) ).
fof(f612,plain,
multiply(multiply(b2,a2),inverse(b2)) != a2,
inference(forward_demodulation,[status(thm)],[f249,f597]) ).
fof(f613,plain,
double_divide(inverse(multiply(b2,a2)),b2) != a2,
inference(forward_demodulation,[status(thm)],[f535,f612]) ).
fof(f614,plain,
double_divide(b2,inverse(multiply(b2,a2))) != a2,
inference(forward_demodulation,[status(thm)],[f508,f613]) ).
fof(f615,plain,
double_divide(b2,double_divide(a2,b2)) != a2,
inference(forward_demodulation,[status(thm)],[f562,f614]) ).
fof(f616,plain,
a2 != a2,
inference(forward_demodulation,[status(thm)],[f483,f615]) ).
fof(f617,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f616]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP594-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:12:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.42 % Elapsed time: 0.044909 seconds
% 0.15/0.42 % CPU time: 0.197243 seconds
% 0.15/0.42 % Total memory used: 9.439 MB
% 0.15/0.42 % Net memory used: 9.040 MB
%------------------------------------------------------------------------------