%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP077-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:32:27 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 5
% Syntax : Number of formulae : 112 ( 105 unt; 0 def)
% Number of atoms : 124 ( 123 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 21 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 206 ( 206 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : double_divide(X,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X,identity),double_divide(Y,Z))),Y),identity)) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = double_divide(double_divide(Y,X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : inverse(X) = double_divide(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : identity = double_divide(X,inverse(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,X2))),X1),identity)) = X2,
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(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,X2))))) = X2,
inference(backward_demodulation,[status(thm)],[f7,f6]) ).
fof(f12,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f13,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(identity,double_divide(inverse(X0),double_divide(X1,X2))))) = X2,
inference(forward_demodulation,[status(thm)],[f8,f11]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,double_divide(identity,double_divide(inverse(X0),X2)))) = multiply(X3,double_divide(identity,double_divide(inverse(X1),double_divide(X3,X2)))),
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f15,plain,
! [X0,X1] : double_divide(X0,multiply(X1,double_divide(identity,double_divide(inverse(X0),identity)))) = inverse(X1),
inference(paramodulation,[status(thm)],[f9,f13]) ).
fof(f17,plain,
! [X0,X1] : double_divide(X0,multiply(X1,double_divide(identity,inverse(inverse(X0))))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f8,f15]) ).
fof(f19,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f12]) ).
fof(f20,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f22,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f12,f9]) ).
fof(f23,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f19,f10]) ).
fof(f24,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f20,f23]) ).
fof(f25,plain,
! [X0,X1] : multiply(multiply(X0,X1),double_divide(X1,X0)) = inverse(identity),
inference(paramodulation,[status(thm)],[f12,f19]) ).
fof(f26,plain,
! [X0,X1] : double_divide(X0,inverse(inverse(double_divide(identity,double_divide(inverse(X0),double_divide(identity,X1)))))) = X1,
inference(paramodulation,[status(thm)],[f20,f13]) ).
fof(f27,plain,
! [X0,X1] : double_divide(X0,inverse(multiply(double_divide(inverse(X0),double_divide(identity,X1)),identity))) = X1,
inference(forward_demodulation,[status(thm)],[f12,f26]) ).
fof(f63,plain,
! [X0,X1,X2] : double_divide(X0,inverse(inverse(double_divide(identity,double_divide(inverse(X0),X1))))) = multiply(X2,double_divide(identity,double_divide(inverse(identity),double_divide(X2,X1)))),
inference(paramodulation,[status(thm)],[f20,f14]) ).
fof(f73,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,double_divide(identity,double_divide(inverse(X0),multiply(X2,X3))))) = multiply(double_divide(X3,X2),double_divide(identity,double_divide(inverse(X1),identity))),
inference(paramodulation,[status(thm)],[f22,f14]) ).
fof(f76,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(identity,double_divide(inverse(X0),inverse(X2))))) = multiply(X2,double_divide(identity,double_divide(inverse(X1),identity))),
inference(paramodulation,[status(thm)],[f9,f14]) ).
fof(f86,plain,
! [X0,X1,X2] : double_divide(X0,inverse(multiply(double_divide(inverse(X0),X1),identity))) = multiply(X2,double_divide(identity,double_divide(inverse(identity),double_divide(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f12,f63]) ).
fof(f93,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,double_divide(identity,double_divide(inverse(X0),multiply(X2,X3))))) = multiply(double_divide(X3,X2),double_divide(identity,inverse(inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f8,f73]) ).
fof(f96,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(identity,double_divide(inverse(X0),inverse(X2))))) = multiply(X2,double_divide(identity,inverse(inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f8,f76]) ).
fof(f100,plain,
! [X0] : double_divide(X0,inverse(identity)) = inverse(multiply(inverse(inverse(X0)),identity)),
inference(paramodulation,[status(thm)],[f25,f17]) ).
fof(f101,plain,
! [X0] : double_divide(X0,inverse(inverse(double_divide(identity,inverse(inverse(X0)))))) = inverse(identity),
inference(paramodulation,[status(thm)],[f20,f17]) ).
fof(f104,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,double_divide(identity,inverse(X2)))) = multiply(X3,double_divide(identity,double_divide(inverse(X1),double_divide(X3,multiply(X2,double_divide(identity,inverse(inverse(inverse(X0))))))))),
inference(paramodulation,[status(thm)],[f17,f14]) ).
fof(f110,plain,
! [X0] : double_divide(X0,inverse(multiply(inverse(inverse(X0)),identity))) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f12,f101]) ).
fof(f111,plain,
! [X0] : double_divide(X0,double_divide(X0,inverse(identity))) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f100,f110]) ).
fof(f117,plain,
! [X0,X1] : double_divide(X0,multiply(X1,double_divide(identity,double_divide(inverse(X0),inverse(identity))))) = multiply(inverse(X1),double_divide(identity,inverse(identity))),
inference(paramodulation,[status(thm)],[f111,f14]) ).
fof(f125,plain,
! [X0] : multiply(identity,double_divide(identity,inverse(inverse(X0)))) = multiply(inverse(X0),double_divide(identity,inverse(identity))),
inference(forward_demodulation,[status(thm)],[f96,f117]) ).
fof(f126,plain,
! [X0] : inverse(inverse(double_divide(identity,inverse(inverse(X0))))) = multiply(inverse(X0),double_divide(identity,inverse(identity))),
inference(forward_demodulation,[status(thm)],[f20,f125]) ).
fof(f127,plain,
! [X0] : inverse(multiply(inverse(inverse(X0)),identity)) = multiply(inverse(X0),double_divide(identity,inverse(identity))),
inference(forward_demodulation,[status(thm)],[f12,f126]) ).
fof(f128,plain,
! [X0] : double_divide(X0,inverse(identity)) = multiply(inverse(X0),double_divide(identity,inverse(identity))),
inference(forward_demodulation,[status(thm)],[f100,f127]) ).
fof(f132,plain,
! [X0] : double_divide(X0,inverse(identity)) = multiply(inverse(X0),identity),
inference(forward_demodulation,[status(thm)],[f9,f128]) ).
fof(f149,plain,
identity = multiply(inverse(identity),identity),
inference(paramodulation,[status(thm)],[f9,f132]) ).
fof(f150,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(identity,multiply(inverse(inverse(X0)),identity)))) = multiply(X2,double_divide(identity,double_divide(inverse(X1),double_divide(X2,inverse(identity))))),
inference(paramodulation,[status(thm)],[f132,f14]) ).
fof(f152,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(identity,double_divide(inverse(X0),inverse(identity))))) = multiply(X2,double_divide(identity,double_divide(inverse(X1),multiply(inverse(X2),identity)))),
inference(paramodulation,[status(thm)],[f132,f14]) ).
fof(f155,plain,
! [X0] : multiply(inverse(identity),X0) = inverse(multiply(inverse(X0),identity)),
inference(paramodulation,[status(thm)],[f132,f12]) ).
fof(f157,plain,
! [X0] : double_divide(X0,identity) = multiply(inverse(X0),identity),
inference(backward_demodulation,[status(thm)],[f167,f132]) ).
fof(f158,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(backward_demodulation,[status(thm)],[f167,f24]) ).
fof(f166,plain,
! [X0,X1,X2] : double_divide(X0,inverse(multiply(double_divide(inverse(X0),X1),identity))) = multiply(X2,double_divide(identity,double_divide(identity,double_divide(X2,X1)))),
inference(backward_demodulation,[status(thm)],[f167,f86]) ).
fof(f167,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f19,f149]) ).
fof(f168,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(identity,multiply(inverse(inverse(X0)),identity)))) = multiply(X2,double_divide(identity,double_divide(inverse(X1),multiply(inverse(X2),identity)))),
inference(forward_demodulation,[status(thm)],[f132,f150]) ).
fof(f170,plain,
! [X0,X1] : multiply(identity,double_divide(identity,inverse(inverse(X0)))) = multiply(X1,double_divide(identity,double_divide(inverse(X0),multiply(inverse(X1),identity)))),
inference(forward_demodulation,[status(thm)],[f96,f152]) ).
fof(f171,plain,
! [X0,X1] : inverse(inverse(double_divide(identity,inverse(inverse(X0))))) = multiply(X1,double_divide(identity,double_divide(inverse(X0),multiply(inverse(X1),identity)))),
inference(forward_demodulation,[status(thm)],[f20,f170]) ).
fof(f172,plain,
! [X0,X1] : double_divide(X0,multiply(X1,double_divide(identity,multiply(inverse(inverse(X0)),identity)))) = inverse(multiply(inverse(inverse(X1)),identity)),
inference(backward_demodulation,[status(thm)],[f173,f168]) ).
fof(f173,plain,
! [X0,X1] : inverse(multiply(inverse(inverse(X0)),identity)) = multiply(X1,double_divide(identity,double_divide(inverse(X0),multiply(inverse(X1),identity)))),
inference(forward_demodulation,[status(thm)],[f12,f171]) ).
fof(f179,plain,
! [X0] : multiply(identity,X0) = inverse(multiply(inverse(X0),identity)),
inference(forward_demodulation,[status(thm)],[f167,f155]) ).
fof(f181,plain,
! [X0] : inverse(inverse(X0)) = inverse(multiply(inverse(X0),identity)),
inference(forward_demodulation,[status(thm)],[f20,f179]) ).
fof(f191,plain,
! [X0] : inverse(X0) = multiply(inverse(X0),identity),
inference(forward_demodulation,[status(thm)],[f8,f157]) ).
fof(f192,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2 ),
inference(trivial_equality_resolution,[status(thm)],[f158]) ).
fof(f200,plain,
! [X0,X1] : double_divide(X0,multiply(X1,double_divide(identity,inverse(inverse(X0))))) = inverse(multiply(inverse(inverse(X1)),identity)),
inference(forward_demodulation,[status(thm)],[f191,f172]) ).
fof(f201,plain,
! [X0] : inverse(X0) = inverse(multiply(inverse(inverse(X0)),identity)),
inference(forward_demodulation,[status(thm)],[f17,f200]) ).
fof(f202,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,double_divide(identity,inverse(X2)))) = multiply(X3,double_divide(identity,double_divide(inverse(X1),double_divide(X3,multiply(X2,double_divide(identity,inverse(X0))))))),
inference(backward_demodulation,[status(thm)],[f203,f104]) ).
fof(f203,plain,
! [X0] : inverse(X0) = inverse(inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f181,f201]) ).
fof(f210,plain,
! [X0] : double_divide(identity,multiply(X0,double_divide(identity,inverse(identity)))) = inverse(X0),
inference(paramodulation,[status(thm)],[f167,f17]) ).
fof(f212,plain,
! [X0,X1,X2] : double_divide(identity,multiply(X0,double_divide(identity,double_divide(identity,X1)))) = multiply(X2,double_divide(identity,double_divide(inverse(X0),double_divide(X2,X1)))),
inference(paramodulation,[status(thm)],[f167,f14]) ).
fof(f215,plain,
! [X0] : double_divide(identity,multiply(X0,identity)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f9,f210]) ).
fof(f218,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(identity,double_divide(inverse(X0),X2)))) = double_divide(identity,multiply(X1,double_divide(identity,double_divide(identity,X2)))),
inference(backward_demodulation,[status(thm)],[f212,f14]) ).
fof(f219,plain,
! [X0,X1] : double_divide(X0,double_divide(identity,multiply(X0,double_divide(identity,double_divide(identity,X1))))) = X1,
inference(backward_demodulation,[status(thm)],[f212,f13]) ).
fof(f221,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(identity,inverse(X2)))) = double_divide(identity,multiply(X1,double_divide(identity,double_divide(identity,multiply(X2,double_divide(identity,inverse(X0))))))),
inference(backward_demodulation,[status(thm)],[f212,f202]) ).
fof(f232,plain,
! [X0,X1,X2] : double_divide(identity,multiply(X0,double_divide(identity,double_divide(identity,multiply(X1,X2))))) = multiply(double_divide(X2,X1),double_divide(identity,inverse(inverse(X0)))),
inference(backward_demodulation,[status(thm)],[f218,f93]) ).
fof(f243,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(identity,inverse(X2)))) = multiply(double_divide(double_divide(identity,inverse(X0)),X2),double_divide(identity,inverse(inverse(X1)))),
inference(backward_demodulation,[status(thm)],[f232,f221]) ).
fof(f246,plain,
! [X0,X1] : inverse(double_divide(X0,X1)) = multiply(multiply(X1,X0),identity),
inference(paramodulation,[status(thm)],[f12,f191]) ).
fof(f252,plain,
! [X0,X1] : multiply(X0,X1) = multiply(multiply(X0,X1),identity),
inference(forward_demodulation,[status(thm)],[f12,f246]) ).
fof(f268,plain,
! [X0] : double_divide(identity,inverse(X0)) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f191,f215]) ).
fof(f271,plain,
! [X0] : multiply(multiply(X0,identity),identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f215,f12]) ).
fof(f272,plain,
! [X0,X1] : double_divide(X0,multiply(X1,inverse(inverse(inverse(X0))))) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f268,f17]) ).
fof(f274,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(identity,inverse(X2)))) = multiply(double_divide(double_divide(identity,inverse(X0)),X2),inverse(inverse(inverse(X1)))),
inference(backward_demodulation,[status(thm)],[f268,f243]) ).
fof(f288,plain,
! [X0,X1] : double_divide(X0,inverse(inverse(inverse(double_divide(inverse(X0),double_divide(identity,X1)))))) = X1,
inference(backward_demodulation,[status(thm)],[f292,f27]) ).
fof(f289,plain,
! [X0,X1,X2] : double_divide(X0,inverse(inverse(inverse(double_divide(inverse(X0),X1))))) = multiply(X2,double_divide(identity,double_divide(identity,double_divide(X2,X1)))),
inference(backward_demodulation,[status(thm)],[f292,f166]) ).
fof(f292,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f252,f271]) ).
fof(f293,plain,
! [X0,X1] : double_divide(X0,multiply(X1,inverse(X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f203,f272]) ).
fof(f295,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,inverse(inverse(X2)))) = multiply(double_divide(double_divide(identity,inverse(X0)),X2),inverse(inverse(inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f268,f274]) ).
fof(f296,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,inverse(inverse(X2)))) = multiply(double_divide(inverse(inverse(X0)),X2),inverse(inverse(inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f268,f295]) ).
fof(f297,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,inverse(inverse(X2)))) = multiply(double_divide(inverse(inverse(X0)),X2),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f203,f296]) ).
fof(f309,plain,
! [X0,X1] : double_divide(X0,inverse(double_divide(inverse(X0),double_divide(identity,X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f203,f288]) ).
fof(f310,plain,
! [X0,X1] : double_divide(X0,multiply(double_divide(identity,X1),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f12,f309]) ).
fof(f311,plain,
! [X0] : inverse(double_divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f293,f310]) ).
fof(f312,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f12,f311]) ).
fof(f316,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f323,f192]) ).
fof(f319,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,inverse(inverse(X2)))) = multiply(double_divide(X0,X2),inverse(X1)),
inference(backward_demodulation,[status(thm)],[f323,f297]) ).
fof(f323,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f292,f312]) ).
fof(f324,plain,
! [X0,X1,X2] : double_divide(X0,inverse(double_divide(inverse(X0),X1))) = multiply(X2,double_divide(identity,double_divide(identity,double_divide(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f203,f289]) ).
fof(f325,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,inverse(X0))) = multiply(X2,double_divide(identity,double_divide(identity,double_divide(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f12,f324]) ).
fof(f327,plain,
! [X0,X1] : inverse(X0) = multiply(X1,double_divide(identity,double_divide(identity,double_divide(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f293,f325]) ).
fof(f329,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(trivial_equality_resolution,[status(thm)],[f316]) ).
fof(f333,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,X2)) = multiply(double_divide(X0,X2),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f323,f319]) ).
fof(f339,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f12,f323]) ).
fof(f358,plain,
! [X0,X1] : double_divide(X0,double_divide(identity,multiply(X0,X1))) = multiply(identity,double_divide(identity,double_divide(identity,X1))),
inference(paramodulation,[status(thm)],[f219,f219]) ).
fof(f364,plain,
! [X0] : multiply(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,X0))))) = X0,
inference(backward_demodulation,[status(thm)],[f358,f219]) ).
fof(f371,plain,
! [X0] : inverse(double_divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f327,f364]) ).
fof(f373,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f12,f371]) ).
fof(f384,plain,
! [X0] : inverse(X0) = double_divide(identity,X0),
inference(paramodulation,[status(thm)],[f373,f339]) ).
fof(f401,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(double_divide(identity,double_divide(X1,X0)))),
inference(backward_demodulation,[status(thm)],[f384,f327]) ).
fof(f451,plain,
! [X0,X1] : inverse(X0) = multiply(X1,multiply(double_divide(X1,X0),identity)),
inference(forward_demodulation,[status(thm)],[f12,f401]) ).
fof(f452,plain,
! [X0,X1] : inverse(X0) = multiply(X1,double_divide(X1,X0)),
inference(forward_demodulation,[status(thm)],[f373,f451]) ).
fof(f522,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X1))) = multiply(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f293,f452]) ).
fof(f530,plain,
! [X0,X1] : double_divide(inverse(X0),X1) = multiply(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f339,f522]) ).
fof(f703,plain,
! [X0,X1,X2] : inverse(double_divide(X0,multiply(X1,X2))) = double_divide(inverse(X1),double_divide(X0,X2)),
inference(paramodulation,[status(thm)],[f333,f339]) ).
fof(f726,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = double_divide(inverse(X0),double_divide(X2,X1)),
inference(forward_demodulation,[status(thm)],[f12,f703]) ).
fof(f727,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,inverse(double_divide(X2,X1))),
inference(forward_demodulation,[status(thm)],[f530,f726]) ).
fof(f728,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f735,f329]) ).
fof(f735,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f12,f727]) ).
fof(f745,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f728]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP077-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n014.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 20 19:56:40 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.14/5.43 % Refutation found
% 0.14/5.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.45 % Elapsed time: 0.063437 seconds
% 0.14/5.45 % CPU time: 0.288378 seconds
% 0.14/5.45 % Total memory used: 72.363 MB
% 0.14/5.45 % Net memory used: 71.793 MB
%------------------------------------------------------------------------------