%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP101-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:32:31 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.64s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 5
% Syntax : Number of formulae : 126 ( 114 unt; 0 def)
% Number of atoms : 150 ( 149 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 39 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 262 ( 262 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(Z,X)),double_divide(Z,identity))),double_divide(identity,identity)) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = double_divide(double_divide(Y,X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : inverse(X) = double_divide(X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : identity = double_divide(X,inverse(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
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(X2,X0)),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(a4,b4) != multiply(b4,a4)
| 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(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))),inverse(identity)) = X1,
inference(backward_demodulation,[status(thm)],[f8,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(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),inverse(X2))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f11]) ).
fof(f14,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f12]) ).
fof(f15,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f16,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f12,f9]) ).
fof(f17,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f14,f10]) ).
fof(f18,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f15,f17]) ).
fof(f45,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(inverse(identity),double_divide(double_divide(X0,X1),inverse(double_divide(X2,double_divide(double_divide(X1,double_divide(X3,X2)),inverse(X3)))))),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f47,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(X1,identity),inverse(X0))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f13]) ).
fof(f49,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X0)),multiply(X3,X2))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f12,f13]) ).
fof(f53,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(inverse(identity),double_divide(double_divide(X0,X1),multiply(double_divide(double_divide(X1,double_divide(X2,X3)),inverse(X2)),X3))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f12,f45]) ).
fof(f56,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(inverse(X1),inverse(X0))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f47]) ).
fof(f60,plain,
! [X0] : double_divide(double_divide(inverse(inverse(X0)),identity),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f56]) ).
fof(f68,plain,
! [X0] : double_divide(inverse(inverse(inverse(X0))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f60]) ).
fof(f73,plain,
! [X0,X1] : double_divide(inverse(inverse(multiply(X0,X1))),inverse(identity)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f12,f68]) ).
fof(f74,plain,
! [X0] : double_divide(double_divide(inverse(identity),X0),inverse(identity)) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f68,f56]) ).
fof(f80,plain,
! [X0,X1,X2,X3] : inverse(inverse(double_divide(double_divide(X0,X1),multiply(double_divide(double_divide(X1,double_divide(X2,X3)),inverse(X2)),X3)))) = X0,
inference(backward_demodulation,[status(thm)],[f74,f53]) ).
fof(f86,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X1)),X2),double_divide(X3,X0))) = X3,
inference(forward_demodulation,[status(thm)],[f12,f80]) ).
fof(f122,plain,
! [X0,X1,X2,X3,X4] : double_divide(double_divide(inverse(identity),double_divide(double_divide(X0,X1),multiply(double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X4)),multiply(X3,X2)),X4))),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f49,f49]) ).
fof(f138,plain,
! [X0,X1,X2,X3,X4] : inverse(inverse(double_divide(double_divide(X0,X1),multiply(double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X4)),multiply(X3,X2)),X4)))) = X0,
inference(forward_demodulation,[status(thm)],[f74,f122]) ).
fof(f139,plain,
! [X0,X1,X2,X3,X4] : inverse(multiply(multiply(double_divide(double_divide(X0,double_divide(double_divide(X1,X2),X3)),multiply(X2,X1)),X3),double_divide(X4,X0))) = X4,
inference(forward_demodulation,[status(thm)],[f12,f138]) ).
fof(f180,plain,
double_divide(identity,inverse(identity)) = inverse(inverse(inverse(inverse(identity)))),
inference(paramodulation,[status(thm)],[f9,f74]) ).
fof(f189,plain,
identity = inverse(inverse(inverse(inverse(identity)))),
inference(forward_demodulation,[status(thm)],[f9,f180]) ).
fof(f198,plain,
double_divide(identity,inverse(identity)) = inverse(identity),
inference(paramodulation,[status(thm)],[f189,f68]) ).
fof(f208,plain,
! [X0] : double_divide(double_divide(inverse(identity),X0),identity) = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f227,f74]) ).
fof(f209,plain,
! [X0,X1] : double_divide(inverse(inverse(multiply(X0,X1))),identity) = double_divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f227,f73]) ).
fof(f210,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X0)),multiply(X3,X2))),identity) = X1,
inference(backward_demodulation,[status(thm)],[f227,f49]) ).
fof(f212,plain,
! [X0] : double_divide(inverse(inverse(inverse(X0))),identity) = X0,
inference(backward_demodulation,[status(thm)],[f227,f68]) ).
fof(f215,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(backward_demodulation,[status(thm)],[f227,f18]) ).
fof(f227,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f9,f198]) ).
fof(f243,plain,
! [X0] : inverse(double_divide(inverse(identity),X0)) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f8,f208]) ).
fof(f244,plain,
! [X0] : multiply(X0,inverse(identity)) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f12,f243]) ).
fof(f246,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f227,f244]) ).
fof(f247,plain,
! [X0,X1] : inverse(inverse(inverse(multiply(X0,X1)))) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f8,f209]) ).
fof(f248,plain,
! [X0,X1,X2,X3] : inverse(double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X0)),multiply(X3,X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f210]) ).
fof(f249,plain,
! [X0,X1] : inverse(multiply(X0,double_divide(X1,X0))) = X1,
inference(backward_demodulation,[status(thm)],[f250,f139]) ).
fof(f250,plain,
! [X0,X1,X2,X3] : multiply(double_divide(double_divide(X0,double_divide(double_divide(X1,X2),X3)),multiply(X2,X1)),X3) = X0,
inference(forward_demodulation,[status(thm)],[f12,f248]) ).
fof(f254,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f212]) ).
fof(f257,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2 ),
inference(trivial_equality_resolution,[status(thm)],[f215]) ).
fof(f307,plain,
! [X0,X1] : inverse(inverse(inverse(X0))) = multiply(X1,double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f249,f254]) ).
fof(f310,plain,
! [X0] : identity = double_divide(inverse(inverse(inverse(X0))),X0),
inference(paramodulation,[status(thm)],[f254,f9]) ).
fof(f323,plain,
! [X0] : multiply(X0,inverse(inverse(inverse(X0)))) = inverse(identity),
inference(paramodulation,[status(thm)],[f310,f12]) ).
fof(f328,plain,
! [X0] : multiply(X0,inverse(inverse(inverse(X0)))) = identity,
inference(forward_demodulation,[status(thm)],[f227,f323]) ).
fof(f331,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(paramodulation,[status(thm)],[f254,f328]) ).
fof(f346,plain,
! [X0,X1] : multiply(multiply(X0,X1),double_divide(X1,X0)) = identity,
inference(paramodulation,[status(thm)],[f12,f331]) ).
fof(f393,plain,
! [X0] : inverse(inverse(inverse(inverse(inverse(X0))))) = double_divide(identity,X0),
inference(paramodulation,[status(thm)],[f246,f247]) ).
fof(f418,plain,
! [X0] : inverse(X0) = double_divide(identity,X0),
inference(forward_demodulation,[status(thm)],[f254,f393]) ).
fof(f425,plain,
! [X0,X1,X2] : inverse(multiply(multiply(double_divide(identity,inverse(X0)),X1),double_divide(X2,inverse(inverse(inverse(double_divide(X0,X1))))))) = X2,
inference(paramodulation,[status(thm)],[f310,f86]) ).
fof(f426,plain,
! [X0,X1,X2] : inverse(multiply(multiply(double_divide(double_divide(X0,identity),inverse(inverse(inverse(inverse(X1))))),X1),double_divide(X2,X0))) = X2,
inference(paramodulation,[status(thm)],[f310,f86]) ).
fof(f450,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(inverse(X0)),X1),double_divide(X2,inverse(inverse(inverse(double_divide(X0,X1))))))) = X2,
inference(forward_demodulation,[status(thm)],[f418,f425]) ).
fof(f451,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(inverse(X0)),X1),double_divide(X2,inverse(inverse(multiply(X1,X0)))))) = X2,
inference(forward_demodulation,[status(thm)],[f12,f450]) ).
fof(f452,plain,
! [X0,X1,X2] : inverse(multiply(multiply(double_divide(inverse(X0),inverse(inverse(inverse(inverse(X1))))),X1),double_divide(X2,X0))) = X2,
inference(forward_demodulation,[status(thm)],[f8,f426]) ).
fof(f454,plain,
! [X0,X1,X2] : inverse(multiply(multiply(double_divide(inverse(X0),X1),X1),double_divide(X2,X0))) = X2,
inference(forward_demodulation,[status(thm)],[f254,f452]) ).
fof(f485,plain,
! [X0,X1,X2] : multiply(double_divide(identity,multiply(X0,X1)),X2) = inverse(inverse(inverse(double_divide(double_divide(X1,X0),X2)))),
inference(paramodulation,[status(thm)],[f310,f250]) ).
fof(f489,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(X0,double_divide(identity,X1)),multiply(X2,inverse(inverse(inverse(X2))))),X1) = X0,
inference(paramodulation,[status(thm)],[f310,f250]) ).
fof(f493,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(double_divide(X3,X4),X1)),multiply(X4,X3))),X5)),X2),X5) = X0,
inference(paramodulation,[status(thm)],[f250,f250]) ).
fof(f500,plain,
! [X0,X1,X2,X3] : inverse(inverse(inverse(X0))) = double_divide(X1,double_divide(double_divide(X0,double_divide(double_divide(X2,X3),X1)),multiply(X3,X2))),
inference(paramodulation,[status(thm)],[f250,f247]) ).
fof(f507,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),X2) = inverse(inverse(inverse(double_divide(double_divide(X1,X0),X2)))),
inference(forward_demodulation,[status(thm)],[f418,f485]) ).
fof(f508,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),X2) = inverse(inverse(multiply(X2,double_divide(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f12,f507]) ).
fof(f516,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(X0,inverse(X1)),multiply(X2,inverse(inverse(inverse(X2))))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f418,f489]) ).
fof(f517,plain,
! [X0,X1] : multiply(double_divide(double_divide(X0,inverse(X1)),identity),X1) = X0,
inference(forward_demodulation,[status(thm)],[f328,f516]) ).
fof(f518,plain,
! [X0,X1] : multiply(inverse(double_divide(X0,inverse(X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f8,f517]) ).
fof(f520,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f12,f518]) ).
fof(f548,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(X0,double_divide(inverse(inverse(inverse(X1))),X2)),X1),X2) = X0,
inference(backward_demodulation,[status(thm)],[f500,f493]) ).
fof(f570,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f331,f520]) ).
fof(f584,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f604,f257]) ).
fof(f585,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f604,f247]) ).
fof(f591,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(X0,double_divide(inverse(X1),X2)),X1),X2) = X0,
inference(backward_demodulation,[status(thm)],[f604,f548]) ).
fof(f597,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,X1)),X2) = multiply(X2,double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f604,f508]) ).
fof(f599,plain,
! [X0,X1,X2] : inverse(multiply(multiply(inverse(inverse(X0)),X1),double_divide(X2,multiply(X1,X0)))) = X2,
inference(backward_demodulation,[status(thm)],[f604,f451]) ).
fof(f604,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f15,f570]) ).
fof(f620,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(trivial_equality_resolution,[status(thm)],[f584]) ).
fof(f622,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),multiply(double_divide(inverse(X1),X2),X2)) = X0,
inference(backward_demodulation,[status(thm)],[f585,f454]) ).
fof(f630,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X0)),multiply(X3,X2))) = X1,
inference(backward_demodulation,[status(thm)],[f636,f250]) ).
fof(f634,plain,
! [X0,X1,X2] : multiply(X0,double_divide(double_divide(X1,double_divide(inverse(X2),X0)),X2)) = X1,
inference(backward_demodulation,[status(thm)],[f636,f591]) ).
fof(f636,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),X2) = multiply(X2,double_divide(X0,X1)),
inference(forward_demodulation,[status(thm)],[f585,f597]) ).
fof(f639,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,multiply(X1,X2)),multiply(inverse(inverse(X2)),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f585,f599]) ).
fof(f640,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,multiply(X1,X2)),multiply(X2,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f604,f639]) ).
fof(f644,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),multiply(X2,double_divide(inverse(X1),X2))) = X0,
inference(forward_demodulation,[status(thm)],[f636,f622]) ).
fof(f645,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),inverse(inverse(inverse(inverse(X1))))) = X0,
inference(forward_demodulation,[status(thm)],[f307,f644]) ).
fof(f646,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f254,f645]) ).
fof(f660,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(double_divide(X1,double_divide(identity,X0)),multiply(multiply(X2,X3),double_divide(X3,X2)))) = X1,
inference(paramodulation,[status(thm)],[f16,f630]) ).
fof(f676,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(double_divide(X1,inverse(X0)),multiply(multiply(X2,X3),double_divide(X3,X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f418,f660]) ).
fof(f677,plain,
! [X0,X1] : multiply(X0,double_divide(double_divide(X1,inverse(X0)),identity)) = X1,
inference(forward_demodulation,[status(thm)],[f346,f676]) ).
fof(f678,plain,
! [X0,X1] : multiply(X0,inverse(double_divide(X1,inverse(X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f677]) ).
fof(f679,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f12,f678]) ).
fof(f799,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X1)),X0),
inference(paramodulation,[status(thm)],[f679,f520]) ).
fof(f808,plain,
( multiply(b4,a4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(backward_demodulation,[status(thm)],[f813,f620]) ).
fof(f813,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f604,f799]) ).
fof(f816,plain,
( multiply(b4,a4) != multiply(b4,a4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)) ),
inference(forward_demodulation,[status(thm)],[f813,f808]) ).
fof(f817,plain,
( multiply(b4,a4) != multiply(b4,a4)
| multiply(c3,multiply(b3,a3)) != multiply(a3,multiply(b3,c3)) ),
inference(forward_demodulation,[status(thm)],[f813,f816]) ).
fof(f818,plain,
( multiply(b4,a4) != multiply(b4,a4)
| multiply(c3,multiply(b3,a3)) != multiply(a3,multiply(c3,b3)) ),
inference(forward_demodulation,[status(thm)],[f813,f817]) ).
fof(f819,plain,
multiply(c3,multiply(b3,a3)) != multiply(a3,multiply(c3,b3)),
inference(trivial_equality_resolution,[status(thm)],[f818]) ).
fof(f838,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X0,X1),
inference(paramodulation,[status(thm)],[f813,f585]) ).
fof(f849,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(backward_demodulation,[status(thm)],[f861,f646]) ).
fof(f857,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),double_divide(X2,multiply(X1,X0))) = X2,
inference(backward_demodulation,[status(thm)],[f861,f640]) ).
fof(f859,plain,
! [X0,X1,X2] : multiply(X0,double_divide(X1,double_divide(X2,double_divide(inverse(X1),X0)))) = X2,
inference(backward_demodulation,[status(thm)],[f861,f634]) ).
fof(f861,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f585,f838]) ).
fof(f956,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f849,f849]) ).
fof(f966,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f861,f956]) ).
fof(f988,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X0) = inverse(X1),
inference(paramodulation,[status(thm)],[f966,f12]) ).
fof(f996,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f813,f988]) ).
fof(f1075,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(inverse(X0),X1),
inference(paramodulation,[status(thm)],[f996,f679]) ).
fof(f1085,plain,
! [X0,X1,X2] : multiply(X0,double_divide(X1,double_divide(X2,multiply(X1,inverse(X0))))) = X2,
inference(backward_demodulation,[status(thm)],[f1075,f859]) ).
fof(f1517,plain,
! [X0,X1,X2] : multiply(X0,X1) = double_divide(X2,double_divide(X1,multiply(X2,inverse(inverse(X0))))),
inference(paramodulation,[status(thm)],[f1085,f679]) ).
fof(f1556,plain,
! [X0,X1,X2] : multiply(X0,X1) = double_divide(X2,double_divide(X1,multiply(X2,X0))),
inference(forward_demodulation,[status(thm)],[f604,f1517]) ).
fof(f2000,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = inverse(double_divide(X2,multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f1556,f996]) ).
fof(f2066,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f12,f2000]) ).
fof(f2151,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = inverse(double_divide(X2,multiply(X1,X0))),
inference(paramodulation,[status(thm)],[f857,f996]) ).
fof(f2215,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = inverse(double_divide(X2,multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f2066,f2151]) ).
fof(f2216,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f12,f2215]) ).
fof(f2217,plain,
multiply(c3,multiply(b3,a3)) != multiply(c3,multiply(a3,b3)),
inference(backward_demodulation,[status(thm)],[f2221,f819]) ).
fof(f2221,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(forward_demodulation,[status(thm)],[f2066,f2216]) ).
fof(f2231,plain,
multiply(c3,multiply(b3,a3)) != multiply(c3,multiply(b3,a3)),
inference(forward_demodulation,[status(thm)],[f813,f2217]) ).
fof(f2232,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP101-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.55 % Computer : n001.cluster.edu
% 0.09/0.55 % Model : x86_64 x86_64
% 0.09/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.55 % Memory : 8046.5625MB
% 0.09/0.55 % OS : Linux 6.8.0-71-generic
% 0.09/0.55 % CPULimit : 300
% 0.09/0.55 % WCLimit : 300
% 0.09/0.55 % DateTime : Sun Sep 20 20:02:57 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.15/0.57 % Drodi V4.1.1
% 0.15/0.64 % Refutation found
% 0.15/0.64 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.67 % Elapsed time: 0.107882 seconds
% 0.15/0.67 % CPU time: 0.592055 seconds
% 0.15/0.67 % Total memory used: 79.906 MB
% 0.15/0.67 % Net memory used: 79.137 MB
%------------------------------------------------------------------------------