%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP099-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:32:30 PM UTC 2026
% Result : Unsatisfiable 1.46s 0.65s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 5
% Syntax : Number of formulae : 136 ( 126 unt; 0 def)
% Number of atoms : 158 ( 157 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 35 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 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 : 272 ( 272 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),double_divide(identity,Z))),double_divide(identity,identity)) = Y,
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(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/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(identity,X2))),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(X0,X2)),double_divide(identity,X2))),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] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f12]) ).
fof(f14,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f16,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)],[f13,f10]) ).
fof(f17,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)],[f14,f16]) ).
fof(f18,plain,
! [X0,X1] : multiply(multiply(X0,X1),double_divide(X1,X0)) = inverse(identity),
inference(paramodulation,[status(thm)],[f12,f13]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(double_divide(X3,X1),double_divide(identity,inverse(identity)))),inverse(identity)) = X3,
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f20,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,identity),double_divide(identity,inverse(X0)))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f21,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,inverse(X0)),double_divide(identity,identity))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f22,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,inverse(identity))),identity)),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f25,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(double_divide(X3,X1),identity)),inverse(identity)) = X3,
inference(forward_demodulation,[status(thm)],[f9,f19]) ).
fof(f26,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),inverse(double_divide(X3,X1))),inverse(identity)) = X3,
inference(forward_demodulation,[status(thm)],[f8,f25]) ).
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(identity,X2))),multiply(X1,X3)),inverse(identity)) = X3,
inference(forward_demodulation,[status(thm)],[f12,f26]) ).
fof(f28,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),double_divide(identity,inverse(X0)))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f20]) ).
fof(f29,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,inverse(X0)),inverse(identity))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f21]) ).
fof(f30,plain,
! [X0,X1] : double_divide(double_divide(X0,inverse(double_divide(X1,double_divide(X0,inverse(identity))))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f22]) ).
fof(f31,plain,
! [X0,X1] : double_divide(double_divide(X0,multiply(double_divide(X0,inverse(identity)),X1)),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f12,f30]) ).
fof(f69,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,inverse(identity))),identity)),multiply(X1,X2)),inverse(identity)) = X2,
inference(paramodulation,[status(thm)],[f9,f27]) ).
fof(f71,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(multiply(X1,X2),double_divide(X0,X3)),double_divide(identity,X3))),inverse(identity)),inverse(identity)) = double_divide(X2,X1),
inference(paramodulation,[status(thm)],[f18,f27]) ).
fof(f73,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(inverse(X1),double_divide(X0,X2)),double_divide(identity,X2))),inverse(identity)),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f13,f27]) ).
fof(f77,plain,
! [X0,X1,X2,X3] : multiply(inverse(identity),double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),multiply(X1,X3))) = inverse(X3),
inference(paramodulation,[status(thm)],[f27,f12]) ).
fof(f87,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,inverse(double_divide(X1,double_divide(X0,inverse(identity))))),multiply(X1,X2)),inverse(identity)) = X2,
inference(forward_demodulation,[status(thm)],[f8,f69]) ).
fof(f88,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,multiply(double_divide(X0,inverse(identity)),X1)),multiply(X1,X2)),inverse(identity)) = X2,
inference(forward_demodulation,[status(thm)],[f12,f87]) ).
fof(f90,plain,
! [X0,X1] : double_divide(multiply(X0,X1),inverse(identity)) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f11,f71]) ).
fof(f91,plain,
! [X0] : double_divide(inverse(X0),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f11,f73]) ).
fof(f104,plain,
! [X0,X1] : multiply(inverse(identity),multiply(X0,X1)) = inverse(double_divide(X1,X0)),
inference(paramodulation,[status(thm)],[f90,f12]) ).
fof(f116,plain,
! [X0,X1] : multiply(inverse(identity),multiply(X0,X1)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f12,f104]) ).
fof(f118,plain,
! [X0] : multiply(inverse(identity),inverse(inverse(X0))) = multiply(identity,X0),
inference(paramodulation,[status(thm)],[f14,f116]) ).
fof(f122,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(inverse(identity),double_divide(X0,X1)),double_divide(identity,X1))),multiply(X2,X3)),inverse(identity)) = multiply(X2,X3),
inference(paramodulation,[status(thm)],[f116,f27]) ).
fof(f126,plain,
! [X0] : multiply(inverse(identity),inverse(inverse(X0))) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f14,f118]) ).
fof(f131,plain,
! [X0] : double_divide(double_divide(identity,double_divide(inverse(X0),identity)),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f28]) ).
fof(f138,plain,
! [X0] : double_divide(double_divide(identity,inverse(inverse(X0))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f131]) ).
fof(f147,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(X0,X1),inverse(identity))),inverse(identity)) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f90,f29]) ).
fof(f148,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)) = double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3))),multiply(X2,X0)),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f150,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)) = double_divide(X1,double_divide(double_divide(X0,inverse(X1)),inverse(identity))),
inference(paramodulation,[status(thm)],[f29,f29]) ).
fof(f151,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(identity,X2))),
inference(paramodulation,[status(thm)],[f11,f29]) ).
fof(f160,plain,
! [X0] : multiply(inverse(identity),double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity))) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f148,f77]) ).
fof(f164,plain,
! [X0,X1] : double_divide(double_divide(double_divide(double_divide(identity,double_divide(inverse(identity),inverse(identity))),inverse(identity)),multiply(X0,X1)),inverse(identity)) = multiply(X0,X1),
inference(backward_demodulation,[status(thm)],[f151,f122]) ).
fof(f166,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)) = double_divide(double_divide(double_divide(identity,double_divide(X1,inverse(identity))),inverse(identity)),multiply(X1,X0)),
inference(backward_demodulation,[status(thm)],[f151,f148]) ).
fof(f178,plain,
! [X0,X1] : double_divide(double_divide(double_divide(double_divide(identity,identity),inverse(identity)),multiply(X0,X1)),inverse(identity)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f91,f164]) ).
fof(f179,plain,
! [X0,X1] : double_divide(double_divide(double_divide(inverse(identity),inverse(identity)),multiply(X0,X1)),inverse(identity)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f8,f178]) ).
fof(f180,plain,
! [X0,X1] : double_divide(double_divide(identity,multiply(X0,X1)),inverse(identity)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f91,f179]) ).
fof(f191,plain,
! [X0] : double_divide(double_divide(identity,multiply(identity,X0)),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f31]) ).
fof(f192,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)) = double_divide(X1,multiply(double_divide(X1,inverse(identity)),X0)),
inference(paramodulation,[status(thm)],[f31,f29]) ).
fof(f196,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f197,f14]) ).
fof(f197,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f180,f191]) ).
fof(f200,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f196,f17]) ).
fof(f201,plain,
! [X0] : double_divide(double_divide(identity,X0),inverse(identity)) = X0,
inference(backward_demodulation,[status(thm)],[f196,f138]) ).
fof(f202,plain,
! [X0] : multiply(inverse(identity),inverse(inverse(X0))) = X0,
inference(backward_demodulation,[status(thm)],[f196,f126]) ).
fof(f203,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(identity) != identity ),
inference(trivial_equality_resolution,[status(thm)],[f200]) ).
fof(f205,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),inverse(identity)) = multiply(X1,X0),
inference(backward_demodulation,[status(thm)],[f201,f147]) ).
fof(f206,plain,
! [X0,X1] : double_divide(X0,inverse(identity)) = double_divide(X1,multiply(double_divide(X1,inverse(identity)),X0)),
inference(backward_demodulation,[status(thm)],[f201,f192]) ).
fof(f207,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(X0,inverse(identity))),inverse(identity)) = double_divide(double_divide(X1,inverse(identity)),multiply(X1,X0)),
inference(backward_demodulation,[status(thm)],[f201,f166]) ).
fof(f208,plain,
! [X0] : multiply(inverse(identity),double_divide(X0,inverse(identity))) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f201,f160]) ).
fof(f210,plain,
! [X0,X1,X2] : double_divide(X0,inverse(identity)) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2))),
inference(backward_demodulation,[status(thm)],[f201,f151]) ).
fof(f211,plain,
! [X0,X1] : double_divide(X0,inverse(identity)) = double_divide(X1,double_divide(double_divide(X0,inverse(X1)),inverse(identity))),
inference(backward_demodulation,[status(thm)],[f201,f150]) ).
fof(f218,plain,
! [X0] : multiply(inverse(identity),X0) = X0,
inference(forward_demodulation,[status(thm)],[f196,f202]) ).
fof(f219,plain,
! [X0,X1] : multiply(multiply(double_divide(X0,inverse(identity)),X1),X0) = X1,
inference(backward_demodulation,[status(thm)],[f205,f31]) ).
fof(f221,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),double_divide(identity,inverse(X1))),X1) = X0,
inference(backward_demodulation,[status(thm)],[f205,f28]) ).
fof(f223,plain,
! [X0] : multiply(X0,identity) = X0,
inference(backward_demodulation,[status(thm)],[f205,f201]) ).
fof(f228,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),double_divide(X2,multiply(double_divide(X2,inverse(identity)),X0))) = X1,
inference(backward_demodulation,[status(thm)],[f205,f88]) ).
fof(f234,plain,
! [X0,X1] : double_divide(X0,inverse(identity)) = double_divide(double_divide(X1,inverse(identity)),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f201,f207]) ).
fof(f235,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f240,f90]) ).
fof(f238,plain,
! [X0,X1] : double_divide(X0,inverse(identity)) = double_divide(inverse(X1),multiply(X1,X0)),
inference(backward_demodulation,[status(thm)],[f240,f234]) ).
fof(f240,plain,
! [X0] : double_divide(X0,inverse(identity)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f218,f208]) ).
fof(f242,plain,
! [X0,X1,X2] : inverse(X0) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2))),
inference(forward_demodulation,[status(thm)],[f240,f210]) ).
fof(f243,plain,
! [X0,X1] : inverse(X0) = double_divide(X1,double_divide(double_divide(X0,inverse(X1)),inverse(identity))),
inference(forward_demodulation,[status(thm)],[f240,f211]) ).
fof(f244,plain,
! [X0,X1] : inverse(X0) = double_divide(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f205,f243]) ).
fof(f248,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f240,f219]) ).
fof(f253,plain,
! [X0,X1] : multiply(multiply(X0,X1),double_divide(X0,inverse(identity))) = X1,
inference(forward_demodulation,[status(thm)],[f206,f228]) ).
fof(f254,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(forward_demodulation,[status(thm)],[f240,f253]) ).
fof(f260,plain,
! [X0,X1] : inverse(X0) = double_divide(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f240,f238]) ).
fof(f270,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f13,f218]) ).
fof(f275,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| identity != identity ),
inference(backward_demodulation,[status(thm)],[f270,f203]) ).
fof(f283,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(trivial_equality_resolution,[status(thm)],[f275]) ).
fof(f285,plain,
! [X0,X1,X2] : inverse(X0) = double_divide(double_divide(X1,X2),multiply(multiply(X2,X1),X0)),
inference(paramodulation,[status(thm)],[f12,f244]) ).
fof(f305,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f254,f254]) ).
fof(f313,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f235,f305]) ).
fof(f323,plain,
! [X0,X1] : multiply(X0,inverse(double_divide(inverse(X0),double_divide(identity,inverse(X1))))) = X1,
inference(paramodulation,[status(thm)],[f221,f254]) ).
fof(f334,plain,
! [X0,X1] : multiply(X0,multiply(double_divide(identity,inverse(X1)),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f12,f323]) ).
fof(f339,plain,
! [X0] : inverse(X0) = double_divide(identity,X0),
inference(paramodulation,[status(thm)],[f223,f235]) ).
fof(f347,plain,
! [X0,X1] : multiply(X0,multiply(inverse(inverse(X1)),inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f339,f334]) ).
fof(f352,plain,
! [X0,X1,X2] : inverse(X0) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X2))),
inference(backward_demodulation,[status(thm)],[f339,f242]) ).
fof(f356,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f196,f347]) ).
fof(f463,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f260,f313]) ).
fof(f465,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),inverse(X2)) = inverse(multiply(multiply(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f285,f313]) ).
fof(f467,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = inverse(multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f244,f313]) ).
fof(f470,plain,
! [X0,X1] : multiply(inverse(X0),X1) = double_divide(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f313,f248]) ).
fof(f479,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f235,f463]) ).
fof(f480,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),inverse(X2)) = double_divide(X2,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f235,f465]) ).
fof(f483,plain,
! [X0,X1,X2] : inverse(X0) = double_divide(X1,multiply(X2,inverse(double_divide(X0,double_divide(X1,X2))))),
inference(backward_demodulation,[status(thm)],[f484,f352]) ).
fof(f484,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(X1,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f235,f467]) ).
fof(f500,plain,
! [X0,X1,X2] : inverse(X0) = double_divide(X1,multiply(X2,multiply(double_divide(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f12,f483]) ).
fof(f981,plain,
! [X0,X1] : inverse(inverse(X0)) = double_divide(X1,double_divide(X1,X0)),
inference(paramodulation,[status(thm)],[f356,f500]) ).
fof(f983,plain,
! [X0,X1,X2] : inverse(multiply(X0,inverse(double_divide(X1,X2)))) = double_divide(X1,multiply(X2,X0)),
inference(paramodulation,[status(thm)],[f356,f500]) ).
fof(f984,plain,
! [X0,X1,X2] : inverse(double_divide(double_divide(X0,X1),X2)) = double_divide(X0,multiply(X1,inverse(X2))),
inference(paramodulation,[status(thm)],[f313,f500]) ).
fof(f1013,plain,
! [X0,X1] : X0 = double_divide(X1,double_divide(X1,X0)),
inference(forward_demodulation,[status(thm)],[f196,f981]) ).
fof(f1014,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(X0,X1)),X2) = double_divide(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f235,f983]) ).
fof(f1016,plain,
! [X0,X1,X2] : multiply(inverse(X0),double_divide(X1,X2)) = double_divide(X1,multiply(X2,X0)),
inference(forward_demodulation,[status(thm)],[f470,f1014]) ).
fof(f1019,plain,
! [X0,X1,X2] : multiply(X0,double_divide(X1,X2)) = double_divide(X1,multiply(X2,inverse(X0))),
inference(forward_demodulation,[status(thm)],[f12,f984]) ).
fof(f1121,plain,
! [X0,X1] : multiply(inverse(X0),X1) = double_divide(X0,inverse(X1)),
inference(paramodulation,[status(thm)],[f244,f1013]) ).
fof(f1131,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f1013,f313]) ).
fof(f1155,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = double_divide(identity,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f339,f1016]) ).
fof(f1163,plain,
! [X0,X1,X2] : inverse(double_divide(X0,X1)) = double_divide(X2,double_divide(X0,multiply(X1,X2))),
inference(paramodulation,[status(thm)],[f1016,f244]) ).
fof(f1168,plain,
! [X0,X1,X2] : inverse(double_divide(X0,multiply(X1,X2))) = double_divide(double_divide(X0,X1),inverse(X2)),
inference(paramodulation,[status(thm)],[f1016,f235]) ).
fof(f1175,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(identity,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f479,f1155]) ).
fof(f1176,plain,
! [X0,X1] : double_divide(X0,X1) = inverse(multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f339,f1175]) ).
fof(f1182,plain,
! [X0,X1,X2] : multiply(X0,X1) = double_divide(X2,double_divide(X1,multiply(X0,X2))),
inference(forward_demodulation,[status(thm)],[f12,f1163]) ).
fof(f1196,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = double_divide(double_divide(X2,X0),inverse(X1)),
inference(forward_demodulation,[status(thm)],[f12,f1168]) ).
fof(f1197,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X1,inverse(double_divide(X2,X0))),
inference(forward_demodulation,[status(thm)],[f484,f1196]) ).
fof(f1200,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(backward_demodulation,[status(thm)],[f1214,f283]) ).
fof(f1214,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X1,multiply(X0,X2)),
inference(forward_demodulation,[status(thm)],[f12,f1197]) ).
fof(f1576,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(X1,double_divide(X2,X3))) = double_divide(X1,double_divide(X0,multiply(X3,X2))),
inference(paramodulation,[status(thm)],[f480,f1019]) ).
fof(f1609,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(X1,double_divide(X2,double_divide(X2,X0))),
inference(backward_demodulation,[status(thm)],[f1576,f1182]) ).
fof(f1623,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)) ),
inference(backward_demodulation,[status(thm)],[f1624,f1200]) ).
fof(f1624,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f1013,f1609]) ).
fof(f1625,plain,
multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)),
inference(trivial_equality_resolution,[status(thm)],[f1623]) ).
fof(f1714,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),inverse(X2)) = inverse(double_divide(X2,multiply(X1,X0))),
inference(paramodulation,[status(thm)],[f480,f1176]) ).
fof(f1734,plain,
! [X0,X1,X2] : multiply(inverse(double_divide(X0,X1)),X2) = inverse(double_divide(X2,multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f1121,f1714]) ).
fof(f1735,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = inverse(double_divide(X2,multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f1131,f1734]) ).
fof(f1736,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = inverse(double_divide(X2,multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1214,f1735]) ).
fof(f1740,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f1742,f1625]) ).
fof(f1742,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X2,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1131,f1736]) ).
fof(f1763,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(forward_demodulation,[status(thm)],[f1624,f1740]) ).
fof(f1764,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1763]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP099-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 19:57:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 1.46/0.65 % Refutation found
% 1.46/0.65 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.46/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.46/0.67 % Elapsed time: 0.306104 seconds
% 1.46/0.67 % CPU time: 2.191257 seconds
% 1.46/0.67 % Total memory used: 99.929 MB
% 1.46/0.67 % Net memory used: 97.707 MB
%------------------------------------------------------------------------------