%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP078-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.18s 0.52s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 120 ( 114 unt; 0 def)
% Number of atoms : 130 ( 129 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 18 ~; 10 |; 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 : 185 ( 185 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : double_divide(double_divide(identity,X),double_divide(identity,double_divide(double_divide(double_divide(X,Y),identity),double_divide(Z,Y)))) = Z,
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(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(identity,X0),double_divide(identity,double_divide(double_divide(double_divide(X0,X1),identity),double_divide(X2,X1)))) = 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(double_divide(identity,X0),double_divide(identity,double_divide(multiply(X1,X0),double_divide(X2,X1)))) = 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] : 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(f15,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f12,f9]) ).
fof(f16,plain,
( 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(f18,plain,
! [X0] : multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(paramodulation,[status(thm)],[f14,f14]) ).
fof(f19,plain,
! [X0,X1] : multiply(identity,double_divide(X0,X1)) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f12,f14]) ).
fof(f30,plain,
! [X0,X1] : double_divide(identity,double_divide(identity,double_divide(multiply(X0,inverse(identity)),double_divide(X1,X0)))) = X1,
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f31,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X0,identity),double_divide(X1,X0)))) = X1,
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f33,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(double_divide(identity,double_divide(multiply(X1,X2),double_divide(X3,X1))),X0),X3))) = double_divide(identity,X2),
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f35,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(inverse(X1),X0),identity))) = X1,
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f38,plain,
! [X0,X1,X2] : multiply(double_divide(identity,double_divide(multiply(X0,X1),double_divide(X2,X0))),double_divide(identity,X1)) = inverse(X2),
inference(paramodulation,[status(thm)],[f11,f12]) ).
fof(f40,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,inverse(multiply(inverse(X1),X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f35]) ).
fof(f135,plain,
! [X0,X1] : multiply(double_divide(identity,double_divide(multiply(X0,inverse(identity)),double_divide(X1,X0))),identity) = inverse(X1),
inference(paramodulation,[status(thm)],[f30,f12]) ).
fof(f149,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,double_divide(multiply(double_divide(identity,double_divide(multiply(X0,inverse(identity)),double_divide(X1,X0))),identity),X1))) = identity,
inference(paramodulation,[status(thm)],[f30,f31]) ).
fof(f154,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,double_divide(multiply(multiply(X0,X1),identity),identity))) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f15,f31]) ).
fof(f162,plain,
! [X0,X1] : multiply(double_divide(identity,double_divide(multiply(X0,identity),double_divide(X1,X0))),inverse(identity)) = inverse(X1),
inference(paramodulation,[status(thm)],[f31,f12]) ).
fof(f163,plain,
! [X0] : double_divide(inverse(identity),double_divide(identity,double_divide(inverse(X0),X0))) = identity,
inference(forward_demodulation,[status(thm)],[f135,f149]) ).
fof(f169,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,inverse(multiply(multiply(X0,X1),identity)))) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f8,f154]) ).
fof(f226,plain,
double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = identity,
inference(paramodulation,[status(thm)],[f8,f163]) ).
fof(f232,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(multiply(double_divide(identity,double_divide(inverse(X0),X0)),inverse(identity)),identity))) = inverse(identity),
inference(paramodulation,[status(thm)],[f163,f30]) ).
fof(f233,plain,
! [X0] : multiply(identity,identity) = inverse(multiply(double_divide(identity,double_divide(inverse(X0),X0)),inverse(identity))),
inference(paramodulation,[status(thm)],[f163,f19]) ).
fof(f238,plain,
double_divide(inverse(identity),double_divide(identity,multiply(identity,identity))) = identity,
inference(forward_demodulation,[status(thm)],[f14,f226]) ).
fof(f241,plain,
! [X0] : double_divide(identity,double_divide(identity,inverse(multiply(double_divide(identity,double_divide(inverse(X0),X0)),inverse(identity))))) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f8,f232]) ).
fof(f242,plain,
double_divide(identity,double_divide(identity,multiply(identity,identity))) = inverse(identity),
inference(backward_demodulation,[status(thm)],[f233,f241]) ).
fof(f247,plain,
! [X0,X1,X2] : double_divide(X0,double_divide(identity,inverse(multiply(inverse(X1),double_divide(identity,double_divide(multiply(X2,inverse(identity)),double_divide(X0,X2))))))) = X1,
inference(paramodulation,[status(thm)],[f30,f40]) ).
fof(f250,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,inverse(inverse(identity)))) = X0,
inference(paramodulation,[status(thm)],[f13,f40]) ).
fof(f262,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,multiply(identity,identity))) = X0,
inference(forward_demodulation,[status(thm)],[f14,f250]) ).
fof(f269,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(double_divide(identity,double_divide(multiply(double_divide(identity,multiply(identity,identity)),X1),identity)),X0),inverse(identity)))) = double_divide(identity,X1),
inference(paramodulation,[status(thm)],[f238,f33]) ).
fof(f277,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(multiply(double_divide(identity,multiply(identity,identity)),X1))),X0),inverse(identity)))) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f8,f269]) ).
fof(f285,plain,
! [X0] : double_divide(inverse(identity),double_divide(identity,inverse(multiply(inverse(X0),double_divide(identity,multiply(identity,identity)))))) = X0,
inference(paramodulation,[status(thm)],[f242,f40]) ).
fof(f287,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X0,double_divide(identity,multiply(identity,identity))),double_divide(X1,X0)))) = X1,
inference(paramodulation,[status(thm)],[f242,f11]) ).
fof(f304,plain,
double_divide(inverse(identity),double_divide(identity,multiply(identity,identity))) = double_divide(identity,multiply(identity,identity)),
inference(paramodulation,[status(thm)],[f242,f262]) ).
fof(f305,plain,
! [X0,X1] : double_divide(X0,double_divide(identity,multiply(identity,identity))) = double_divide(identity,double_divide(multiply(X1,inverse(identity)),double_divide(X0,X1))),
inference(paramodulation,[status(thm)],[f30,f262]) ).
fof(f307,plain,
double_divide(inverse(identity),double_divide(identity,multiply(identity,identity))) = identity,
inference(paramodulation,[status(thm)],[f8,f262]) ).
fof(f315,plain,
! [X0] : multiply(double_divide(identity,multiply(identity,identity)),double_divide(identity,X0)) = inverse(X0),
inference(paramodulation,[status(thm)],[f262,f12]) ).
fof(f316,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = X0,
inference(backward_demodulation,[status(thm)],[f328,f262]) ).
fof(f322,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X0,identity),double_divide(X1,X0)))) = X1,
inference(backward_demodulation,[status(thm)],[f328,f287]) ).
fof(f324,plain,
! [X0] : double_divide(inverse(identity),double_divide(identity,inverse(multiply(inverse(X0),identity)))) = X0,
inference(backward_demodulation,[status(thm)],[f328,f285]) ).
fof(f327,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(double_divide(identity,inverse(multiply(identity,X1))),X0),inverse(identity)))) = double_divide(identity,X1),
inference(backward_demodulation,[status(thm)],[f328,f277]) ).
fof(f328,plain,
identity = double_divide(identity,multiply(identity,identity)),
inference(forward_demodulation,[status(thm)],[f238,f304]) ).
fof(f329,plain,
! [X0,X1] : double_divide(X0,identity) = double_divide(identity,double_divide(multiply(X1,inverse(identity)),double_divide(X0,X1))),
inference(forward_demodulation,[status(thm)],[f328,f305]) ).
fof(f330,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f336,f30]) ).
fof(f331,plain,
! [X0,X1] : double_divide(X0,double_divide(identity,inverse(multiply(inverse(X1),inverse(X0))))) = X1,
inference(backward_demodulation,[status(thm)],[f336,f247]) ).
fof(f336,plain,
! [X0,X1] : inverse(X0) = double_divide(identity,double_divide(multiply(X1,inverse(identity)),double_divide(X0,X1))),
inference(forward_demodulation,[status(thm)],[f8,f329]) ).
fof(f338,plain,
double_divide(inverse(identity),identity) = identity,
inference(forward_demodulation,[status(thm)],[f328,f307]) ).
fof(f339,plain,
inverse(inverse(identity)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f338]) ).
fof(f340,plain,
identity = double_divide(identity,identity),
inference(backward_demodulation,[status(thm)],[f343,f328]) ).
fof(f343,plain,
multiply(identity,identity) = identity,
inference(forward_demodulation,[status(thm)],[f14,f339]) ).
fof(f358,plain,
! [X0] : multiply(identity,double_divide(identity,X0)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f328,f315]) ).
fof(f361,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,inverse(multiply(X0,X1)))) = double_divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f364,f169]) ).
fof(f364,plain,
! [X0] : inverse(multiply(X0,identity)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f19,f358]) ).
fof(f365,plain,
! [X0] : inverse(double_divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f316]) ).
fof(f366,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,double_divide(X0,double_divide(X1,X0)))) = X1,
inference(backward_demodulation,[status(thm)],[f376,f31]) ).
fof(f375,plain,
! [X0,X1] : multiply(double_divide(identity,double_divide(X0,double_divide(X1,X0))),inverse(identity)) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f376,f162]) ).
fof(f376,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f12,f365]) ).
fof(f380,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,double_divide(X0,double_divide(X1,X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f376,f322]) ).
fof(f382,plain,
! [X0] : double_divide(inverse(identity),double_divide(identity,inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f364,f324]) ).
fof(f384,plain,
! [X0] : double_divide(inverse(identity),double_divide(identity,multiply(identity,X0))) = X0,
inference(forward_demodulation,[status(thm)],[f14,f382]) ).
fof(f387,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(double_divide(identity,multiply(identity,inverse(X1))),X0),inverse(identity)))) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f18,f327]) ).
fof(f388,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),multiply(inverse(X1),X0)) = X1,
inference(backward_demodulation,[status(thm)],[f330,f40]) ).
fof(f404,plain,
! [X0,X1] : double_divide(X0,multiply(inverse(X1),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f330,f331]) ).
fof(f411,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(backward_demodulation,[status(thm)],[f434,f16]) ).
fof(f413,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(double_divide(identity,multiply(identity,inverse(X1))),X0),identity))) = double_divide(identity,X1),
inference(backward_demodulation,[status(thm)],[f434,f387]) ).
fof(f416,plain,
! [X0] : double_divide(identity,double_divide(identity,multiply(identity,X0))) = X0,
inference(backward_demodulation,[status(thm)],[f434,f384]) ).
fof(f418,plain,
! [X0,X1] : double_divide(identity,double_divide(identity,double_divide(X0,double_divide(X1,X0)))) = X1,
inference(backward_demodulation,[status(thm)],[f434,f380]) ).
fof(f421,plain,
! [X0,X1] : inverse(X0) = double_divide(identity,double_divide(multiply(X1,identity),double_divide(X0,X1))),
inference(backward_demodulation,[status(thm)],[f434,f336]) ).
fof(f434,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f8,f340]) ).
fof(f443,plain,
! [X0,X1] : double_divide(identity,double_divide(identity,inverse(multiply(X0,X1)))) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f434,f361]) ).
fof(f444,plain,
! [X0,X1] : double_divide(identity,multiply(X0,X1)) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f330,f443]) ).
fof(f446,plain,
! [X0,X1] : double_divide(identity,double_divide(identity,double_divide(X0,double_divide(X1,X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f434,f366]) ).
fof(f454,plain,
! [X0,X1] : multiply(double_divide(identity,double_divide(X0,double_divide(X1,X0))),identity) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f434,f375]) ).
fof(f456,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f457,f446]) ).
fof(f457,plain,
! [X0,X1] : double_divide(identity,double_divide(X0,double_divide(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f376,f454]) ).
fof(f477,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(trivial_equality_resolution,[status(thm)],[f411]) ).
fof(f478,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,inverse(multiply(double_divide(identity,multiply(identity,inverse(X1))),X0)))) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f8,f413]) ).
fof(f479,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),multiply(double_divide(identity,multiply(identity,inverse(X1))),X0)) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f330,f478]) ).
fof(f480,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),multiply(double_divide(inverse(X1),identity),X0)) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f444,f479]) ).
fof(f481,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),multiply(inverse(inverse(X1)),X0)) = double_divide(identity,X1),
inference(forward_demodulation,[status(thm)],[f8,f480]) ).
fof(f484,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f514,f444]) ).
fof(f509,plain,
! [X0,X1,X2] : multiply(inverse(double_divide(multiply(X0,X1),double_divide(X2,X0))),double_divide(identity,X1)) = inverse(X2),
inference(backward_demodulation,[status(thm)],[f514,f38]) ).
fof(f514,plain,
! [X0] : inverse(X0) = double_divide(identity,X0),
inference(forward_demodulation,[status(thm)],[f388,f481]) ).
fof(f519,plain,
! [X0] : inverse(double_divide(identity,multiply(identity,X0))) = X0,
inference(forward_demodulation,[status(thm)],[f514,f416]) ).
fof(f520,plain,
! [X0] : multiply(multiply(identity,X0),identity) = X0,
inference(forward_demodulation,[status(thm)],[f12,f519]) ).
fof(f526,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f531,f477]) ).
fof(f531,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f376,f520]) ).
fof(f538,plain,
! [X0,X1] : inverse(double_divide(identity,double_divide(X0,double_divide(X1,X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f514,f418]) ).
fof(f539,plain,
! [X0,X1] : multiply(double_divide(X0,double_divide(X1,X0)),identity) = X1,
inference(forward_demodulation,[status(thm)],[f12,f538]) ).
fof(f540,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f376,f539]) ).
fof(f545,plain,
! [X0,X1] : inverse(X0) = inverse(double_divide(multiply(X1,identity),double_divide(X0,X1))),
inference(forward_demodulation,[status(thm)],[f514,f421]) ).
fof(f546,plain,
! [X0,X1] : inverse(X0) = multiply(double_divide(X0,X1),multiply(X1,identity)),
inference(forward_demodulation,[status(thm)],[f12,f545]) ).
fof(f547,plain,
! [X0,X1] : inverse(X0) = multiply(double_divide(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f376,f546]) ).
fof(f611,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f514,f456]) ).
fof(f727,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(X0,X1),multiply(X1,X2)),double_divide(identity,X2)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f12,f509]) ).
fof(f728,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(X0,X1),multiply(X1,X2)),inverse(X2)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f514,f727]) ).
fof(f734,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(trivial_equality_resolution,[status(thm)],[f526]) ).
fof(f803,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f540,f540]) ).
fof(f1014,plain,
! [X0,X1] : double_divide(X0,multiply(X1,inverse(X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f611,f404]) ).
fof(f1061,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(X1,X2)),inverse(X2)) = inverse(double_divide(X1,X0)),
inference(paramodulation,[status(thm)],[f803,f728]) ).
fof(f1066,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f803,f12]) ).
fof(f1102,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(X1,X2)),inverse(X2)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f12,f1061]) ).
fof(f1440,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(paramodulation,[status(thm)],[f1014,f1066]) ).
fof(f1464,plain,
! [X0,X1,X2] : double_divide(inverse(multiply(X0,multiply(X1,X2))),X2) = multiply(X0,X1),
inference(backward_demodulation,[status(thm)],[f1465,f1102]) ).
fof(f1465,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(inverse(X0),X1),
inference(forward_demodulation,[status(thm)],[f484,f1440]) ).
fof(f1480,plain,
! [X0,X1,X2] : double_divide(double_divide(multiply(X0,X1),X2),X1) = multiply(X2,X0),
inference(forward_demodulation,[status(thm)],[f484,f1464]) ).
fof(f2163,plain,
! [X0,X1,X2] : inverse(double_divide(multiply(X0,X1),X2)) = multiply(multiply(X2,X0),X1),
inference(paramodulation,[status(thm)],[f1480,f547]) ).
fof(f2198,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f2209,f734]) ).
fof(f2209,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f12,f2163]) ).
fof(f2237,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP078-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n002.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 20 19:59:32 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.18/0.52 % Refutation found
% 0.18/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.56 % Elapsed time: 0.088678 seconds
% 0.23/0.56 % CPU time: 0.217566 seconds
% 0.23/0.56 % Total memory used: 21.549 MB
% 0.23/0.56 % Net memory used: 21.299 MB
%------------------------------------------------------------------------------