%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP583-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:34:43 PM UTC 2026
% Result : Unsatisfiable 0.93s 0.55s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 5
% Syntax : Number of formulae : 150 ( 150 unt; 0 def)
% Number of atoms : 150 ( 149 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 246 ( 246 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),double_divide(identity,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)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),inverse(identity)) = X2,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f17,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f18,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f17]) ).
fof(f19,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f17,f9]) ).
fof(f47,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(identity,double_divide(X1,double_divide(inverse(identity),X0)))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f16]) ).
fof(f50,plain,
! [X0,X1,X2] : double_divide(double_divide(multiply(X0,X1),double_divide(double_divide(identity,double_divide(X1,X0)),double_divide(X2,identity))),inverse(identity)) = X2,
inference(paramodulation,[status(thm)],[f19,f16]) ).
fof(f51,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X0),double_divide(X1,identity))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f16]) ).
fof(f55,plain,
! [X0,X1,X2] : multiply(inverse(identity),double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0))))) = inverse(X2),
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f56,plain,
! [X0,X1,X2] : double_divide(double_divide(multiply(X0,X1),double_divide(double_divide(identity,double_divide(X1,X0)),inverse(X2))),inverse(identity)) = X2,
inference(forward_demodulation,[status(thm)],[f8,f50]) ).
fof(f57,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f51]) ).
fof(f64,plain,
! [X0,X1] : multiply(inverse(identity),double_divide(inverse(X0),double_divide(double_divide(identity,X0),double_divide(X1,identity)))) = inverse(X1),
inference(paramodulation,[status(thm)],[f9,f55]) ).
fof(f69,plain,
! [X0,X1] : multiply(inverse(identity),double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1)))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f8,f64]) ).
fof(f74,plain,
! [X0] : multiply(inverse(identity),double_divide(inverse(X0),identity)) = inverse(double_divide(identity,X0)),
inference(paramodulation,[status(thm)],[f9,f69]) ).
fof(f76,plain,
! [X0] : multiply(inverse(identity),double_divide(inverse(identity),double_divide(inverse(identity),inverse(X0)))) = inverse(X0),
inference(paramodulation,[status(thm)],[f8,f69]) ).
fof(f82,plain,
! [X0] : multiply(inverse(identity),inverse(inverse(X0))) = inverse(double_divide(identity,X0)),
inference(forward_demodulation,[status(thm)],[f8,f74]) ).
fof(f83,plain,
! [X0] : multiply(inverse(identity),inverse(inverse(X0))) = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f17,f82]) ).
fof(f87,plain,
! [X0,X1] : multiply(inverse(identity),inverse(multiply(X0,X1))) = multiply(double_divide(X1,X0),identity),
inference(paramodulation,[status(thm)],[f17,f83]) ).
fof(f118,plain,
! [X0,X1] : double_divide(double_divide(multiply(X0,X1),identity),inverse(identity)) = double_divide(identity,double_divide(X1,X0)),
inference(paramodulation,[status(thm)],[f9,f56]) ).
fof(f140,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,X1)),inverse(identity)) = double_divide(identity,double_divide(X1,X0)),
inference(forward_demodulation,[status(thm)],[f8,f118]) ).
fof(f177,plain,
! [X0,X1] : double_divide(inverse(inverse(X0)),inverse(identity)) = double_divide(identity,double_divide(double_divide(inverse(X1),double_divide(double_divide(identity,X1),inverse(X0))),inverse(identity))),
inference(paramodulation,[status(thm)],[f69,f140]) ).
fof(f201,plain,
! [X0] : double_divide(inverse(inverse(X0)),inverse(identity)) = double_divide(identity,X0),
inference(forward_demodulation,[status(thm)],[f57,f177]) ).
fof(f227,plain,
! [X0] : double_divide(double_divide(inverse(identity),double_divide(inverse(identity),inverse(X0))),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f8,f57]) ).
fof(f231,plain,
! [X0,X1,X2] : double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1)))),double_divide(X2,X1))),inverse(identity)) = X2,
inference(paramodulation,[status(thm)],[f57,f16]) ).
fof(f299,plain,
! [X0] : double_divide(double_divide(multiply(double_divide(X0,double_divide(inverse(identity),identity)),identity),X0),inverse(identity)) = identity,
inference(paramodulation,[status(thm)],[f47,f56]) ).
fof(f309,plain,
! [X0] : double_divide(double_divide(multiply(double_divide(X0,inverse(inverse(identity))),identity),X0),inverse(identity)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f299]) ).
fof(f318,plain,
double_divide(double_divide(multiply(identity,identity),inverse(identity)),inverse(identity)) = identity,
inference(paramodulation,[status(thm)],[f9,f309]) ).
fof(f326,plain,
double_divide(double_divide(inverse(inverse(identity)),inverse(identity)),inverse(identity)) = identity,
inference(forward_demodulation,[status(thm)],[f18,f318]) ).
fof(f327,plain,
double_divide(double_divide(identity,identity),inverse(identity)) = identity,
inference(forward_demodulation,[status(thm)],[f201,f326]) ).
fof(f328,plain,
double_divide(inverse(identity),inverse(identity)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f327]) ).
fof(f334,plain,
multiply(inverse(identity),double_divide(inverse(identity),identity)) = inverse(identity),
inference(paramodulation,[status(thm)],[f328,f76]) ).
fof(f335,plain,
double_divide(double_divide(inverse(identity),identity),inverse(identity)) = identity,
inference(paramodulation,[status(thm)],[f328,f227]) ).
fof(f336,plain,
! [X0] : double_divide(double_divide(inverse(identity),double_divide(identity,double_divide(X0,identity))),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f328,f47]) ).
fof(f344,plain,
multiply(inverse(identity),inverse(inverse(identity))) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f8,f334]) ).
fof(f345,plain,
multiply(identity,identity) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f83,f344]) ).
fof(f346,plain,
! [X0] : double_divide(double_divide(multiply(double_divide(X0,inverse(identity)),identity),X0),inverse(identity)) = identity,
inference(backward_demodulation,[status(thm)],[f359,f309]) ).
fof(f359,plain,
inverse(inverse(identity)) = inverse(identity),
inference(forward_demodulation,[status(thm)],[f18,f345]) ).
fof(f360,plain,
double_divide(inverse(inverse(identity)),inverse(identity)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f335]) ).
fof(f361,plain,
double_divide(identity,identity) = identity,
inference(forward_demodulation,[status(thm)],[f201,f360]) ).
fof(f363,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(identity,double_divide(X1,double_divide(inverse(identity),X0)))),identity) = X1,
inference(backward_demodulation,[status(thm)],[f405,f47]) ).
fof(f366,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1))),identity) = X1,
inference(backward_demodulation,[status(thm)],[f405,f57]) ).
fof(f367,plain,
! [X0] : double_divide(inverse(inverse(X0)),identity) = double_divide(identity,X0),
inference(backward_demodulation,[status(thm)],[f405,f201]) ).
fof(f368,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,X1)),identity) = double_divide(identity,double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f405,f140]) ).
fof(f371,plain,
! [X0,X1] : multiply(identity,inverse(multiply(X0,X1))) = multiply(double_divide(X1,X0),identity),
inference(backward_demodulation,[status(thm)],[f405,f87]) ).
fof(f372,plain,
! [X0] : multiply(identity,inverse(inverse(X0))) = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f405,f83]) ).
fof(f375,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),identity) = X2,
inference(backward_demodulation,[status(thm)],[f405,f16]) ).
fof(f385,plain,
! [X0,X1,X2] : double_divide(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1)))),double_divide(X2,X1))),identity) = X2,
inference(backward_demodulation,[status(thm)],[f405,f231]) ).
fof(f405,plain,
inverse(identity) = identity,
inference(forward_demodulation,[status(thm)],[f8,f361]) ).
fof(f406,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f405,f336]) ).
fof(f407,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f406]) ).
fof(f408,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),identity) = X0,
inference(forward_demodulation,[status(thm)],[f405,f407]) ).
fof(f409,plain,
! [X0] : inverse(double_divide(identity,double_divide(identity,inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f408]) ).
fof(f410,plain,
! [X0] : multiply(double_divide(identity,inverse(X0)),identity) = X0,
inference(forward_demodulation,[status(thm)],[f17,f409]) ).
fof(f443,plain,
! [X0] : double_divide(double_divide(multiply(double_divide(X0,identity),identity),X0),inverse(identity)) = identity,
inference(forward_demodulation,[status(thm)],[f405,f346]) ).
fof(f444,plain,
! [X0] : double_divide(double_divide(multiply(inverse(X0),identity),X0),inverse(identity)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f443]) ).
fof(f445,plain,
! [X0] : double_divide(double_divide(multiply(inverse(X0),identity),X0),identity) = identity,
inference(forward_demodulation,[status(thm)],[f405,f444]) ).
fof(f446,plain,
! [X0] : inverse(double_divide(multiply(inverse(X0),identity),X0)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f445]) ).
fof(f447,plain,
! [X0] : multiply(X0,multiply(inverse(X0),identity)) = identity,
inference(forward_demodulation,[status(thm)],[f17,f446]) ).
fof(f506,plain,
! [X0,X1] : inverse(double_divide(X0,double_divide(identity,double_divide(X1,double_divide(inverse(identity),X0))))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f363]) ).
fof(f507,plain,
! [X0,X1] : multiply(double_divide(identity,double_divide(X0,double_divide(inverse(identity),X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f17,f506]) ).
fof(f508,plain,
! [X0,X1] : multiply(double_divide(identity,double_divide(X0,double_divide(identity,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f405,f507]) ).
fof(f517,plain,
! [X0,X1] : inverse(double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f366]) ).
fof(f518,plain,
! [X0,X1] : multiply(double_divide(double_divide(identity,X0),inverse(X1)),inverse(X0)) = X1,
inference(forward_demodulation,[status(thm)],[f17,f517]) ).
fof(f519,plain,
! [X0] : inverse(inverse(inverse(X0))) = double_divide(identity,X0),
inference(forward_demodulation,[status(thm)],[f8,f367]) ).
fof(f522,plain,
! [X0,X1] : multiply(inverse(inverse(multiply(double_divide(identity,X0),X1))),X0) = X1,
inference(backward_demodulation,[status(thm)],[f523,f508]) ).
fof(f523,plain,
! [X0,X1] : inverse(inverse(multiply(X0,X1))) = double_divide(identity,double_divide(X1,X0)),
inference(forward_demodulation,[status(thm)],[f8,f368]) ).
fof(f530,plain,
! [X0,X1] : inverse(inverse(inverse(multiply(X0,X1)))) = multiply(double_divide(X1,X0),identity),
inference(forward_demodulation,[status(thm)],[f18,f371]) ).
fof(f532,plain,
! [X0,X1] : double_divide(identity,multiply(X0,X1)) = multiply(double_divide(X1,X0),identity),
inference(forward_demodulation,[status(thm)],[f519,f530]) ).
fof(f533,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f18,f372]) ).
fof(f534,plain,
! [X0] : multiply(multiply(X0,identity),identity) = X0,
inference(backward_demodulation,[status(thm)],[f535,f410]) ).
fof(f535,plain,
! [X0] : double_divide(identity,inverse(X0)) = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f519,f533]) ).
fof(f540,plain,
! [X0,X1,X2] : inverse(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0))))) = X2,
inference(forward_demodulation,[status(thm)],[f8,f375]) ).
fof(f542,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(identity,X0),double_divide(X1,double_divide(X0,X2))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f17,f540]) ).
fof(f583,plain,
! [X0,X1,X2] : inverse(double_divide(inverse(identity),double_divide(double_divide(identity,double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1)))),double_divide(X2,X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f8,f385]) ).
fof(f584,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(identity,double_divide(inverse(X0),double_divide(double_divide(identity,X0),inverse(X1)))),double_divide(X2,X1)),inverse(identity)) = X2,
inference(forward_demodulation,[status(thm)],[f17,f583]) ).
fof(f585,plain,
! [X0,X1,X2] : multiply(double_divide(inverse(inverse(multiply(double_divide(double_divide(identity,X0),inverse(X1)),inverse(X0)))),double_divide(X2,X1)),inverse(identity)) = X2,
inference(forward_demodulation,[status(thm)],[f523,f584]) ).
fof(f586,plain,
! [X0,X1] : multiply(double_divide(inverse(inverse(X0)),double_divide(X1,X0)),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f518,f585]) ).
fof(f588,plain,
! [X0,X1] : multiply(double_divide(inverse(inverse(X0)),double_divide(X1,X0)),identity) = X1,
inference(forward_demodulation,[status(thm)],[f405,f586]) ).
fof(f734,plain,
! [X0] : identity = double_divide(double_divide(identity,multiply(X0,identity)),X0),
inference(paramodulation,[status(thm)],[f534,f19]) ).
fof(f741,plain,
! [X0] : identity = double_divide(multiply(double_divide(identity,X0),identity),X0),
inference(forward_demodulation,[status(thm)],[f532,f734]) ).
fof(f759,plain,
! [X0] : inverse(inverse(double_divide(identity,X0))) = double_divide(identity,inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f519,f519]) ).
fof(f767,plain,
! [X0] : inverse(multiply(X0,identity)) = double_divide(identity,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f17,f759]) ).
fof(f768,plain,
! [X0] : multiply(X0,inverse(multiply(X0,identity))) = identity,
inference(backward_demodulation,[status(thm)],[f771,f447]) ).
fof(f771,plain,
! [X0] : inverse(multiply(X0,identity)) = multiply(inverse(X0),identity),
inference(forward_demodulation,[status(thm)],[f535,f767]) ).
fof(f809,plain,
! [X0] : multiply(inverse(inverse(identity)),X0) = inverse(multiply(double_divide(identity,X0),identity)),
inference(paramodulation,[status(thm)],[f768,f522]) ).
fof(f815,plain,
! [X0] : multiply(inverse(identity),X0) = inverse(multiply(double_divide(identity,X0),identity)),
inference(forward_demodulation,[status(thm)],[f405,f809]) ).
fof(f816,plain,
! [X0] : multiply(identity,X0) = inverse(multiply(double_divide(identity,X0),identity)),
inference(forward_demodulation,[status(thm)],[f405,f815]) ).
fof(f817,plain,
! [X0] : inverse(inverse(X0)) = inverse(multiply(double_divide(identity,X0),identity)),
inference(forward_demodulation,[status(thm)],[f18,f816]) ).
fof(f893,plain,
! [X0,X1] : multiply(double_divide(double_divide(identity,X0),identity),X1) = multiply(double_divide(identity,double_divide(X0,X1)),identity),
inference(paramodulation,[status(thm)],[f741,f542]) ).
fof(f897,plain,
! [X0] : multiply(X0,multiply(double_divide(identity,X0),identity)) = inverse(identity),
inference(paramodulation,[status(thm)],[f741,f17]) ).
fof(f914,plain,
! [X0,X1] : multiply(inverse(double_divide(identity,X0)),X1) = multiply(double_divide(identity,double_divide(X0,X1)),identity),
inference(forward_demodulation,[status(thm)],[f8,f893]) ).
fof(f915,plain,
! [X0,X1] : multiply(multiply(X0,identity),X1) = multiply(double_divide(identity,double_divide(X0,X1)),identity),
inference(forward_demodulation,[status(thm)],[f17,f914]) ).
fof(f916,plain,
! [X0,X1] : multiply(multiply(X0,identity),X1) = multiply(inverse(inverse(multiply(X1,X0))),identity),
inference(forward_demodulation,[status(thm)],[f523,f915]) ).
fof(f917,plain,
! [X0,X1] : multiply(multiply(X0,identity),X1) = inverse(multiply(inverse(multiply(X1,X0)),identity)),
inference(forward_demodulation,[status(thm)],[f771,f916]) ).
fof(f918,plain,
! [X0,X1] : multiply(multiply(X0,identity),X1) = inverse(inverse(multiply(multiply(X1,X0),identity))),
inference(forward_demodulation,[status(thm)],[f771,f917]) ).
fof(f936,plain,
! [X0] : multiply(X0,multiply(double_divide(identity,X0),identity)) = identity,
inference(forward_demodulation,[status(thm)],[f405,f897]) ).
fof(f938,plain,
! [X0] : multiply(inverse(X0),multiply(multiply(X0,identity),identity)) = identity,
inference(paramodulation,[status(thm)],[f535,f936]) ).
fof(f947,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(forward_demodulation,[status(thm)],[f534,f938]) ).
fof(f981,plain,
! [X0,X1] : multiply(multiply(X0,X1),double_divide(X1,X0)) = identity,
inference(paramodulation,[status(thm)],[f17,f947]) ).
fof(f1087,plain,
! [X0,X1] : inverse(multiply(double_divide(X0,X1),identity)) = multiply(multiply(X1,X0),identity),
inference(paramodulation,[status(thm)],[f17,f771]) ).
fof(f1111,plain,
! [X0] : inverse(inverse(X0)) = multiply(multiply(X0,identity),identity),
inference(backward_demodulation,[status(thm)],[f1087,f817]) ).
fof(f1122,plain,
! [X0,X1] : multiply(multiply(double_divide(identity,X0),X1),X0) = X1,
inference(backward_demodulation,[status(thm)],[f1143,f522]) ).
fof(f1123,plain,
! [X0] : inverse(X0) = double_divide(identity,X0),
inference(backward_demodulation,[status(thm)],[f1143,f519]) ).
fof(f1127,plain,
! [X0,X1] : multiply(multiply(X0,identity),X1) = multiply(multiply(X1,X0),identity),
inference(backward_demodulation,[status(thm)],[f1143,f918]) ).
fof(f1142,plain,
! [X0,X1] : multiply(double_divide(X0,double_divide(X1,X0)),identity) = X1,
inference(backward_demodulation,[status(thm)],[f1143,f588]) ).
fof(f1143,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f534,f1111]) ).
fof(f1144,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f1123,f535]) ).
fof(f1148,plain,
! [X0,X1,X2] : multiply(double_divide(inverse(X0),double_divide(X1,double_divide(X0,X2))),X2) = X1,
inference(backward_demodulation,[status(thm)],[f1123,f542]) ).
fof(f1150,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(backward_demodulation,[status(thm)],[f1123,f1122]) ).
fof(f1173,plain,
! [X0,X1] : multiply(multiply(X0,identity),X1) = multiply(X1,X0),
inference(backward_demodulation,[status(thm)],[f1183,f1127]) ).
fof(f1176,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(backward_demodulation,[status(thm)],[f1183,f1142]) ).
fof(f1183,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f1143,f1144]) ).
fof(f1195,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(c3,b3)),
inference(backward_demodulation,[status(thm)],[f1203,f10]) ).
fof(f1196,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(backward_demodulation,[status(thm)],[f1203,f1150]) ).
fof(f1199,plain,
! [X0,X1,X2] : multiply(X0,double_divide(inverse(X1),double_divide(X2,double_divide(X1,X0)))) = X2,
inference(backward_demodulation,[status(thm)],[f1203,f1148]) ).
fof(f1203,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f1183,f1173]) ).
fof(f1210,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(c3,b3)),
inference(forward_demodulation,[status(thm)],[f1203,f1195]) ).
fof(f1211,plain,
multiply(c3,multiply(b3,a3)) != multiply(a3,multiply(c3,b3)),
inference(forward_demodulation,[status(thm)],[f1203,f1210]) ).
fof(f1213,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(multiply(X1,X2),double_divide(X3,double_divide(double_divide(X2,X1),X0)))) = X3,
inference(paramodulation,[status(thm)],[f17,f1199]) ).
fof(f1258,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f1176,f1176]) ).
fof(f1265,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f1176,f17]) ).
fof(f1277,plain,
! [X0,X1] : multiply(X0,double_divide(X1,X0)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f1203,f1265]) ).
fof(f1333,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f1258,f17]) ).
fof(f1364,plain,
! [X0,X1] : multiply(multiply(X0,X1),double_divide(X0,X1)) = identity,
inference(paramodulation,[status(thm)],[f1203,f981]) ).
fof(f1446,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(multiply(X1,X0),X2)) = X2,
inference(paramodulation,[status(thm)],[f17,f1196]) ).
fof(f1486,plain,
! [X0,X1,X2,X3] : multiply(X0,X1) = double_divide(multiply(X2,X3),double_divide(X1,double_divide(double_divide(X3,X2),inverse(X0)))),
inference(paramodulation,[status(thm)],[f1213,f1196]) ).
fof(f1649,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f1277,f1196]) ).
fof(f1659,plain,
! [X0,X1,X2,X3] : multiply(X0,X1) = double_divide(multiply(X2,X3),double_divide(X1,multiply(X0,inverse(double_divide(X3,X2))))),
inference(backward_demodulation,[status(thm)],[f1649,f1486]) ).
fof(f1670,plain,
! [X0,X1,X2,X3] : multiply(X0,X1) = double_divide(multiply(X2,X3),double_divide(X1,multiply(X0,multiply(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f17,f1659]) ).
fof(f2398,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,X1) = double_divide(X2,double_divide(X1,multiply(X0,multiply(double_divide(X3,X4),multiply(multiply(X4,X3),X2))))),
inference(paramodulation,[status(thm)],[f1446,f1670]) ).
fof(f2444,plain,
! [X0,X1,X2] : multiply(X0,X1) = double_divide(X2,double_divide(X1,multiply(X0,X2))),
inference(forward_demodulation,[status(thm)],[f1446,f2398]) ).
fof(f2716,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = double_divide(double_divide(X0,X1),double_divide(X2,identity)),
inference(paramodulation,[status(thm)],[f1364,f2444]) ).
fof(f2736,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = inverse(double_divide(X2,multiply(X1,X0))),
inference(paramodulation,[status(thm)],[f2444,f1333]) ).
fof(f2760,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = double_divide(double_divide(X0,X1),inverse(X2)),
inference(forward_demodulation,[status(thm)],[f8,f2716]) ).
fof(f2761,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X2,inverse(double_divide(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1649,f2760]) ).
fof(f2762,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X2,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f2761]) ).
fof(f2807,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X2,multiply(X0,X1)),
inference(backward_demodulation,[status(thm)],[f2811,f2762]) ).
fof(f2811,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f17,f2736]) ).
fof(f2853,plain,
multiply(c3,multiply(b3,a3)) != multiply(b3,multiply(a3,c3)),
inference(backward_demodulation,[status(thm)],[f2807,f1211]) ).
fof(f2864,plain,
multiply(c3,multiply(b3,a3)) != multiply(c3,multiply(b3,a3)),
inference(forward_demodulation,[status(thm)],[f2807,f2853]) ).
fof(f2865,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP583-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:22:42 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.93/0.55 % Refutation found
% 0.93/0.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.93/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.93/0.58 % Elapsed time: 0.212049 seconds
% 0.93/0.58 % CPU time: 1.508199 seconds
% 0.93/0.58 % Total memory used: 43.666 MB
% 0.93/0.58 % Net memory used: 38.832 MB
%------------------------------------------------------------------------------