%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP108-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:32:32 PM UTC 2026
% Result : Unsatisfiable 0.12s 5.57s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 3
% Syntax : Number of formulae : 107 ( 100 unt; 0 def)
% Number of atoms : 123 ( 122 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 25 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 337 ( 337 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : inverse(double_divide(inverse(double_divide(X,inverse(double_divide(Y,double_divide(X,Z))))),Z)) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = inverse(double_divide(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : inverse(double_divide(inverse(double_divide(X0,inverse(double_divide(X1,double_divide(X0,X2))))),X2)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f7,plain,
! [X0,X1,X2] : multiply(X0,inverse(double_divide(X1,inverse(double_divide(X2,double_divide(X1,X0)))))) = X2,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f8,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(double_divide(X1,double_divide(X2,X0))),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f7]) ).
fof(f9,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(double_divide(X1,X0),X2),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f5,f8]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = multiply(multiply(double_divide(X3,double_divide(X2,X0)),X1),X3),
inference(paramodulation,[status(thm)],[f9,f9]) ).
fof(f12,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X1,multiply(X2,X0))) = X2,
inference(paramodulation,[status(thm)],[f10,f9]) ).
fof(f14,plain,
! [X0,X1,X2] : multiply(double_divide(multiply(X0,X1),double_divide(X1,X2)),X0) = X2,
inference(paramodulation,[status(thm)],[f12,f12]) ).
fof(f15,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(X0,multiply(double_divide(multiply(X1,X0),double_divide(X2,X3)),X4)),multiply(X3,multiply(X4,X2))) = X1,
inference(paramodulation,[status(thm)],[f10,f12]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(X0,multiply(X1,X2)),X3),multiply(X3,X1)) = double_divide(X2,X0),
inference(paramodulation,[status(thm)],[f12,f12]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(X0,X1),multiply(X1,multiply(X2,multiply(X3,X4)))) = multiply(double_divide(X0,double_divide(X4,X2)),X3),
inference(paramodulation,[status(thm)],[f10,f12]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(double_divide(X0,multiply(double_divide(X1,double_divide(X2,X3)),X4)),multiply(X3,multiply(X4,X2))) = double_divide(multiply(X0,X5),double_divide(X5,X1)),
inference(paramodulation,[status(thm)],[f14,f15]) ).
fof(f55,plain,
! [X0,X1,X2] : X0 = double_divide(X1,multiply(double_divide(multiply(X2,X1),X0),X2)),
inference(paramodulation,[status(thm)],[f14,f17]) ).
fof(f57,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(X0,X1),multiply(X1,X2)) = double_divide(X3,double_divide(multiply(multiply(X2,X3),X4),double_divide(X4,X0))),
inference(paramodulation,[status(thm)],[f14,f17]) ).
fof(f89,plain,
! [X0,X1,X2] : X0 = double_divide(multiply(X1,X2),double_divide(X2,multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f17,f55]) ).
fof(f106,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(multiply(X0,X1),X2),X0),X1) = inverse(X2),
inference(paramodulation,[status(thm)],[f55,f5]) ).
fof(f131,plain,
! [X0,X1,X2] : multiply(double_divide(X0,multiply(X1,X2)),multiply(X2,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f89,f5]) ).
fof(f155,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),multiply(X1,inverse(X2))) = multiply(double_divide(multiply(X3,X0),X2),X3),
inference(paramodulation,[status(thm)],[f106,f12]) ).
fof(f161,plain,
! [X0,X1,X2] : X0 = inverse(double_divide(multiply(X0,multiply(X1,X2)),double_divide(X2,X1))),
inference(paramodulation,[status(thm)],[f15,f131]) ).
fof(f166,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,inverse(X1)),multiply(multiply(X2,X3),X0)) = inverse(double_divide(X3,multiply(X1,X2))),
inference(paramodulation,[status(thm)],[f131,f131]) ).
fof(f168,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,inverse(X1)),multiply(X2,X0)) = inverse(multiply(double_divide(multiply(X3,X2),X1),X3)),
inference(paramodulation,[status(thm)],[f106,f131]) ).
fof(f184,plain,
! [X0,X1,X2,X3] : multiply(multiply(double_divide(inverse(X0),X1),double_divide(X2,multiply(X0,X3))),multiply(X3,X2)) = inverse(X1),
inference(paramodulation,[status(thm)],[f131,f106]) ).
fof(f187,plain,
! [X0,X1,X2,X3] : X0 = double_divide(multiply(X1,X2),multiply(double_divide(inverse(X3),X0),double_divide(X2,multiply(X3,X1)))),
inference(paramodulation,[status(thm)],[f131,f55]) ).
fof(f192,plain,
! [X0,X1,X2,X3] : multiply(double_divide(inverse(X0),double_divide(multiply(X1,X2),X3)),double_divide(X2,multiply(X0,X1))) = X3,
inference(paramodulation,[status(thm)],[f131,f14]) ).
fof(f193,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(X0,X1),X2),multiply(X2,inverse(X3))) = double_divide(X1,multiply(X3,X0)),
inference(paramodulation,[status(thm)],[f131,f12]) ).
fof(f194,plain,
! [X0,X1,X2] : X0 = multiply(double_divide(X1,X2),multiply(X0,multiply(X2,X1))),
inference(forward_demodulation,[status(thm)],[f5,f161]) ).
fof(f198,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,inverse(X1)),multiply(multiply(X2,X3),X0)) = multiply(multiply(X1,X2),X3),
inference(forward_demodulation,[status(thm)],[f5,f166]) ).
fof(f206,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,multiply(X1,X2)),X3) = multiply(double_divide(X1,X3),double_divide(X2,X0)),
inference(paramodulation,[status(thm)],[f17,f194]) ).
fof(f207,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(X0,X1),X2),double_divide(X2,X3)) = multiply(double_divide(X1,X0),X3),
inference(paramodulation,[status(thm)],[f14,f194]) ).
fof(f209,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,X2)) = multiply(double_divide(X0,X2),inverse(X1)),
inference(paramodulation,[status(thm)],[f131,f194]) ).
fof(f211,plain,
! [X0,X1,X2] : double_divide(X0,X1) = multiply(double_divide(multiply(X2,X0),X1),X2),
inference(paramodulation,[status(thm)],[f12,f194]) ).
fof(f213,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(multiply(X0,X1),double_divide(X2,X3)),X4) = multiply(double_divide(X1,X0),multiply(X3,multiply(X4,X2))),
inference(paramodulation,[status(thm)],[f10,f194]) ).
fof(f218,plain,
! [X0,X1,X2,X3] : X0 = multiply(double_divide(multiply(X1,X2),double_divide(X2,multiply(X3,X1))),multiply(X0,inverse(X3))),
inference(paramodulation,[status(thm)],[f131,f194]) ).
fof(f289,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),multiply(X1,X2)) = double_divide(X3,multiply(double_divide(X3,X2),X0)),
inference(backward_demodulation,[status(thm)],[f207,f57]) ).
fof(f309,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(backward_demodulation,[status(thm)],[f211,f14]) ).
fof(f310,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X0) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f211,f106]) ).
fof(f313,plain,
! [X0,X1,X2] : multiply(double_divide(X0,inverse(X1)),multiply(X2,X0)) = inverse(double_divide(X2,X1)),
inference(backward_demodulation,[status(thm)],[f211,f168]) ).
fof(f314,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X1,inverse(X2))) = double_divide(X0,X2),
inference(backward_demodulation,[status(thm)],[f211,f155]) ).
fof(f335,plain,
! [X0,X1,X2,X3] : X0 = multiply(double_divide(X1,X2),multiply(multiply(X3,X2),multiply(multiply(X0,inverse(X3)),X1))),
inference(forward_demodulation,[status(thm)],[f213,f218]) ).
fof(f405,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(backward_demodulation,[status(thm)],[f406,f198]) ).
fof(f406,plain,
! [X0,X1,X2] : multiply(double_divide(X0,inverse(X1)),multiply(X2,X0)) = multiply(X1,X2),
inference(forward_demodulation,[status(thm)],[f5,f313]) ).
fof(f407,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),X2) = double_divide(X1,multiply(X2,X0)),
inference(backward_demodulation,[status(thm)],[f314,f193]) ).
fof(f419,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = multiply(double_divide(X3,double_divide(X2,X0)),multiply(X1,X3)),
inference(backward_demodulation,[status(thm)],[f405,f10]) ).
fof(f421,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f405,f6]) ).
fof(f426,plain,
! [X0,X1,X2,X3] : multiply(double_divide(inverse(X0),X1),multiply(double_divide(X2,multiply(X0,X3)),multiply(X3,X2))) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f405,f184]) ).
fof(f462,plain,
! [X0,X1,X2,X3] : X0 = multiply(double_divide(X1,X2),multiply(multiply(X3,X2),multiply(X0,multiply(inverse(X3),X1)))),
inference(backward_demodulation,[status(thm)],[f405,f335]) ).
fof(f472,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,multiply(X1,X2)),double_divide(X2,X3)) = multiply(double_divide(X1,X0),X3),
inference(backward_demodulation,[status(thm)],[f405,f207]) ).
fof(f475,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),multiply(X2,X3)) = multiply(double_divide(X0,X2),double_divide(X1,X3)),
inference(backward_demodulation,[status(thm)],[f407,f206]) ).
fof(f476,plain,
! [X0,X1,X2,X3] : X0 = double_divide(X1,multiply(multiply(double_divide(inverse(X2),X0),double_divide(X1,multiply(X2,X3))),X3)),
inference(backward_demodulation,[status(thm)],[f407,f187]) ).
fof(f489,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(X0,multiply(double_divide(X1,X2),X3)),X4) = multiply(double_divide(X0,X3),multiply(X2,multiply(X4,X1))),
inference(backward_demodulation,[status(thm)],[f407,f213]) ).
fof(f494,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(double_divide(X0,multiply(double_divide(X1,double_divide(X2,X3)),X4)),multiply(X3,multiply(X4,X2))) = double_divide(X5,multiply(double_divide(X5,X1),X0)),
inference(backward_demodulation,[status(thm)],[f407,f33]) ).
fof(f505,plain,
! [X0,X1,X2,X3] : multiply(double_divide(inverse(X0),double_divide(X1,multiply(X2,X3))),double_divide(X1,multiply(X0,X3))) = X2,
inference(backward_demodulation,[status(thm)],[f407,f192]) ).
fof(f507,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(inverse(b2),multiply(b2,a2)) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(forward_demodulation,[status(thm)],[f405,f421]) ).
fof(f508,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(b2),multiply(b2,a2)) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(trivial_equality_resolution,[status(thm)],[f507]) ).
fof(f516,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),X1),inverse(X0)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f131,f426]) ).
fof(f517,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(X0,X1)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f209,f516]) ).
fof(f570,plain,
! [X0,X1,X2,X3] : X0 = multiply(double_divide(X1,X2),multiply(X3,multiply(X2,multiply(X0,multiply(inverse(X3),X1))))),
inference(forward_demodulation,[status(thm)],[f405,f462]) ).
fof(f579,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X1,X2)),double_divide(X1,X3)) = multiply(double_divide(X0,X3),X2),
inference(forward_demodulation,[status(thm)],[f206,f472]) ).
fof(f580,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(multiply(X1,X2),X3)) = multiply(double_divide(X3,X1),double_divide(X0,X2)),
inference(forward_demodulation,[status(thm)],[f407,f475]) ).
fof(f589,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,multiply(X2,X3))) = multiply(double_divide(X3,X1),double_divide(X0,X2)),
inference(forward_demodulation,[status(thm)],[f405,f580]) ).
fof(f590,plain,
! [X0,X1,X2,X3] : X0 = double_divide(X1,multiply(double_divide(inverse(X2),X0),multiply(double_divide(X1,multiply(X2,X3)),X3))),
inference(forward_demodulation,[status(thm)],[f405,f476]) ).
fof(f591,plain,
! [X0,X1,X2,X3] : X0 = multiply(double_divide(X1,double_divide(inverse(X2),X0)),double_divide(X3,double_divide(X3,multiply(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f589,f590]) ).
fof(f592,plain,
! [X0,X1,X2] : X0 = multiply(double_divide(X1,double_divide(inverse(X2),X0)),multiply(X2,X1)),
inference(forward_demodulation,[status(thm)],[f309,f591]) ).
fof(f593,plain,
! [X0,X1] : X0 = multiply(X0,multiply(X1,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f419,f592]) ).
fof(f633,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(double_divide(X0,X1),multiply(double_divide(X2,X3),multiply(multiply(X3,multiply(X1,X2)),X4))) = double_divide(X5,multiply(double_divide(X5,X4),X0)),
inference(forward_demodulation,[status(thm)],[f489,f494]) ).
fof(f634,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(double_divide(X0,X1),multiply(double_divide(X2,X3),multiply(X3,multiply(multiply(X1,X2),X4)))) = double_divide(X5,multiply(double_divide(X5,X4),X0)),
inference(forward_demodulation,[status(thm)],[f405,f633]) ).
fof(f635,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(double_divide(X0,X1),multiply(double_divide(X2,X3),multiply(X3,multiply(X1,multiply(X2,X4))))) = double_divide(X5,multiply(double_divide(X5,X4),X0)),
inference(forward_demodulation,[status(thm)],[f405,f634]) ).
fof(f636,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(X0,X1),multiply(double_divide(X2,double_divide(X3,X1)),X2)) = double_divide(X4,multiply(double_divide(X4,X3),X0)),
inference(forward_demodulation,[status(thm)],[f18,f635]) ).
fof(f637,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),inverse(double_divide(X2,X1))) = double_divide(X3,multiply(double_divide(X3,X2),X0)),
inference(forward_demodulation,[status(thm)],[f310,f636]) ).
fof(f638,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(double_divide(X1,X2),X2)) = double_divide(X3,multiply(double_divide(X3,X1),X0)),
inference(forward_demodulation,[status(thm)],[f209,f637]) ).
fof(f660,plain,
! [X0,X1,X2] : multiply(double_divide(inverse(X0),multiply(X0,X1)),multiply(X2,X1)) = X2,
inference(forward_demodulation,[status(thm)],[f579,f505]) ).
fof(f661,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f517,f660]) ).
fof(f786,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(paramodulation,[status(thm)],[f661,f661]) ).
fof(f788,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,multiply(X1,X2))),X0) = double_divide(X2,X1),
inference(paramodulation,[status(thm)],[f194,f661]) ).
fof(f794,plain,
! [X0,X1] : inverse(X0) = multiply(double_divide(X0,X1),X1),
inference(paramodulation,[status(thm)],[f661,f194]) ).
fof(f807,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f786,f788]) ).
fof(f815,plain,
! [X0,X1,X2] : double_divide(X0,inverse(X1)) = double_divide(X2,multiply(double_divide(X2,X1),X0)),
inference(backward_demodulation,[status(thm)],[f794,f638]) ).
fof(f834,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X1,X2)) = double_divide(X0,inverse(X2)),
inference(backward_demodulation,[status(thm)],[f815,f289]) ).
fof(f843,plain,
! [X0,X1,X2,X3] : double_divide(X0,inverse(multiply(X1,multiply(X2,X3)))) = multiply(double_divide(X0,double_divide(X3,X1)),X2),
inference(backward_demodulation,[status(thm)],[f834,f18]) ).
fof(f848,plain,
! [X0,X1,X2,X3] : double_divide(X0,double_divide(multiply(X1,X2),X3)) = multiply(double_divide(X0,double_divide(X2,X3)),X1),
inference(forward_demodulation,[status(thm)],[f807,f843]) ).
fof(f852,plain,
! [X0,X1,X2,X3] : double_divide(X0,double_divide(X1,multiply(X2,X3))) = multiply(double_divide(X0,double_divide(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f407,f848]) ).
fof(f862,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(inverse(X1),X2)) = multiply(double_divide(multiply(X3,X1),double_divide(X2,X0)),X3),
inference(paramodulation,[status(thm)],[f661,f419]) ).
fof(f870,plain,
! [X0,X1,X2,X3] : double_divide(X0,double_divide(X1,X2)) = multiply(double_divide(X0,X3),multiply(X2,multiply(X3,X1))),
inference(paramodulation,[status(thm)],[f419,f194]) ).
fof(f877,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(inverse(X1),X2)) = multiply(double_divide(X1,multiply(double_divide(X2,X0),X3)),X3),
inference(forward_demodulation,[status(thm)],[f407,f862]) ).
fof(f881,plain,
! [X0,X1,X2] : X0 = multiply(X1,multiply(inverse(X2),multiply(X0,multiply(inverse(X1),X2)))),
inference(backward_demodulation,[status(thm)],[f887,f570]) ).
fof(f887,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(inverse(X1),X2)) = multiply(double_divide(X1,X3),multiply(X0,multiply(X3,X2))),
inference(forward_demodulation,[status(thm)],[f489,f877]) ).
fof(f918,plain,
! [X0,X1,X2] : double_divide(X0,double_divide(X1,X2)) = multiply(X2,multiply(inverse(X0),X1)),
inference(forward_demodulation,[status(thm)],[f887,f870]) ).
fof(f950,plain,
! [X0,X1,X2] : X0 = double_divide(X1,double_divide(multiply(X0,multiply(inverse(X2),X1)),X2)),
inference(forward_demodulation,[status(thm)],[f918,f881]) ).
fof(f951,plain,
! [X0,X1,X2] : X0 = double_divide(X1,double_divide(multiply(inverse(X2),X1),multiply(X2,X0))),
inference(forward_demodulation,[status(thm)],[f407,f950]) ).
fof(f952,plain,
! [X0,X1,X2] : X0 = multiply(double_divide(X1,double_divide(multiply(inverse(X2),X1),X2)),X0),
inference(forward_demodulation,[status(thm)],[f852,f951]) ).
fof(f953,plain,
! [X0,X1,X2] : X0 = multiply(double_divide(X1,double_divide(X1,multiply(X2,inverse(X2)))),X0),
inference(forward_demodulation,[status(thm)],[f407,f952]) ).
fof(f954,plain,
! [X0,X1] : X0 = multiply(multiply(X1,inverse(X1)),X0),
inference(forward_demodulation,[status(thm)],[f309,f953]) ).
fof(f955,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(forward_demodulation,[status(thm)],[f405,f954]) ).
fof(f959,plain,
! [X0,X1] : X0 = double_divide(X1,double_divide(X0,X1)),
inference(forward_demodulation,[status(thm)],[f918,f955]) ).
fof(f1158,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f959,f310]) ).
fof(f1171,plain,
( multiply(inverse(b2),multiply(b2,a2)) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_subsumption_resolution,[status(thm)],[f508,f1172]) ).
fof(f1172,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f5,f1158]) ).
fof(f1208,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f1172,f661]) ).
fof(f1220,plain,
( a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f1208,f1171]) ).
fof(f1224,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(trivial_equality_resolution,[status(thm)],[f1220]) ).
fof(f1352,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f593,f1208]) ).
fof(f1772,plain,
multiply(inverse(a1),a1) != multiply(b1,inverse(b1)),
inference(paramodulation,[status(thm)],[f1172,f1224]) ).
fof(f1774,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1772,f1352]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP108-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n005.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sun Sep 20 19:57:39 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.12/5.57 % Refutation found
% 0.12/5.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/5.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/5.59 % Elapsed time: 0.205976 seconds
% 0.12/5.59 % CPU time: 1.456602 seconds
% 0.12/5.59 % Total memory used: 99.564 MB
% 0.12/5.59 % Net memory used: 96.403 MB
%------------------------------------------------------------------------------