%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP110-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.14s 0.53s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 3
% Syntax : Number of formulae : 123 ( 116 unt; 0 def)
% Number of atoms : 141 ( 140 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 26 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 7 ( 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 : 399 ( 399 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : inverse(double_divide(inverse(double_divide(inverse(double_divide(X,Y)),Z)),double_divide(X,Z))) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = inverse(double_divide(Y,X)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : inverse(double_divide(inverse(double_divide(inverse(double_divide(X0,X1)),X2)),double_divide(X0,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(double_divide(X0,X1),inverse(double_divide(inverse(double_divide(X0,X2)),X1))) = X2,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f8,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X1,inverse(double_divide(X0,X2)))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f7]) ).
fof(f9,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X1,multiply(X2,X0))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f8]) ).
fof(f10,plain,
! [X0,X1,X2] : multiply(double_divide(multiply(X0,X1),double_divide(X1,X2)),X0) = X2,
inference(paramodulation,[status(thm)],[f9,f9]) ).
fof(f11,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)],[f9,f9]) ).
fof(f12,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X1,X2)),double_divide(multiply(X1,X3),double_divide(X3,X0))) = X2,
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),multiply(X1,X2)) = double_divide(multiply(X0,X3),double_divide(X3,X2)),
inference(paramodulation,[status(thm)],[f10,f9]) ).
fof(f16,plain,
! [X0,X1,X2] : X0 = double_divide(X1,multiply(double_divide(multiply(X2,X1),X0),X2)),
inference(paramodulation,[status(thm)],[f10,f11]) ).
fof(f22,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(multiply(X0,X1),X2),multiply(X2,double_divide(X3,X4))) = double_divide(multiply(X4,multiply(X1,X3)),X0),
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f32,plain,
! [X0,X1,X2] : X0 = double_divide(multiply(X1,X2),double_divide(X2,multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f11,f16]) ).
fof(f34,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(X0,multiply(X1,X2)),X3),X0) = double_divide(X2,multiply(X3,X1)),
inference(paramodulation,[status(thm)],[f16,f16]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4] : X0 = double_divide(multiply(X1,X2),multiply(double_divide(double_divide(X3,X4),X0),double_divide(multiply(X4,multiply(X2,X3)),X1))),
inference(paramodulation,[status(thm)],[f11,f16]) ).
fof(f41,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(multiply(X0,X1),X2),X0),X1) = inverse(X2),
inference(paramodulation,[status(thm)],[f16,f5]) ).
fof(f73,plain,
! [X0,X1,X2] : multiply(double_divide(X0,multiply(X1,X2)),multiply(X2,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f32,f5]) ).
fof(f82,plain,
! [X0,X1,X2,X3] : multiply(multiply(double_divide(X0,X1),double_divide(X2,X3)),multiply(X3,multiply(X0,X2))) = inverse(X1),
inference(paramodulation,[status(thm)],[f9,f41]) ).
fof(f84,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,multiply(double_divide(multiply(X1,multiply(X2,X0)),X3),X1)),inverse(X3)) = X2,
inference(paramodulation,[status(thm)],[f41,f9]) ).
fof(f88,plain,
! [X0,X1,X2,X3] : X0 = double_divide(X1,multiply(double_divide(inverse(X2),X0),multiply(double_divide(multiply(X3,X1),X2),X3))),
inference(paramodulation,[status(thm)],[f41,f16]) ).
fof(f91,plain,
! [X0,X1,X2,X3] : multiply(double_divide(inverse(X0),double_divide(X1,X2)),multiply(double_divide(multiply(X3,X1),X0),X3)) = X2,
inference(paramodulation,[status(thm)],[f41,f10]) ).
fof(f95,plain,
! [X0,X1,X2] : multiply(double_divide(X0,double_divide(X0,multiply(X1,X2))),inverse(X1)) = X2,
inference(forward_demodulation,[status(thm)],[f34,f84]) ).
fof(f97,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)],[f41,f73]) ).
fof(f100,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)],[f73,f73]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(X0,X1),multiply(double_divide(multiply(X2,X3),double_divide(X3,X4)),X0)) = inverse(double_divide(X4,double_divide(X2,X1))),
inference(paramodulation,[status(thm)],[f12,f73]) ).
fof(f122,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,f100]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(X0,X1),multiply(double_divide(multiply(X2,X3),double_divide(X3,X4)),X0)) = multiply(double_divide(X2,X1),X4),
inference(forward_demodulation,[status(thm)],[f5,f101]) ).
fof(f127,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X0,inverse(X1))),inverse(multiply(double_divide(multiply(X2,X3),X1),X2))) = X3,
inference(paramodulation,[status(thm)],[f41,f95]) ).
fof(f133,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X0,X1)),inverse(double_divide(X2,X3))) = multiply(X3,multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f9,f95]) ).
fof(f134,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X0,multiply(double_divide(X1,X2),X3))),multiply(X2,X1)) = X3,
inference(paramodulation,[status(thm)],[f5,f95]) ).
fof(f135,plain,
! [X0,X1,X2] : multiply(X0,X1) = inverse(double_divide(multiply(inverse(X2),X1),multiply(X2,X0))),
inference(paramodulation,[status(thm)],[f95,f41]) ).
fof(f136,plain,
! [X0,X1,X2] : double_divide(multiply(inverse(X0),X1),multiply(X0,X2)) = double_divide(X1,X2),
inference(paramodulation,[status(thm)],[f95,f16]) ).
fof(f159,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X0,X1)),multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(forward_demodulation,[status(thm)],[f5,f133]) ).
fof(f160,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(double_divide(X1,X0),X2),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f159,f134]) ).
fof(f162,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(multiply(X2,X0),multiply(inverse(X2),X1)),
inference(forward_demodulation,[status(thm)],[f5,f135]) ).
fof(f176,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X0,X1)),inverse(X2)) = multiply(multiply(double_divide(X3,X2),X1),X3),
inference(paramodulation,[status(thm)],[f160,f95]) ).
fof(f180,plain,
! [X0,X1,X2,X3] : X0 = double_divide(multiply(multiply(multiply(double_divide(X1,X0),X2),X1),X3),double_divide(X3,X2)),
inference(paramodulation,[status(thm)],[f160,f32]) ).
fof(f185,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(multiply(X0,X1),X2),multiply(X2,X3)) = double_divide(multiply(multiply(double_divide(X4,X3),X1),X4),X0),
inference(paramodulation,[status(thm)],[f160,f11]) ).
fof(f195,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,multiply(X1,X2)),X3) = multiply(X1,multiply(inverse(double_divide(X2,X0)),X3)),
inference(paramodulation,[status(thm)],[f9,f162]) ).
fof(f196,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(double_divide(X0,X1),X2),X0),X3) = multiply(X2,multiply(inverse(X1),X3)),
inference(paramodulation,[status(thm)],[f160,f162]) ).
fof(f197,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(double_divide(X1,inverse(X2)),X3),X1)) = multiply(multiply(X2,X0),X3),
inference(paramodulation,[status(thm)],[f160,f162]) ).
fof(f205,plain,
! [X0,X1,X2,X3] : multiply(X0,X1) = double_divide(multiply(multiply(inverse(X0),X2),X3),double_divide(X3,multiply(X1,X2))),
inference(paramodulation,[status(thm)],[f162,f32]) ).
fof(f212,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(inverse(X0),X1),X2),multiply(X2,multiply(X3,X1))) = multiply(X0,X3),
inference(paramodulation,[status(thm)],[f162,f9]) ).
fof(f224,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,multiply(X1,X2)),X3) = multiply(X1,multiply(multiply(X0,X2),X3)),
inference(forward_demodulation,[status(thm)],[f5,f195]) ).
fof(f226,plain,
! [X0,X1,X2] : X0 = double_divide(multiply(X1,multiply(inverse(X0),X2)),double_divide(X2,X1)),
inference(backward_demodulation,[status(thm)],[f196,f180]) ).
fof(f230,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,X2)) = double_divide(multiply(multiply(double_divide(X3,inverse(X1)),X0),X3),X2),
inference(paramodulation,[status(thm)],[f160,f136]) ).
fof(f239,plain,
! [X0,X1,X2,X3] : double_divide(multiply(inverse(double_divide(X0,X1)),X2),X3) = double_divide(X2,multiply(X1,multiply(X3,X0))),
inference(paramodulation,[status(thm)],[f9,f136]) ).
fof(f241,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(X0,X1),X2),multiply(multiply(X3,X2),X0)) = double_divide(X1,inverse(X3)),
inference(paramodulation,[status(thm)],[f136,f11]) ).
fof(f243,plain,
! [X0,X1,X2] : multiply(X0,X1) = double_divide(X2,multiply(double_divide(X2,X1),inverse(X0))),
inference(paramodulation,[status(thm)],[f136,f16]) ).
fof(f262,plain,
! [X0,X1,X2,X3] : multiply(X0,X1) = double_divide(X2,multiply(inverse(X0),multiply(double_divide(X2,multiply(X1,X3)),X3))),
inference(backward_demodulation,[status(thm)],[f279,f205]) ).
fof(f264,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,X2)) = double_divide(X3,multiply(double_divide(X3,inverse(X1)),multiply(X2,X0))),
inference(backward_demodulation,[status(thm)],[f279,f230]) ).
fof(f271,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(multiply(X0,X1),X2),multiply(X2,X3)) = double_divide(X4,multiply(double_divide(X4,X3),multiply(X0,X1))),
inference(backward_demodulation,[status(thm)],[f279,f185]) ).
fof(f279,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(X0,X1),X2),X3) = double_divide(X2,multiply(X0,multiply(X3,X1))),
inference(forward_demodulation,[status(thm)],[f5,f239]) ).
fof(f295,plain,
! [X0,X1,X2] : multiply(X0,multiply(double_divide(X1,X2),inverse(X0))) = double_divide(X1,X2),
inference(paramodulation,[status(thm)],[f226,f11]) ).
fof(f315,plain,
! [X0,X1,X2] : multiply(X0,double_divide(X1,X2)) = double_divide(multiply(inverse(X0),X1),X2),
inference(paramodulation,[status(thm)],[f10,f243]) ).
fof(f320,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(double_divide(multiply(X1,X2),X3),X1)) = double_divide(X2,multiply(X3,inverse(X0))),
inference(paramodulation,[status(thm)],[f16,f243]) ).
fof(f322,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),X2) = double_divide(X3,multiply(double_divide(X3,X2),multiply(X1,X0))),
inference(paramodulation,[status(thm)],[f5,f243]) ).
fof(f325,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(X0,X1),X2),inverse(X3)) = double_divide(X1,multiply(multiply(X3,X2),X0)),
inference(paramodulation,[status(thm)],[f243,f16]) ).
fof(f346,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,double_divide(X1,X2)),multiply(X2,multiply(X3,X1))) = multiply(X0,X3),
inference(backward_demodulation,[status(thm)],[f315,f212]) ).
fof(f353,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,inverse(double_divide(inverse(X1),double_divide(X0,X2))))) = X2,
inference(backward_demodulation,[status(thm)],[f320,f91]) ).
fof(f354,plain,
! [X0,X1,X2] : X0 = double_divide(X1,double_divide(X1,multiply(X2,inverse(double_divide(inverse(X2),X0))))),
inference(backward_demodulation,[status(thm)],[f320,f88]) ).
fof(f359,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,X2)) = multiply(double_divide(X0,X2),inverse(X1)),
inference(backward_demodulation,[status(thm)],[f322,f264]) ).
fof(f364,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(X0,X1),X2),multiply(X2,X3)) = multiply(double_divide(X1,X0),X3),
inference(backward_demodulation,[status(thm)],[f322,f271]) ).
fof(f379,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X0) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f346,f82]) ).
fof(f381,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,multiply(double_divide(X0,X2),inverse(X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f353]) ).
fof(f382,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(backward_demodulation,[status(thm)],[f397,f95]) ).
fof(f383,plain,
! [X0,X1,X2] : multiply(inverse(X0),inverse(multiply(double_divide(multiply(X1,X2),X0),X1))) = X2,
inference(backward_demodulation,[status(thm)],[f397,f127]) ).
fof(f395,plain,
! [X0,X1,X2] : multiply(X0,inverse(X1)) = multiply(multiply(double_divide(X2,X1),X0),X2),
inference(backward_demodulation,[status(thm)],[f397,f176]) ).
fof(f397,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f295,f381]) ).
fof(f398,plain,
! [X0,X1] : X0 = multiply(X1,inverse(double_divide(inverse(X1),X0))),
inference(forward_demodulation,[status(thm)],[f397,f354]) ).
fof(f400,plain,
! [X0,X1] : X0 = multiply(X1,multiply(X0,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f5,f398]) ).
fof(f403,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),multiply(X2,X3)) = double_divide(X1,multiply(multiply(X2,X3),X0)),
inference(backward_demodulation,[status(thm)],[f359,f325]) ).
fof(f411,plain,
! [X0,X1,X2] : multiply(double_divide(multiply(X0,X1),X2),X0) = double_divide(X1,X2),
inference(backward_demodulation,[status(thm)],[f364,f11]) ).
fof(f413,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),double_divide(X2,X3)) = double_divide(multiply(X3,multiply(X0,X2)),X1),
inference(backward_demodulation,[status(thm)],[f364,f22]) ).
fof(f427,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,inverse(inverse(X2)))) = multiply(multiply(X2,X0),X1),
inference(backward_demodulation,[status(thm)],[f395,f197]) ).
fof(f439,plain,
! [X0,X1,X2,X3,X4] : X0 = double_divide(X1,multiply(multiply(double_divide(double_divide(X2,X3),X0),double_divide(multiply(X3,multiply(X1,X2)),X4)),X4)),
inference(backward_demodulation,[status(thm)],[f403,f35]) ).
fof(f454,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),X2) = double_divide(X1,multiply(X2,X0)),
inference(backward_demodulation,[status(thm)],[f411,f34]) ).
fof(f455,plain,
! [X0,X1] : multiply(inverse(X0),inverse(double_divide(X1,X0))) = X1,
inference(backward_demodulation,[status(thm)],[f411,f383]) ).
fof(f457,plain,
! [X0,X1,X2] : multiply(X0,double_divide(X1,X2)) = double_divide(X1,multiply(X2,inverse(X0))),
inference(backward_demodulation,[status(thm)],[f411,f320]) ).
fof(f461,plain,
! [X0,X1,X2] : multiply(double_divide(X0,inverse(X1)),multiply(X2,X0)) = inverse(double_divide(X2,X1)),
inference(backward_demodulation,[status(thm)],[f411,f97]) ).
fof(f501,plain,
! [X0,X1,X2,X3,X4] : X0 = double_divide(X1,multiply(multiply(double_divide(double_divide(X2,X3),X0),multiply(double_divide(X1,X4),double_divide(X2,X3))),X4)),
inference(forward_demodulation,[status(thm)],[f413,f439]) ).
fof(f502,plain,
! [X0,X1,X2,X3,X4] : X0 = double_divide(X1,multiply(double_divide(X1,X2),multiply(multiply(double_divide(double_divide(X3,X4),X0),double_divide(X3,X4)),X2))),
inference(forward_demodulation,[status(thm)],[f224,f501]) ).
fof(f503,plain,
! [X0,X1,X2,X3] : X0 = multiply(double_divide(X1,multiply(double_divide(double_divide(X2,X3),X0),double_divide(X2,X3))),X1),
inference(forward_demodulation,[status(thm)],[f322,f502]) ).
fof(f504,plain,
! [X0,X1,X2] : X0 = inverse(multiply(double_divide(double_divide(X1,X2),X0),double_divide(X1,X2))),
inference(forward_demodulation,[status(thm)],[f379,f503]) ).
fof(f505,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X2,X0),X1),
inference(backward_demodulation,[status(thm)],[f506,f427]) ).
fof(f506,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f379,f504]) ).
fof(f524,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),double_divide(X2,X3)) = double_divide(multiply(X0,X2),multiply(X1,X3)),
inference(backward_demodulation,[status(thm)],[f454,f413]) ).
fof(f531,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(X0,X1),multiply(double_divide(X2,multiply(double_divide(X2,X3),X4)),X0)) = multiply(double_divide(X4,X1),X3),
inference(backward_demodulation,[status(thm)],[f454,f123]) ).
fof(f542,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)],[f454,f15]) ).
fof(f545,plain,
! [X0,X1,X2] : multiply(double_divide(X0,multiply(X1,X2)),X2) = double_divide(X0,X1),
inference(backward_demodulation,[status(thm)],[f454,f411]) ).
fof(f547,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,multiply(X1,X2)),multiply(X1,X3)) = multiply(double_divide(X0,X2),X3),
inference(backward_demodulation,[status(thm)],[f454,f364]) ).
fof(f549,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,multiply(X1,X2)),multiply(multiply(X3,X1),X2)) = double_divide(X0,inverse(X3)),
inference(backward_demodulation,[status(thm)],[f454,f241]) ).
fof(f553,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f455]) ).
fof(f558,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(backward_demodulation,[status(thm)],[f559,f122]) ).
fof(f559,plain,
! [X0,X1,X2] : multiply(double_divide(X0,inverse(X1)),multiply(X2,X0)) = multiply(X1,X2),
inference(forward_demodulation,[status(thm)],[f5,f461]) ).
fof(f590,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(b3,multiply(c3,a3)) != 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)],[f505,f6]) ).
fof(f617,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(backward_demodulation,[status(thm)],[f505,f382]) ).
fof(f629,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),double_divide(X2,X3)) = double_divide(X2,multiply(multiply(X1,X3),X0)),
inference(forward_demodulation,[status(thm)],[f403,f524]) ).
fof(f633,plain,
! [X0,X1,X2,X3] : multiply(X0,X1) = multiply(double_divide(double_divide(X2,multiply(X1,X3)),X3),double_divide(X2,inverse(X0))),
inference(backward_demodulation,[status(thm)],[f645,f262]) ).
fof(f645,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),double_divide(X2,X3)) = double_divide(X2,multiply(X3,multiply(X0,X1))),
inference(forward_demodulation,[status(thm)],[f505,f629]) ).
fof(f665,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = double_divide(X0,inverse(X3)),
inference(forward_demodulation,[status(thm)],[f505,f549]) ).
fof(f671,plain,
! [X0,X1,X2] : double_divide(X0,inverse(X1)) = double_divide(X2,multiply(double_divide(X2,X1),X0)),
inference(backward_demodulation,[status(thm)],[f672,f542]) ).
fof(f672,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X1,X2)) = double_divide(X0,inverse(X2)),
inference(forward_demodulation,[status(thm)],[f547,f665]) ).
fof(f674,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X2,X0)),
inference(forward_demodulation,[status(thm)],[f505,f558]) ).
fof(f675,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(b3,multiply(c3,a3)) != multiply(a3,multiply(b3,c3))
| multiply(b2,multiply(a2,inverse(b2))) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(forward_demodulation,[status(thm)],[f505,f590]) ).
fof(f676,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(b3,multiply(c3,a3)) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(forward_demodulation,[status(thm)],[f400,f675]) ).
fof(f677,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(b3,multiply(c3,a3)) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(trivial_equality_resolution,[status(thm)],[f676]) ).
fof(f678,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(forward_subsumption_resolution,[status(thm)],[f677,f674]) ).
fof(f754,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),multiply(double_divide(X2,inverse(X3)),X0)) = multiply(double_divide(X2,X1),X3),
inference(backward_demodulation,[status(thm)],[f671,f531]) ).
fof(f849,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(double_divide(X0,multiply(X1,X2)),X2),double_divide(X3,X4)) = double_divide(X3,multiply(X4,double_divide(X0,X1))),
inference(paramodulation,[status(thm)],[f545,f645]) ).
fof(f857,plain,
! [X0,X1,X2] : multiply(X0,X1) = double_divide(X2,multiply(inverse(X0),double_divide(X2,X1))),
inference(backward_demodulation,[status(thm)],[f849,f633]) ).
fof(f899,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,multiply(X1,inverse(X0))),double_divide(X2,X3)) = double_divide(X2,multiply(X3,X1)),
inference(paramodulation,[status(thm)],[f400,f645]) ).
fof(f904,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,double_divide(X0,X1)),double_divide(X2,X3)) = double_divide(X2,multiply(X3,X1)),
inference(forward_demodulation,[status(thm)],[f457,f899]) ).
fof(f906,plain,
! [X0,X1,X2] : double_divide(X0,multiply(inverse(X1),X2)) = multiply(double_divide(X0,X2),X1),
inference(backward_demodulation,[status(thm)],[f907,f754]) ).
fof(f907,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),multiply(double_divide(X2,X3),X0)) = double_divide(X2,multiply(X3,X1)),
inference(forward_demodulation,[status(thm)],[f505,f904]) ).
fof(f912,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(double_divide(X2,double_divide(X2,X1)),X0),
inference(backward_demodulation,[status(thm)],[f906,f857]) ).
fof(f915,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(backward_subsumption_resolution,[status(thm)],[f678,f916]) ).
fof(f916,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f397,f912]) ).
fof(f1359,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f617,f553]) ).
fof(f1397,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f915,f1359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP110-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 19:59:45 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.53 % Refutation found
% 0.14/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.32/0.56 % Elapsed time: 0.185651 seconds
% 0.32/0.56 % CPU time: 1.148921 seconds
% 0.32/0.56 % Total memory used: 92.696 MB
% 0.32/0.56 % Net memory used: 91.610 MB
%------------------------------------------------------------------------------