TSTP Solution File: GRP059-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GRP059-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 21:14:45 EDT 2024

% Result   : Unsatisfiable 2.52s 0.72s
% Output   : Refutation 2.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   37
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   98 (  90 unt;   0 def)
%            Number of atoms       :  108 ( 107 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   31 (  21   ~;  10   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :   13 (   3 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :  300 ( 300   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6991,plain,
    $false,
    inference(equality_resolution,[],[f6913]) ).

fof(f6913,plain,
    ! [X0,X1] : multiply(X0,inverse(X0)) != multiply(X1,inverse(X1)),
    inference(superposition,[],[f6841,f2283]) ).

fof(f2283,plain,
    ! [X2,X4] : multiply(X4,inverse(X4)) = multiply(inverse(X2),X2),
    inference(backward_demodulation,[],[f1388,f2200]) ).

fof(f2200,plain,
    ! [X3] : inverse(inverse(X3)) = X3,
    inference(forward_demodulation,[],[f2199,f1925]) ).

fof(f1925,plain,
    ! [X2,X1] : multiply(X1,multiply(X2,inverse(X2))) = X1,
    inference(backward_demodulation,[],[f1622,f1351]) ).

fof(f1351,plain,
    ! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = X1,
    inference(superposition,[],[f1147,f895]) ).

fof(f895,plain,
    ! [X0,X1] : inverse(inverse(inverse(inverse(multiply(multiply(X0,inverse(X0)),X1))))) = X1,
    inference(superposition,[],[f648,f35]) ).

fof(f35,plain,
    ! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X1,inverse(X1)),X2)),X0),inverse(X0)),multiply(X3,inverse(X3)))) = X2,
    inference(superposition,[],[f1,f15]) ).

fof(f15,plain,
    ! [X4,X5] : multiply(X4,inverse(X4)) = multiply(X5,inverse(X5)),
    inference(superposition,[],[f3,f3]) ).

fof(f3,plain,
    ! [X2,X3,X0,X1,X4] : multiply(X3,inverse(X3)) = inverse(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X0,X1),X2)),X0)),X1),multiply(X4,inverse(X4)))),
    inference(superposition,[],[f1,f1]) ).

fof(f1,axiom,
    ! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).

fof(f648,plain,
    ! [X2,X3,X1] : inverse(X2) = inverse(multiply(multiply(multiply(X1,inverse(X1)),X2),multiply(X3,inverse(X3)))),
    inference(backward_demodulation,[],[f80,f644]) ).

fof(f644,plain,
    ! [X3,X0] : inverse(X3) = inverse(multiply(inverse(inverse(multiply(X0,inverse(X0)))),X3)),
    inference(backward_demodulation,[],[f216,f619]) ).

fof(f619,plain,
    ! [X2,X3,X0,X1] : inverse(X1) = inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X0,inverse(X0)))),X1),multiply(X3,inverse(X3)))),
    inference(superposition,[],[f1,f374]) ).

fof(f374,plain,
    ! [X2,X3,X0] : multiply(X3,inverse(X3)) = inverse(multiply(multiply(inverse(multiply(X2,inverse(X2))),X0),inverse(X0))),
    inference(superposition,[],[f94,f137]) ).

fof(f137,plain,
    ! [X2,X0,X1] : multiply(X2,inverse(X2)) = multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1)))),
    inference(superposition,[],[f15,f93]) ).

fof(f93,plain,
    ! [X0,X1] : inverse(multiply(X0,inverse(X0))) = inverse(multiply(X1,inverse(X1))),
    inference(superposition,[],[f37,f35]) ).

fof(f37,plain,
    ! [X2,X3,X0,X1] : inverse(multiply(X0,X1)) = inverse(multiply(multiply(multiply(inverse(multiply(X2,inverse(X2))),X0),X1),multiply(X3,inverse(X3)))),
    inference(superposition,[],[f1,f15]) ).

fof(f94,plain,
    ! [X2,X0,X1,X4] : multiply(X4,inverse(X4)) = inverse(multiply(multiply(inverse(multiply(multiply(X1,X2),inverse(multiply(X0,inverse(X0))))),X1),X2)),
    inference(superposition,[],[f37,f3]) ).

fof(f216,plain,
    ! [X2,X3,X0,X1,X4] : inverse(multiply(inverse(inverse(multiply(X0,inverse(X0)))),X3)) = inverse(multiply(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))),X3),multiply(X4,inverse(X4)))),
    inference(superposition,[],[f37,f137]) ).

fof(f80,plain,
    ! [X2,X3,X0,X1] : inverse(multiply(inverse(inverse(multiply(X0,inverse(X0)))),X2)) = inverse(multiply(multiply(multiply(X1,inverse(X1)),X2),multiply(X3,inverse(X3)))),
    inference(superposition,[],[f37,f15]) ).

fof(f1147,plain,
    ! [X2] : inverse(inverse(inverse(inverse(X2)))) = X2,
    inference(forward_demodulation,[],[f1086,f676]) ).

fof(f676,plain,
    ! [X0,X1] : inverse(X1) = inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X0,inverse(X0))))))),X1)),
    inference(superposition,[],[f644,f644]) ).

fof(f1086,plain,
    ! [X2,X1] : inverse(inverse(inverse(inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(X1,inverse(X1))))))),X2))))) = X2,
    inference(superposition,[],[f895,f962]) ).

fof(f962,plain,
    ! [X0,X1] : multiply(X1,inverse(X1)) = inverse(inverse(inverse(inverse(inverse(multiply(X0,inverse(X0))))))),
    inference(superposition,[],[f895,f648]) ).

fof(f1622,plain,
    ! [X2,X0,X1] : multiply(multiply(multiply(X0,inverse(X0)),X1),multiply(X2,inverse(X2))) = X1,
    inference(forward_demodulation,[],[f1335,f1147]) ).

fof(f1335,plain,
    ! [X2,X0,X1] : multiply(multiply(multiply(X0,inverse(X0)),X1),multiply(X2,inverse(X2))) = inverse(inverse(inverse(inverse(X1)))),
    inference(superposition,[],[f1147,f648]) ).

fof(f2199,plain,
    ! [X3,X0] : inverse(multiply(inverse(X3),multiply(X0,inverse(X0)))) = X3,
    inference(forward_demodulation,[],[f2125,f1925]) ).

fof(f2125,plain,
    ! [X3,X0,X1] : inverse(multiply(multiply(inverse(X3),multiply(X0,inverse(X0))),multiply(X1,inverse(X1)))) = X3,
    inference(backward_demodulation,[],[f1833,f1925]) ).

fof(f1833,plain,
    ! [X3,X0,X1,X4] : inverse(multiply(multiply(multiply(inverse(X3),multiply(X0,inverse(X0))),multiply(X1,inverse(X1))),multiply(X4,inverse(X4)))) = X3,
    inference(backward_demodulation,[],[f1190,f1811]) ).

fof(f1811,plain,
    ! [X2,X3] : inverse(X3) = inverse(multiply(multiply(X2,inverse(X2)),X3)),
    inference(forward_demodulation,[],[f1810,f1147]) ).

fof(f1810,plain,
    ! [X2,X3] : inverse(X3) = inverse(multiply(inverse(inverse(inverse(inverse(multiply(X2,inverse(X2)))))),X3)),
    inference(forward_demodulation,[],[f1808,f1347]) ).

fof(f1347,plain,
    ! [X0,X1] : inverse(inverse(multiply(multiply(X0,inverse(X0)),X1))) = inverse(inverse(X1)),
    inference(superposition,[],[f1147,f895]) ).

fof(f1808,plain,
    ! [X2,X3,X1] : inverse(X3) = inverse(multiply(inverse(inverse(inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2))))))),X3)),
    inference(backward_demodulation,[],[f661,f1347]) ).

fof(f661,plain,
    ! [X2,X3,X0,X1] : inverse(X3) = inverse(multiply(inverse(inverse(multiply(multiply(X0,inverse(X0)),inverse(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))))))),X3)),
    inference(superposition,[],[f644,f112]) ).

fof(f112,plain,
    ! [X2,X0,X1] : inverse(multiply(X2,inverse(X2))) = inverse(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1))))),
    inference(superposition,[],[f93,f93]) ).

fof(f1190,plain,
    ! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X2,inverse(X2)),X3)),multiply(X0,inverse(X0))),multiply(X1,inverse(X1))),multiply(X4,inverse(X4)))) = X3,
    inference(backward_demodulation,[],[f799,f1147]) ).

fof(f799,plain,
    ! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X2,inverse(X2)),X3)),multiply(X0,inverse(X0))),inverse(inverse(inverse(inverse(multiply(X1,inverse(X1))))))),multiply(X4,inverse(X4)))) = X3,
    inference(superposition,[],[f35,f680]) ).

fof(f680,plain,
    ! [X0,X1] : inverse(multiply(X1,inverse(X1))) = inverse(inverse(inverse(inverse(multiply(X0,inverse(X0)))))),
    inference(superposition,[],[f644,f15]) ).

fof(f1388,plain,
    ! [X2,X4] : multiply(X4,inverse(X4)) = multiply(inverse(inverse(inverse(X2))),X2),
    inference(backward_demodulation,[],[f21,f1330]) ).

fof(f1330,plain,
    ! [X2,X3,X0,X1] : multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3))) = inverse(inverse(inverse(X2))),
    inference(superposition,[],[f1147,f1]) ).

fof(f21,plain,
    ! [X2,X3,X0,X1,X4] : multiply(X4,inverse(X4)) = multiply(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3))),X2),
    inference(superposition,[],[f15,f1]) ).

fof(f6841,plain,
    ! [X2] : multiply(inverse(a1),a1) != multiply(X2,inverse(X2)),
    inference(superposition,[],[f6403,f3177]) ).

fof(f3177,plain,
    ! [X2,X0,X1] : multiply(X2,inverse(X2)) = multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1)),
    inference(superposition,[],[f15,f2668]) ).

fof(f2668,plain,
    ! [X9,X5] : multiply(inverse(X5),X5) = inverse(multiply(inverse(X9),X9)),
    inference(backward_demodulation,[],[f2349,f2660]) ).

fof(f2660,plain,
    ! [X2,X0,X1,X4] : multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),X4) = X4,
    inference(forward_demodulation,[],[f2627,f1925]) ).

fof(f2627,plain,
    ! [X2,X3,X0,X1,X4] : multiply(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(X3,inverse(X3))),X4) = X4,
    inference(superposition,[],[f1351,f2088]) ).

fof(f2088,plain,
    ! [X2,X3,X0,X1] : multiply(X3,inverse(X3)) = inverse(multiply(multiply(X2,multiply(inverse(multiply(multiply(X0,X1),X2)),X0)),X1)),
    inference(backward_demodulation,[],[f3,f1925]) ).

fof(f2349,plain,
    ! [X2,X0,X1,X9,X5] : multiply(inverse(X5),X5) = inverse(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X0,X1),X2)),X0)),X1),multiply(inverse(X9),X9))),
    inference(forward_demodulation,[],[f2300,f2200]) ).

fof(f2300,plain,
    ! [X2,X0,X1,X9,X5] : inverse(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X0,X1),X2)),X0)),X1),multiply(inverse(inverse(inverse(X9))),X9))) = multiply(inverse(X5),X5),
    inference(backward_demodulation,[],[f1480,f2200]) ).

fof(f1480,plain,
    ! [X2,X0,X1,X9,X5] : multiply(inverse(inverse(inverse(X5))),X5) = inverse(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X0,X1),X2)),X0)),X1),multiply(inverse(inverse(inverse(X9))),X9))),
    inference(forward_demodulation,[],[f1414,f1330]) ).

fof(f1414,plain,
    ! [X2,X10,X0,X1,X8,X9,X7,X5] : inverse(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X0,X1),X2)),X0)),X1),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X7,X8),X9)),X7),X8),multiply(X10,inverse(X10))),X9))) = multiply(inverse(inverse(inverse(X5))),X5),
    inference(backward_demodulation,[],[f453,f1330]) ).

fof(f453,plain,
    ! [X2,X3,X10,X0,X1,X8,X6,X9,X7,X4,X5] : multiply(multiply(multiply(multiply(inverse(multiply(multiply(X3,X4),X5)),X3),X4),multiply(X6,inverse(X6))),X5) = inverse(multiply(multiply(multiply(X2,multiply(inverse(multiply(multiply(X0,X1),X2)),X0)),X1),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X7,X8),X9)),X7),X8),multiply(X10,inverse(X10))),X9))),
    inference(superposition,[],[f4,f4]) ).

fof(f4,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,X5),X6)),X4),X5),multiply(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3))),X2))) = X6,
    inference(superposition,[],[f1,f1]) ).

fof(f6403,plain,
    ! [X0,X1] : multiply(inverse(a1),a1) != multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1)),
    inference(trivial_inequality_removal,[],[f6402]) ).

fof(f6402,plain,
    ! [X0,X1] :
      ( a2 != a2
      | multiply(inverse(a1),a1) != multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1)) ),
    inference(forward_demodulation,[],[f6401,f4052]) ).

fof(f4052,plain,
    ! [X0,X1] : multiply(inverse(X1),multiply(X1,X0)) = X0,
    inference(superposition,[],[f3978,f3034]) ).

fof(f3034,plain,
    ! [X0,X1] : inverse(X1) = multiply(X0,inverse(multiply(X1,X0))),
    inference(superposition,[],[f2200,f2926]) ).

fof(f2926,plain,
    ! [X0,X1] : inverse(multiply(X1,inverse(multiply(X0,X1)))) = X0,
    inference(superposition,[],[f2485,f2485]) ).

fof(f2485,plain,
    ! [X0,X1] : inverse(multiply(inverse(multiply(X0,X1)),X0)) = X1,
    inference(forward_demodulation,[],[f2484,f2021]) ).

fof(f2021,plain,
    ! [X2,X1] : inverse(X2) = inverse(multiply(X2,inverse(multiply(X1,inverse(X1))))),
    inference(forward_demodulation,[],[f1912,f1351]) ).

fof(f1912,plain,
    ! [X2,X0,X1] : inverse(X2) = inverse(multiply(X2,multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1)))))),
    inference(backward_demodulation,[],[f884,f1351]) ).

fof(f884,plain,
    ! [X2,X3,X0,X1] : inverse(X2) = inverse(multiply(multiply(multiply(X3,inverse(X3)),X2),multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1)))))),
    inference(superposition,[],[f648,f93]) ).

fof(f2484,plain,
    ! [X2,X0,X1] : inverse(multiply(inverse(multiply(multiply(X0,X1),inverse(multiply(X2,inverse(X2))))),X0)) = X1,
    inference(forward_demodulation,[],[f2015,f1925]) ).

fof(f2015,plain,
    ! [X2,X0,X1,X4] : inverse(multiply(multiply(inverse(multiply(multiply(X0,X1),inverse(multiply(X2,inverse(X2))))),X0),multiply(X4,inverse(X4)))) = X1,
    inference(backward_demodulation,[],[f414,f1351]) ).

fof(f414,plain,
    ! [X2,X3,X0,X1,X4] : inverse(multiply(multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(multiply(X0,X1),inverse(multiply(X2,inverse(X2)))))),X0),multiply(X4,inverse(X4)))) = X1,
    inference(superposition,[],[f1,f94]) ).

fof(f3978,plain,
    ! [X0,X1] : multiply(multiply(X0,inverse(X1)),X1) = X0,
    inference(superposition,[],[f3575,f2200]) ).

fof(f3575,plain,
    ! [X0,X1] : inverse(X0) = multiply(multiply(inverse(X0),inverse(X1)),X1),
    inference(backward_demodulation,[],[f3521,f3522]) ).

fof(f3522,plain,
    ! [X0,X1] : inverse(X0) = inverse(multiply(multiply(X0,inverse(X1)),X1)),
    inference(superposition,[],[f2309,f2200]) ).

fof(f2309,plain,
    ! [X2,X5] : inverse(multiply(multiply(inverse(X5),inverse(X2)),X2)) = X5,
    inference(backward_demodulation,[],[f2083,f2200]) ).

fof(f2083,plain,
    ! [X2,X5] : inverse(multiply(multiply(inverse(X5),inverse(inverse(inverse(X2)))),X2)) = X5,
    inference(backward_demodulation,[],[f1835,f1925]) ).

fof(f1835,plain,
    ! [X2,X6,X5] : inverse(multiply(multiply(multiply(inverse(X5),inverse(inverse(inverse(X2)))),X2),multiply(X6,inverse(X6)))) = X5,
    inference(backward_demodulation,[],[f1390,f1811]) ).

fof(f1390,plain,
    ! [X2,X6,X4,X5] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,inverse(X4)),X5)),inverse(inverse(inverse(X2)))),X2),multiply(X6,inverse(X6)))) = X5,
    inference(backward_demodulation,[],[f57,f1330]) ).

fof(f57,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X4,inverse(X4)),X5)),multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))),X2),multiply(X6,inverse(X6)))) = X5,
    inference(superposition,[],[f35,f1]) ).

fof(f3521,plain,
    ! [X2,X0,X1] : multiply(multiply(inverse(X0),inverse(X1)),X1) = inverse(multiply(multiply(X0,inverse(X2)),X2)),
    inference(superposition,[],[f2309,f2309]) ).

fof(f6401,plain,
    ! [X0,X1] :
      ( a2 != multiply(inverse(b2),multiply(b2,a2))
      | multiply(inverse(a1),a1) != multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1)) ),
    inference(forward_demodulation,[],[f6400,f6270]) ).

fof(f6270,plain,
    ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
    inference(forward_demodulation,[],[f6123,f2200]) ).

fof(f6123,plain,
    ! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = inverse(inverse(multiply(X0,multiply(X1,X2)))),
    inference(superposition,[],[f2200,f5828]) ).

fof(f5828,plain,
    ! [X2,X0,X1] : inverse(multiply(multiply(X2,X0),X1)) = inverse(multiply(X2,multiply(X0,X1))),
    inference(forward_demodulation,[],[f5698,f2200]) ).

fof(f5698,plain,
    ! [X2,X0,X1] : inverse(multiply(X2,multiply(X0,X1))) = inverse(multiply(multiply(inverse(inverse(X2)),X0),X1)),
    inference(superposition,[],[f2787,f3034]) ).

fof(f2787,plain,
    ! [X2,X3,X4] : inverse(multiply(multiply(inverse(multiply(multiply(X2,X3),X4)),X2),X3)) = X4,
    inference(backward_demodulation,[],[f1154,f2784]) ).

fof(f2784,plain,
    ! [X2,X1] : multiply(X2,inverse(multiply(X1,inverse(X1)))) = X2,
    inference(forward_demodulation,[],[f2768,f1351]) ).

fof(f2768,plain,
    ! [X2,X0,X1] : multiply(X2,multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,inverse(X1))))) = X2,
    inference(superposition,[],[f1925,f93]) ).

fof(f1154,plain,
    ! [X2,X3,X1,X4] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X2,X3),X4)),X2),X3),inverse(multiply(X1,inverse(X1))))) = X4,
    inference(backward_demodulation,[],[f1059,f1147]) ).

fof(f1059,plain,
    ! [X2,X3,X1,X4] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X2,X3),X4)),X2),X3),inverse(inverse(inverse(inverse(inverse(multiply(X1,inverse(X1))))))))) = X4,
    inference(superposition,[],[f1,f962]) ).

fof(f6400,plain,
    ! [X0,X1] :
      ( multiply(inverse(a1),a1) != multiply(multiply(inverse(X0),X0),multiply(inverse(X1),X1))
      | a2 != multiply(multiply(inverse(b2),b2),a2) ),
    inference(forward_demodulation,[],[f6378,f3539]) ).

fof(f3539,plain,
    ! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
    inference(superposition,[],[f2309,f2939]) ).

fof(f2939,plain,
    ! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
    inference(superposition,[],[f2200,f2485]) ).

fof(f6378,plain,
    ! [X0,X1] :
      ( multiply(inverse(a1),a1) != multiply(multiply(inverse(X0),X0),inverse(multiply(inverse(X1),X1)))
      | a2 != multiply(multiply(inverse(b2),b2),a2) ),
    inference(superposition,[],[f6374,f3000]) ).

fof(f3000,plain,
    ! [X2,X5] : inverse(multiply(inverse(X2),X2)) = inverse(multiply(inverse(X5),X5)),
    inference(forward_demodulation,[],[f2975,f2939]) ).

fof(f2975,plain,
    ! [X2,X4,X5] : inverse(multiply(multiply(inverse(multiply(X4,X5)),X4),X5)) = inverse(multiply(inverse(X2),X2)),
    inference(backward_demodulation,[],[f2074,f2939]) ).

fof(f2074,plain,
    ! [X2,X1,X4,X5] : inverse(multiply(multiply(inverse(multiply(X1,X2)),X1),X2)) = inverse(multiply(multiply(inverse(multiply(X4,X5)),X4),X5)),
    inference(forward_demodulation,[],[f2026,f2021]) ).

fof(f2026,plain,
    ! [X2,X1,X6,X4,X5] : inverse(multiply(multiply(inverse(multiply(multiply(X4,X5),inverse(multiply(X6,inverse(X6))))),X4),X5)) = inverse(multiply(multiply(inverse(multiply(X1,X2)),X1),X2)),
    inference(backward_demodulation,[],[f343,f2021]) ).

fof(f343,plain,
    ! [X2,X3,X1,X6,X4,X5] : inverse(multiply(multiply(inverse(multiply(multiply(X1,X2),inverse(multiply(X3,inverse(X3))))),X1),X2)) = inverse(multiply(multiply(inverse(multiply(multiply(X4,X5),inverse(multiply(X6,inverse(X6))))),X4),X5)),
    inference(superposition,[],[f94,f94]) ).

fof(f6374,plain,
    ! [X0] :
      ( multiply(inverse(a1),a1) != multiply(X0,inverse(X0))
      | a2 != multiply(multiply(inverse(b2),b2),a2) ),
    inference(superposition,[],[f6306,f2283]) ).

fof(f6306,plain,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | a2 != multiply(multiply(inverse(b2),b2),a2) ),
    inference(trivial_inequality_removal,[],[f6305]) ).

fof(f6305,plain,
    ( multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
    | multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | a2 != multiply(multiply(inverse(b2),b2),a2) ),
    inference(backward_demodulation,[],[f2,f6270]) ).

fof(f2,axiom,
    ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | a2 != multiply(multiply(inverse(b2),b2),a2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GRP059-1 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n021.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun May 19 04:34:38 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (12079)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (12081)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (12082)WARNING: value z3 for option sas not known
% 0.15/0.38  % (12080)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (12082)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  % (12084)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38  % (12083)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (12085)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38  % (12086)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [3]
% 0.15/0.39  TRYING [3]
% 0.22/0.40  TRYING [4]
% 0.22/0.58  TRYING [4]
% 2.52/0.71  % (12085)First to succeed.
% 2.52/0.71  % (12085)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12079"
% 2.52/0.72  % (12085)Refutation found. Thanks to Tanya!
% 2.52/0.72  % SZS status Unsatisfiable for theBenchmark
% 2.52/0.72  % SZS output start Proof for theBenchmark
% See solution above
% 2.52/0.72  % (12085)------------------------------
% 2.52/0.72  % (12085)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.52/0.72  % (12085)Termination reason: Refutation
% 2.52/0.72  
% 2.52/0.72  % (12085)Memory used [KB]: 3266
% 2.52/0.72  % (12085)Time elapsed: 0.338 s
% 2.52/0.72  % (12085)Instructions burned: 709 (million)
% 2.52/0.72  % (12079)Success in time 0.342 s
%------------------------------------------------------------------------------