TSTP Solution File: LCL021-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : LCL021-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n024.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 : Tue Apr 30 13:40:13 EDT 2024

% Result   : Unsatisfiable 145.80s 21.14s
% Output   : Refutation 145.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   65
%            Number of leaves      :    3
% Syntax   : Number of formulae    :  155 ( 103 unt;   0 def)
%            Number of atoms       :  208 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  107 (  54   ~;  53   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :   13 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  649 ( 649   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f868081,plain,
    $false,
    inference(resolution,[],[f758805,f3]) ).

fof(f3,axiom,
    ~ is_a_theorem(equivalent(a,equivalent(equivalent(b,c),equivalent(equivalent(a,c),b)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_xhk) ).

fof(f758805,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X0,X2),X1)))),
    inference(resolution,[],[f713425,f699317]) ).

fof(f699317,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X1),equivalent(X0,X2)))),
    inference(resolution,[],[f688290,f641093]) ).

fof(f641093,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(equivalent(X2,X0),X1))
      | is_a_theorem(equivalent(X0,equivalent(X1,X2))) ),
    inference(resolution,[],[f640387,f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,X1))
      | is_a_theorem(X1)
      | ~ is_a_theorem(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).

fof(f640387,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,equivalent(X2,X0)))),
    inference(resolution,[],[f80888,f1595]) ).

fof(f1595,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X4),X2)),equivalent(X0,X1)),X4)))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f1578,f1]) ).

fof(f1578,plain,
    ! [X2,X3,X0,X1,X4] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X3),X1)),equivalent(X4,X0)),X3)),X4)),
    inference(resolution,[],[f1555,f271]) ).

fof(f271,plain,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X0)),equivalent(equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4))),equivalent(X6,equivalent(equivalent(X7,X8),equivalent(equivalent(X8,X6),X7))))),X2)),
    inference(resolution,[],[f217,f2]) ).

fof(f2,axiom,
    ! [X2,X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xhn) ).

fof(f217,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ is_a_theorem(equivalent(X7,X0))
      | is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X1),X2))),equivalent(X4,equivalent(equivalent(X5,X6),equivalent(equivalent(X6,X4),X5))))),X7)) ),
    inference(resolution,[],[f121,f1]) ).

fof(f121,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(equivalent(X3,X4),equivalent(equivalent(X4,X2),X3))),equivalent(X5,equivalent(equivalent(X6,X7),equivalent(equivalent(X7,X5),X6))))),X0))),
    inference(resolution,[],[f104,f4]) ).

fof(f4,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(X2)
      | is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X0))) ),
    inference(resolution,[],[f2,f1]) ).

fof(f104,plain,
    ! [X2,X3,X0,X1,X4,X5] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1))),equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4))))),
    inference(resolution,[],[f103,f11]) ).

fof(f11,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1)),equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4)))))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f8,f1]) ).

fof(f8,plain,
    ! [X2,X3,X0,X1,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X0)),equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4)))),X2)),
    inference(resolution,[],[f6,f2]) ).

fof(f6,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ is_a_theorem(equivalent(X4,X0))
      | is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X1),X2)))),X4)) ),
    inference(resolution,[],[f5,f1]) ).

fof(f5,plain,
    ! [X2,X3,X0,X1,X4] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X3,X4),equivalent(equivalent(X4,X2),X3)))),X0))),
    inference(resolution,[],[f4,f2]) ).

fof(f103,plain,
    ! [X2,X3,X0,X1,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4))))),X0)),X2)),
    inference(subsumption_resolution,[],[f100,f2]) ).

fof(f100,plain,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4))))),X0)),X2))
      | ~ is_a_theorem(equivalent(X6,equivalent(equivalent(X7,X8),equivalent(equivalent(X8,X6),X7)))) ),
    inference(resolution,[],[f36,f1]) ).

fof(f36,plain,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1))),equivalent(equivalent(equivalent(X3,X4),equivalent(equivalent(X4,equivalent(X5,equivalent(X6,equivalent(equivalent(X7,X8),equivalent(equivalent(X8,X6),X7))))),X3)),X5))),
    inference(resolution,[],[f22,f8]) ).

fof(f22,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X3,X4),equivalent(equivalent(X4,X2),X3)))),X0),equivalent(X5,equivalent(equivalent(X6,X7),equivalent(equivalent(X7,X5),X6)))))
      | is_a_theorem(equivalent(X0,X1)) ),
    inference(resolution,[],[f9,f1]) ).

fof(f9,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X1),X2)))),X4),equivalent(X5,equivalent(equivalent(X6,X7),equivalent(equivalent(X7,X5),X6)))),equivalent(X4,X0))),
    inference(resolution,[],[f6,f5]) ).

fof(f1555,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X3,X0)),X1)),X3))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f1526,f1]) ).

fof(f1526,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,X3)),X0)),X2),X3)),
    inference(resolution,[],[f838,f111]) ).

fof(f111,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X0,equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4))))),X1)))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f103,f1]) ).

fof(f838,plain,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(equivalent(equivalent(equivalent(equivalent(X2,X3),equivalent(equivalent(X3,equivalent(X4,X5)),X2)),X4),X5),equivalent(X6,equivalent(equivalent(X7,X8),equivalent(equivalent(X8,X6),X7))))),X0))),
    inference(resolution,[],[f819,f526]) ).

fof(f526,plain,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( ~ is_a_theorem(equivalent(X2,equivalent(X6,equivalent(equivalent(X7,X8),equivalent(equivalent(X8,X6),X7)))))
      | is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4))))),X0))) ),
    inference(resolution,[],[f110,f1]) ).

fof(f110,plain,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X1),X2)))),equivalent(equivalent(X4,X5),equivalent(equivalent(X5,equivalent(X0,equivalent(X6,equivalent(equivalent(X7,X8),equivalent(equivalent(X8,X6),X7))))),X4)))),
    inference(resolution,[],[f103,f6]) ).

fof(f819,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,X3)),X0)),X2),X3),equivalent(X4,equivalent(equivalent(X5,X6),equivalent(equivalent(X6,X4),X5))))),
    inference(resolution,[],[f166,f134]) ).

fof(f134,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] :
      ( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X6),X4)),X0),X6))
      | is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X1),X2))))) ),
    inference(resolution,[],[f126,f1]) ).

fof(f126,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X0)),X3),X2),equivalent(X3,equivalent(X4,equivalent(equivalent(X5,X6),equivalent(equivalent(X6,X4),X5)))))),
    inference(resolution,[],[f111,f36]) ).

fof(f166,plain,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4))))),equivalent(X2,X0)),equivalent(X6,equivalent(equivalent(X7,X8),equivalent(equivalent(X8,X6),X7))))),
    inference(resolution,[],[f134,f103]) ).

fof(f80888,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X3,X0)),X1)),X3))),
    inference(resolution,[],[f80635,f1940]) ).

fof(f1940,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(equivalent(X3,X4),equivalent(equivalent(X4,X2),X3))),X0),X1))
      | is_a_theorem(equivalent(X0,X1)) ),
    inference(resolution,[],[f1909,f1]) ).

fof(f1909,plain,
    ! [X2,X3,X0,X1,X4] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1))),X3),X4),equivalent(X3,X4))),
    inference(resolution,[],[f1556,f1595]) ).

fof(f1556,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X1),X2)))),equivalent(equivalent(equivalent(X4,X5),equivalent(equivalent(X5,equivalent(X6,X0)),X4)),X6))),
    inference(resolution,[],[f1526,f6]) ).

fof(f80635,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),X2),X1),equivalent(X2,X0))),
    inference(resolution,[],[f79950,f1641]) ).

fof(f1641,plain,
    ! [X2,X3,X0,X1,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,equivalent(equivalent(X2,X0),equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4))))))),
    inference(resolution,[],[f1595,f32]) ).

fof(f32,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X3,equivalent(X0,equivalent(X4,equivalent(equivalent(X5,X6),equivalent(equivalent(X6,X4),X5)))))),X1)),X3))),
    inference(resolution,[],[f22,f5]) ).

fof(f79950,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X2,equivalent(X1,X2)))))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f78672,f1]) ).

fof(f78672,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X2,equivalent(X1,X2)))),X0)),
    inference(resolution,[],[f77168,f69318]) ).

fof(f69318,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X0,X1))),equivalent(X2,X2))),
    inference(resolution,[],[f69086,f15847]) ).

fof(f15847,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(X0)
      | is_a_theorem(equivalent(X0,equivalent(X1,X1))) ),
    inference(resolution,[],[f15770,f1]) ).

fof(f15770,plain,
    ! [X0,X1] : is_a_theorem(equivalent(X0,equivalent(X0,equivalent(X1,X1)))),
    inference(resolution,[],[f15360,f1213]) ).

fof(f1213,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,equivalent(X0,X1)),equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4)))))))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f1201,f1]) ).

fof(f1201,plain,
    ! [X2,X3,X0,X1,X4,X5] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(equivalent(X1,equivalent(X2,X0)),equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4)))))),X2)),
    inference(resolution,[],[f727,f5]) ).

fof(f727,plain,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
      ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1)),equivalent(equivalent(equivalent(X3,X4),equivalent(equivalent(X4,equivalent(X5,equivalent(X6,equivalent(equivalent(X7,X8),equivalent(equivalent(X8,X6),X7))))),X3)),X5)))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f248,f1]) ).

fof(f248,plain,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X0)),equivalent(equivalent(equivalent(X3,X4),equivalent(equivalent(X4,equivalent(X5,equivalent(X6,equivalent(equivalent(X7,X8),equivalent(equivalent(X8,X6),X7))))),X3)),X5)),X2)),
    inference(resolution,[],[f206,f2]) ).

fof(f206,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ is_a_theorem(equivalent(X7,X0))
      | is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X3,equivalent(X4,equivalent(equivalent(X5,X6),equivalent(equivalent(X6,X4),X5))))),X1)),X3)),X7)) ),
    inference(resolution,[],[f113,f1]) ).

fof(f113,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(equivalent(X3,equivalent(X4,equivalent(X5,equivalent(equivalent(X6,X7),equivalent(equivalent(X7,X5),X6))))),X2)),X4)),X0))),
    inference(resolution,[],[f103,f4]) ).

fof(f15360,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X0),X1),equivalent(equivalent(X1,equivalent(X2,X2)),equivalent(X3,X3)))),
    inference(resolution,[],[f15297,f6359]) ).

fof(f6359,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_a_theorem(equivalent(equivalent(X2,X0),X1))
      | is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(X3,X3)))) ),
    inference(resolution,[],[f6290,f1]) ).

fof(f6290,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,equivalent(equivalent(X2,X0),equivalent(X3,X3))))),
    inference(resolution,[],[f2076,f1595]) ).

fof(f2076,plain,
    ! [X2,X3,X0,X1,X4] : is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X3,equivalent(X0,equivalent(X4,X4)))),X1)),X3))),
    inference(resolution,[],[f2015,f22]) ).

fof(f2015,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,X2)),X0))),
    inference(resolution,[],[f1902,f1555]) ).

fof(f1902,plain,
    ! [X2,X3,X0,X1,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,equivalent(equivalent(X3,X4),equivalent(equivalent(X4,X2),X3)))),X0)),equivalent(X5,X5))),
    inference(resolution,[],[f1556,f111]) ).

fof(f15297,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X0),equivalent(equivalent(X1,X1),X2)),X2)),
    inference(resolution,[],[f15162,f6290]) ).

fof(f15162,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X3,X3)),X1))))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f15092,f1]) ).

fof(f15092,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X3,X3)),X1))),X0)),
    inference(resolution,[],[f2102,f2213]) ).

fof(f2213,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(X1,X1)))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f2140,f1]) ).

fof(f2140,plain,
    ! [X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X1)),X0)),
    inference(resolution,[],[f2089,f2043]) ).

fof(f2043,plain,
    ! [X0] : is_a_theorem(equivalent(X0,X0)),
    inference(subsumption_resolution,[],[f2020,f5]) ).

fof(f2020,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( is_a_theorem(equivalent(X0,X0))
      | ~ is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X3,equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X3),X4)))),X1))) ),
    inference(resolution,[],[f1902,f1]) ).

fof(f2089,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(X2,X0))
      | is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X1)),X2)) ),
    inference(resolution,[],[f2015,f1]) ).

fof(f2102,plain,
    ! [X2,X3,X0,X1,X4] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,equivalent(X4,X4)),X2))),X0))),
    inference(resolution,[],[f2015,f4]) ).

fof(f69086,plain,
    ! [X0,X1] : is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X0,X1)))),
    inference(resolution,[],[f62740,f1213]) ).

fof(f62740,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,equivalent(X1,X0)),X1),X2),equivalent(X2,equivalent(X3,X3)))),
    inference(resolution,[],[f50399,f60241]) ).

fof(f60241,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X1)),X2),equivalent(X0,equivalent(X3,X3))))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f43161,f1]) ).

fof(f43161,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,equivalent(X1,X0)),X1),equivalent(X2,equivalent(X3,X3))),X2)),
    inference(resolution,[],[f34315,f2567]) ).

fof(f2567,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X2)),X0),equivalent(X3,X3)))
      | is_a_theorem(equivalent(X0,X1)) ),
    inference(resolution,[],[f2182,f1]) ).

fof(f2182,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,equivalent(X1,X1)),X2),equivalent(X3,X3)),equivalent(X2,X0))),
    inference(resolution,[],[f2089,f2015]) ).

fof(f34315,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X1,equivalent(X2,X1)),X2),X0)),equivalent(X3,X3))),
    inference(resolution,[],[f27603,f18361]) ).

fof(f18361,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X0)),equivalent(X2,X2)),equivalent(X1,equivalent(X3,X3)))),
    inference(resolution,[],[f18168,f2089]) ).

fof(f18168,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X1)),equivalent(X2,equivalent(X0,X2)))),
    inference(resolution,[],[f18006,f2089]) ).

fof(f18006,plain,
    ! [X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X0)),X1)),
    inference(resolution,[],[f17926,f6290]) ).

fof(f17926,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X1,equivalent(X2,X2)))))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f17851,f1]) ).

fof(f17851,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X1,equivalent(X2,X2)))),X0)),
    inference(resolution,[],[f15890,f2213]) ).

fof(f15890,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,equivalent(X2,equivalent(X3,X3)))),X0))),
    inference(resolution,[],[f15770,f4]) ).

fof(f27603,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,equivalent(X2,X1)),X2),equivalent(X3,X3))))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f18208,f1]) ).

fof(f18208,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X1,equivalent(X2,X1)),X2),equivalent(X3,X3))),X0)),
    inference(resolution,[],[f18006,f2946]) ).

fof(f2946,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(X1)
      | is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X2,X2))),X0)) ),
    inference(resolution,[],[f2902,f1]) ).

fof(f2902,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,equivalent(X0,equivalent(X2,X2))),X1))),
    inference(resolution,[],[f2567,f1526]) ).

fof(f50399,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X0,X1),equivalent(X1,equivalent(X2,X2))),equivalent(X3,X3)))),
    inference(resolution,[],[f50250,f6359]) ).

fof(f50250,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(X1,X1)),X2),equivalent(X2,X0))),
    inference(resolution,[],[f38079,f1595]) ).

fof(f38079,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1)),equivalent(X3,X3)))),
    inference(resolution,[],[f21054,f1595]) ).

fof(f21054,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(X1,equivalent(X3,X3))),X2)),X0))),
    inference(resolution,[],[f16044,f18347]) ).

fof(f18347,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(X1,equivalent(X2,X2)))
      | is_a_theorem(equivalent(X0,equivalent(X1,X0))) ),
    inference(resolution,[],[f18168,f1]) ).

fof(f16044,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,equivalent(X0,equivalent(X2,X2))),X1)),equivalent(X3,X3))),
    inference(resolution,[],[f15847,f2902]) ).

fof(f77168,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(X1,equivalent(X2,X2)))
      | is_a_theorem(equivalent(equivalent(X0,X1),X0)) ),
    inference(resolution,[],[f76449,f1]) ).

fof(f76449,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X1)),equivalent(equivalent(X2,X0),X2))),
    inference(resolution,[],[f76070,f2089]) ).

fof(f76070,plain,
    ! [X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X0),X1)),
    inference(resolution,[],[f64706,f38079]) ).

fof(f64706,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X2),X0),equivalent(X3,X3))))
      | is_a_theorem(equivalent(X0,X1)) ),
    inference(resolution,[],[f50909,f1]) ).

fof(f50909,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X1,X1),X2),equivalent(X3,X3))),equivalent(X2,X0))),
    inference(resolution,[],[f50446,f6290]) ).

fof(f50446,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X0))
      | is_a_theorem(equivalent(X0,X1)) ),
    inference(resolution,[],[f50250,f1]) ).

fof(f688290,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),equivalent(X1,X2))),
    inference(resolution,[],[f669043,f641093]) ).

fof(f669043,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(X1,X0))),X2)),
    inference(resolution,[],[f663869,f126321]) ).

fof(f126321,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(equivalent(X1,X0))
      | is_a_theorem(equivalent(X0,X1)) ),
    inference(resolution,[],[f126010,f1]) ).

fof(f126010,plain,
    ! [X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X1,X0))),
    inference(resolution,[],[f124306,f104733]) ).

fof(f104733,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(X2,X2))))
      | is_a_theorem(equivalent(X0,X1)) ),
    inference(resolution,[],[f103774,f1]) ).

fof(f103774,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X2,X2))),equivalent(X0,X1))),
    inference(resolution,[],[f99663,f2606]) ).

fof(f2606,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,equivalent(X3,X3))),X0)),X2)),
    inference(resolution,[],[f2464,f2015]) ).

fof(f2464,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X1),X2)))))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f2045,f1]) ).

fof(f2045,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X1),X2)))),X0)),
    inference(resolution,[],[f2043,f6]) ).

fof(f99663,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X1),X0),X2))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f93666,f1]) ).

fof(f93666,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),X0),X2),X1),X2)),
    inference(resolution,[],[f90289,f80635]) ).

fof(f90289,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X1),X2))))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f85448,f1]) ).

fof(f85448,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X1),X2))),X0)),
    inference(resolution,[],[f85004,f84765]) ).

fof(f84765,plain,
    ! [X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X0),X1))),
    inference(resolution,[],[f82555,f50446]) ).

fof(f82555,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X0)),X2)),
    inference(resolution,[],[f80941,f2598]) ).

fof(f2598,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1))),X3),X3)),
    inference(resolution,[],[f2464,f761]) ).

fof(f761,plain,
    ! [X2,X3,X0,X1,X6,X4,X5] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1))),X3),X3),equivalent(X4,equivalent(equivalent(X5,X6),equivalent(equivalent(X6,X4),X5))))),
    inference(resolution,[],[f745,f10]) ).

fof(f10,plain,
    ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X1),X2)))),equivalent(equivalent(equivalent(X4,X5),equivalent(equivalent(X5,X0),X4)),equivalent(X6,equivalent(equivalent(X7,X8),equivalent(equivalent(X8,X6),X7)))))),
    inference(resolution,[],[f8,f6]) ).

fof(f745,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] :
      ( ~ is_a_theorem(equivalent(X4,equivalent(equivalent(X4,X0),equivalent(X5,equivalent(equivalent(X6,X7),equivalent(equivalent(X7,X5),X6))))))
      | is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X1),X2))))) ),
    inference(resolution,[],[f723,f1]) ).

fof(f723,plain,
    ! [X2,X3,X0,X1,X6,X7,X4,X5] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X0,X1),equivalent(X2,equivalent(equivalent(X3,X4),equivalent(equivalent(X4,X2),X3))))),equivalent(X1,equivalent(X5,equivalent(equivalent(X6,X7),equivalent(equivalent(X7,X5),X6)))))),
    inference(resolution,[],[f248,f11]) ).

fof(f80941,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X0),X2))
      | is_a_theorem(equivalent(X0,X1)) ),
    inference(resolution,[],[f80635,f1]) ).

fof(f85004,plain,
    ! [X0,X1] :
      ( ~ is_a_theorem(X1)
      | is_a_theorem(equivalent(equivalent(X0,X1),X0)) ),
    inference(resolution,[],[f84765,f1]) ).

fof(f124306,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X0),equivalent(X2,X2)))),
    inference(resolution,[],[f124136,f6359]) ).

fof(f124136,plain,
    ! [X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X0,X1)),X1)),
    inference(resolution,[],[f123902,f84821]) ).

fof(f84821,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1)))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f82555,f1]) ).

fof(f123902,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,equivalent(equivalent(X2,X0),X1)),X2))),
    inference(resolution,[],[f69279,f104733]) ).

fof(f69279,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X0),X1)),X2),equivalent(X3,X3)))),
    inference(resolution,[],[f69086,f6359]) ).

fof(f663869,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X0),equivalent(X2,X1))))),
    inference(resolution,[],[f655904,f641093]) ).

fof(f655904,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X1),X2)),
    inference(resolution,[],[f642834,f566323]) ).

fof(f566323,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),equivalent(X3,X1))))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f479559,f1]) ).

fof(f479559,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X2),equivalent(X3,X1))),X0)),
    inference(resolution,[],[f410345,f1641]) ).

fof(f410345,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X3,equivalent(X2,X3)))))
      | is_a_theorem(equivalent(equivalent(X0,X1),X0)) ),
    inference(resolution,[],[f329569,f1]) ).

fof(f329569,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X2,equivalent(X1,X2)))),equivalent(equivalent(X3,X0),X3))),
    inference(resolution,[],[f276364,f76070]) ).

fof(f276364,plain,
    ! [X2,X3,X0,X1] :
      ( ~ is_a_theorem(equivalent(X3,X0))
      | is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(X2,equivalent(X1,X2)))),X3)) ),
    inference(resolution,[],[f69292,f1]) ).

fof(f69292,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,equivalent(X3,equivalent(X2,X3)))),X0))),
    inference(resolution,[],[f69086,f4]) ).

fof(f642834,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(X0,equivalent(equivalent(X2,X1),X2)))),
    inference(resolution,[],[f641093,f92127]) ).

fof(f92127,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),X0),equivalent(X2,X1)),X2)),
    inference(resolution,[],[f89126,f80941]) ).

fof(f89126,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),X1),X0)),X2)),
    inference(resolution,[],[f86714,f81731]) ).

fof(f81731,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(equivalent(X1,X0),equivalent(equivalent(X2,X1),X2)))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f80914,f1]) ).

fof(f80914,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X2,X0),X2)),X1)),
    inference(resolution,[],[f80635,f79624]) ).

fof(f79624,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),X1),X2)))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f78661,f1]) ).

fof(f78661,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),X1),X2)),X0)),
    inference(resolution,[],[f77168,f76529]) ).

fof(f76529,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),X0),X1),equivalent(X2,X2))),
    inference(resolution,[],[f76070,f15847]) ).

fof(f86714,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,equivalent(X2,X1)),X0)),X2)),
    inference(resolution,[],[f84809,f80941]) ).

fof(f84809,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,equivalent(equivalent(X2,X0),X1))),X2)),
    inference(resolution,[],[f82555,f81314]) ).

fof(f81314,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(equivalent(X1,X0),equivalent(X2,equivalent(X1,X2))))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f80912,f1]) ).

fof(f80912,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,equivalent(X0,X2))),X1)),
    inference(resolution,[],[f80635,f27345]) ).

fof(f27345,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(equivalent(X1,equivalent(X2,X1)),X2)))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f27240,f1]) ).

fof(f27240,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(X1,equivalent(X2,X1)),X2)),X0)),
    inference(resolution,[],[f18197,f2213]) ).

fof(f18197,plain,
    ! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X2)),X3)),X0))),
    inference(resolution,[],[f18006,f4]) ).

fof(f713425,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(equivalent(equivalent(X0,X2),X2),X1))
      | is_a_theorem(equivalent(X0,X1)) ),
    inference(resolution,[],[f692522,f1]) ).

fof(f692522,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),X1),X2),equivalent(X0,X2))),
    inference(resolution,[],[f685423,f157266]) ).

fof(f157266,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(X0,equivalent(equivalent(X1,X0),equivalent(equivalent(X1,X2),X2)))),
    inference(resolution,[],[f144147,f126321]) ).

fof(f144147,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),X2)),X1)),
    inference(resolution,[],[f133493,f80635]) ).

fof(f133493,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),X2),X1)))
      | is_a_theorem(X0) ),
    inference(resolution,[],[f124778,f1]) ).

fof(f124778,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(equivalent(equivalent(X1,X2),X2),X1)),X0)),
    inference(resolution,[],[f124294,f85004]) ).

fof(f124294,plain,
    ! [X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X1),X0)),
    inference(resolution,[],[f124136,f80941]) ).

fof(f685423,plain,
    ! [X2,X0,X1] :
      ( ~ is_a_theorem(equivalent(X1,equivalent(X2,X0)))
      | is_a_theorem(equivalent(equivalent(X0,X1),X2)) ),
    inference(resolution,[],[f641120,f1]) ).

fof(f641120,plain,
    ! [X2,X0,X1] : is_a_theorem(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(equivalent(X2,X0),X1))),
    inference(resolution,[],[f640387,f126321]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : LCL021-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Apr 29 22:52:51 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (7049)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (7056)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37  % (7055)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.37  % (7053)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  % (7052)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37  % (7057)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37  % (7054)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.37  % (7058)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [1]
% 0.14/0.38  TRYING [2]
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% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [4]
% 0.14/0.39  TRYING [4]
% 0.20/0.54  TRYING [5]
% 0.20/0.54  TRYING [5]
% 0.20/0.54  TRYING [5]
% 0.20/0.54  TRYING [5]
% 62.98/9.31  TRYING [6]
% 82.02/12.06  TRYING [6]
% 82.70/12.12  TRYING [6]
% 82.70/12.14  TRYING [6]
% 145.80/21.11  % (7056)First to succeed.
% 145.80/21.14  % (7056)Refutation found. Thanks to Tanya!
% 145.80/21.14  % SZS status Unsatisfiable for theBenchmark
% 145.80/21.14  % SZS output start Proof for theBenchmark
% See solution above
% 145.80/21.14  % (7056)------------------------------
% 145.80/21.14  % (7056)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 145.80/21.14  % (7056)Termination reason: Refutation
% 145.80/21.14  
% 145.80/21.14  % (7056)Memory used [KB]: 243968
% 145.80/21.14  % (7056)Time elapsed: 20.743 s
% 145.80/21.14  % (7056)Instructions burned: 77099 (million)
% 145.80/21.14  % (7056)------------------------------
% 145.80/21.14  % (7056)------------------------------
% 145.80/21.14  % (7049)Success in time 20.426 s
%------------------------------------------------------------------------------