%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG024+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n031.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 Aug 22 10:30:55 EDT 2023

% Result   : Unsatisfiable 14.00s 4.56s
% Output   : CNFRefutation 14.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   29
% Syntax   : Number of formulae    :  703 ( 607 unt;   7 typ;   0 def)
%            Number of atoms       : 1109 (1063 equ)
%            Maximal formula atoms :   64 (   1 avg)
%            Number of connectives :  701 ( 288   ~; 192   |; 205   &)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   64 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ op > #nlpp > inv > unit > e3 > e2 > e1 > e0

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(e1,type,
    e1: $i ).

tff(e0,type,
    e0: $i ).

tff(e2,type,
    e2: $i ).

tff(inv,type,
    inv: $i > $i ).

tff(op,type,
    op: ( $i * $i ) > $i ).

tff(unit,type,
    unit: $i ).

tff(e3,type,
    e3: $i ).

tff(f_597,axiom,
    ( ( e0 != e1 )
    & ( e0 != e2 )
    & ( e0 != e3 )
    & ( e1 != e2 )
    & ( e1 != e3 )
    & ( e2 != e3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10) ).

tff(f_420,axiom,
    ( ( ( inv(e0) = e0 )
     => ( inv(e0) = e0 ) )
    & ( ( inv(e0) = e1 )
     => ( inv(e1) = e0 ) )
    & ( ( inv(e0) = e2 )
     => ( inv(e2) = e0 ) )
    & ( ( inv(e0) = e3 )
     => ( inv(e3) = e0 ) )
    & ( ( inv(e1) = e0 )
     => ( inv(e0) = e1 ) )
    & ( ( inv(e1) = e1 )
     => ( inv(e1) = e1 ) )
    & ( ( inv(e1) = e2 )
     => ( inv(e2) = e1 ) )
    & ( ( inv(e1) = e3 )
     => ( inv(e3) = e1 ) )
    & ( ( inv(e2) = e0 )
     => ( inv(e0) = e2 ) )
    & ( ( inv(e2) = e1 )
     => ( inv(e1) = e2 ) )
    & ( ( inv(e2) = e2 )
     => ( inv(e2) = e2 ) )
    & ( ( inv(e2) = e3 )
     => ( inv(e3) = e2 ) )
    & ( ( inv(e3) = e0 )
     => ( inv(e0) = e3 ) )
    & ( ( inv(e3) = e1 )
     => ( inv(e1) = e3 ) )
    & ( ( inv(e3) = e2 )
     => ( inv(e2) = e3 ) )
    & ( ( inv(e3) = e3 )
     => ( inv(e3) = e3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).

tff(f_349,axiom,
    ( ( op(e0,inv(e0)) = unit )
    & ( op(inv(e0),e0) = unit )
    & ( op(e1,inv(e1)) = unit )
    & ( op(inv(e1),e1) = unit )
    & ( op(e2,inv(e2)) = unit )
    & ( op(inv(e2),e2) = unit )
    & ( op(e3,inv(e3)) = unit )
    & ( op(inv(e3),e3) = unit )
    & ( ( inv(e0) = e0 )
      | ( inv(e0) = e1 )
      | ( inv(e0) = e2 )
      | ( inv(e0) = e3 ) )
    & ( ( inv(e1) = e0 )
      | ( inv(e1) = e1 )
      | ( inv(e1) = e2 )
      | ( inv(e1) = e3 ) )
    & ( ( inv(e2) = e0 )
      | ( inv(e2) = e1 )
      | ( inv(e2) = e2 )
      | ( inv(e2) = e3 ) )
    & ( ( inv(e3) = e0 )
      | ( inv(e3) = e1 )
      | ( inv(e3) = e2 )
      | ( inv(e3) = e3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

tff(f_302,axiom,
    ( ( op(unit,e0) = e0 )
    & ( op(e0,unit) = e0 )
    & ( op(unit,e1) = e1 )
    & ( op(e1,unit) = e1 )
    & ( op(unit,e2) = e2 )
    & ( op(e2,unit) = e2 )
    & ( op(unit,e3) = e3 )
    & ( op(e3,unit) = e3 )
    & ( ( unit = e0 )
      | ( unit = e1 )
      | ( unit = e2 )
      | ( unit = e3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

tff(f_629,axiom,
    ~ ( ( ( op(e0,e0) = e0 )
        & ( op(e1,e1) = e0 )
        & ( op(e2,e2) = e0 )
        & ( op(e3,e3) = e0 ) )
      | ( ( op(e0,e0) = e1 )
        & ( op(e1,e1) = e1 )
        & ( op(e2,e2) = e1 )
        & ( op(e3,e3) = e1 ) )
      | ( ( op(e0,e0) = e2 )
        & ( op(e1,e1) = e2 )
        & ( op(e2,e2) = e2 )
        & ( op(e3,e3) = e2 ) )
      | ( ( op(e0,e0) = e3 )
        & ( op(e1,e1) = e3 )
        & ( op(e2,e2) = e3 )
        & ( op(e3,e3) = e3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11) ).

tff(f_350,axiom,
    inv(unit) = unit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

tff(f_580,axiom,
    ( ( op(e0,e0) != op(e1,e0) )
    & ( op(e0,e0) != op(e2,e0) )
    & ( op(e0,e0) != op(e3,e0) )
    & ( op(e1,e0) != op(e2,e0) )
    & ( op(e1,e0) != op(e3,e0) )
    & ( op(e2,e0) != op(e3,e0) )
    & ( op(e0,e1) != op(e1,e1) )
    & ( op(e0,e1) != op(e2,e1) )
    & ( op(e0,e1) != op(e3,e1) )
    & ( op(e1,e1) != op(e2,e1) )
    & ( op(e1,e1) != op(e3,e1) )
    & ( op(e2,e1) != op(e3,e1) )
    & ( op(e0,e2) != op(e1,e2) )
    & ( op(e0,e2) != op(e2,e2) )
    & ( op(e0,e2) != op(e3,e2) )
    & ( op(e1,e2) != op(e2,e2) )
    & ( op(e1,e2) != op(e3,e2) )
    & ( op(e2,e2) != op(e3,e2) )
    & ( op(e0,e3) != op(e1,e3) )
    & ( op(e0,e3) != op(e2,e3) )
    & ( op(e0,e3) != op(e3,e3) )
    & ( op(e1,e3) != op(e2,e3) )
    & ( op(e1,e3) != op(e3,e3) )
    & ( op(e2,e3) != op(e3,e3) )
    & ( op(e0,e0) != op(e0,e1) )
    & ( op(e0,e0) != op(e0,e2) )
    & ( op(e0,e0) != op(e0,e3) )
    & ( op(e0,e1) != op(e0,e2) )
    & ( op(e0,e1) != op(e0,e3) )
    & ( op(e0,e2) != op(e0,e3) )
    & ( op(e1,e0) != op(e1,e1) )
    & ( op(e1,e0) != op(e1,e2) )
    & ( op(e1,e0) != op(e1,e3) )
    & ( op(e1,e1) != op(e1,e2) )
    & ( op(e1,e1) != op(e1,e3) )
    & ( op(e1,e2) != op(e1,e3) )
    & ( op(e2,e0) != op(e2,e1) )
    & ( op(e2,e0) != op(e2,e2) )
    & ( op(e2,e0) != op(e2,e3) )
    & ( op(e2,e1) != op(e2,e2) )
    & ( op(e2,e1) != op(e2,e3) )
    & ( op(e2,e2) != op(e2,e3) )
    & ( op(e3,e0) != op(e3,e1) )
    & ( op(e3,e0) != op(e3,e2) )
    & ( op(e3,e0) != op(e3,e3) )
    & ( op(e3,e1) != op(e3,e2) )
    & ( op(e3,e1) != op(e3,e3) )
    & ( op(e3,e2) != op(e3,e3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9) ).

tff(f_152,axiom,
    ( ( ( op(e0,e0) = e0 )
      | ( op(e0,e0) = e1 )
      | ( op(e0,e0) = e2 )
      | ( op(e0,e0) = e3 ) )
    & ( ( op(e0,e1) = e0 )
      | ( op(e0,e1) = e1 )
      | ( op(e0,e1) = e2 )
      | ( op(e0,e1) = e3 ) )
    & ( ( op(e0,e2) = e0 )
      | ( op(e0,e2) = e1 )
      | ( op(e0,e2) = e2 )
      | ( op(e0,e2) = e3 ) )
    & ( ( op(e0,e3) = e0 )
      | ( op(e0,e3) = e1 )
      | ( op(e0,e3) = e2 )
      | ( op(e0,e3) = e3 ) )
    & ( ( op(e1,e0) = e0 )
      | ( op(e1,e0) = e1 )
      | ( op(e1,e0) = e2 )
      | ( op(e1,e0) = e3 ) )
    & ( ( op(e1,e1) = e0 )
      | ( op(e1,e1) = e1 )
      | ( op(e1,e1) = e2 )
      | ( op(e1,e1) = e3 ) )
    & ( ( op(e1,e2) = e0 )
      | ( op(e1,e2) = e1 )
      | ( op(e1,e2) = e2 )
      | ( op(e1,e2) = e3 ) )
    & ( ( op(e1,e3) = e0 )
      | ( op(e1,e3) = e1 )
      | ( op(e1,e3) = e2 )
      | ( op(e1,e3) = e3 ) )
    & ( ( op(e2,e0) = e0 )
      | ( op(e2,e0) = e1 )
      | ( op(e2,e0) = e2 )
      | ( op(e2,e0) = e3 ) )
    & ( ( op(e2,e1) = e0 )
      | ( op(e2,e1) = e1 )
      | ( op(e2,e1) = e2 )
      | ( op(e2,e1) = e3 ) )
    & ( ( op(e2,e2) = e0 )
      | ( op(e2,e2) = e1 )
      | ( op(e2,e2) = e2 )
      | ( op(e2,e2) = e3 ) )
    & ( ( op(e2,e3) = e0 )
      | ( op(e2,e3) = e1 )
      | ( op(e2,e3) = e2 )
      | ( op(e2,e3) = e3 ) )
    & ( ( op(e3,e0) = e0 )
      | ( op(e3,e0) = e1 )
      | ( op(e3,e0) = e2 )
      | ( op(e3,e0) = e3 ) )
    & ( ( op(e3,e1) = e0 )
      | ( op(e3,e1) = e1 )
      | ( op(e3,e1) = e2 )
      | ( op(e3,e1) = e3 ) )
    & ( ( op(e3,e2) = e0 )
      | ( op(e3,e2) = e1 )
      | ( op(e3,e2) = e2 )
      | ( op(e3,e2) = e3 ) )
    & ( ( op(e3,e3) = e0 )
      | ( op(e3,e3) = e1 )
      | ( op(e3,e3) = e2 )
      | ( op(e3,e3) = e3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

tff(f_279,axiom,
    ( ( op(op(e0,e0),e0) = op(e0,op(e0,e0)) )
    & ( op(op(e0,e0),e1) = op(e0,op(e0,e1)) )
    & ( op(op(e0,e0),e2) = op(e0,op(e0,e2)) )
    & ( op(op(e0,e0),e3) = op(e0,op(e0,e3)) )
    & ( op(op(e0,e1),e0) = op(e0,op(e1,e0)) )
    & ( op(op(e0,e1),e1) = op(e0,op(e1,e1)) )
    & ( op(op(e0,e1),e2) = op(e0,op(e1,e2)) )
    & ( op(op(e0,e1),e3) = op(e0,op(e1,e3)) )
    & ( op(op(e0,e2),e0) = op(e0,op(e2,e0)) )
    & ( op(op(e0,e2),e1) = op(e0,op(e2,e1)) )
    & ( op(op(e0,e2),e2) = op(e0,op(e2,e2)) )
    & ( op(op(e0,e2),e3) = op(e0,op(e2,e3)) )
    & ( op(op(e0,e3),e0) = op(e0,op(e3,e0)) )
    & ( op(op(e0,e3),e1) = op(e0,op(e3,e1)) )
    & ( op(op(e0,e3),e2) = op(e0,op(e3,e2)) )
    & ( op(op(e0,e3),e3) = op(e0,op(e3,e3)) )
    & ( op(op(e1,e0),e0) = op(e1,op(e0,e0)) )
    & ( op(op(e1,e0),e1) = op(e1,op(e0,e1)) )
    & ( op(op(e1,e0),e2) = op(e1,op(e0,e2)) )
    & ( op(op(e1,e0),e3) = op(e1,op(e0,e3)) )
    & ( op(op(e1,e1),e0) = op(e1,op(e1,e0)) )
    & ( op(op(e1,e1),e1) = op(e1,op(e1,e1)) )
    & ( op(op(e1,e1),e2) = op(e1,op(e1,e2)) )
    & ( op(op(e1,e1),e3) = op(e1,op(e1,e3)) )
    & ( op(op(e1,e2),e0) = op(e1,op(e2,e0)) )
    & ( op(op(e1,e2),e1) = op(e1,op(e2,e1)) )
    & ( op(op(e1,e2),e2) = op(e1,op(e2,e2)) )
    & ( op(op(e1,e2),e3) = op(e1,op(e2,e3)) )
    & ( op(op(e1,e3),e0) = op(e1,op(e3,e0)) )
    & ( op(op(e1,e3),e1) = op(e1,op(e3,e1)) )
    & ( op(op(e1,e3),e2) = op(e1,op(e3,e2)) )
    & ( op(op(e1,e3),e3) = op(e1,op(e3,e3)) )
    & ( op(op(e2,e0),e0) = op(e2,op(e0,e0)) )
    & ( op(op(e2,e0),e1) = op(e2,op(e0,e1)) )
    & ( op(op(e2,e0),e2) = op(e2,op(e0,e2)) )
    & ( op(op(e2,e0),e3) = op(e2,op(e0,e3)) )
    & ( op(op(e2,e1),e0) = op(e2,op(e1,e0)) )
    & ( op(op(e2,e1),e1) = op(e2,op(e1,e1)) )
    & ( op(op(e2,e1),e2) = op(e2,op(e1,e2)) )
    & ( op(op(e2,e1),e3) = op(e2,op(e1,e3)) )
    & ( op(op(e2,e2),e0) = op(e2,op(e2,e0)) )
    & ( op(op(e2,e2),e1) = op(e2,op(e2,e1)) )
    & ( op(op(e2,e2),e2) = op(e2,op(e2,e2)) )
    & ( op(op(e2,e2),e3) = op(e2,op(e2,e3)) )
    & ( op(op(e2,e3),e0) = op(e2,op(e3,e0)) )
    & ( op(op(e2,e3),e1) = op(e2,op(e3,e1)) )
    & ( op(op(e2,e3),e2) = op(e2,op(e3,e2)) )
    & ( op(op(e2,e3),e3) = op(e2,op(e3,e3)) )
    & ( op(op(e3,e0),e0) = op(e3,op(e0,e0)) )
    & ( op(op(e3,e0),e1) = op(e3,op(e0,e1)) )
    & ( op(op(e3,e0),e2) = op(e3,op(e0,e2)) )
    & ( op(op(e3,e0),e3) = op(e3,op(e0,e3)) )
    & ( op(op(e3,e1),e0) = op(e3,op(e1,e0)) )
    & ( op(op(e3,e1),e1) = op(e3,op(e1,e1)) )
    & ( op(op(e3,e1),e2) = op(e3,op(e1,e2)) )
    & ( op(op(e3,e1),e3) = op(e3,op(e1,e3)) )
    & ( op(op(e3,e2),e0) = op(e3,op(e2,e0)) )
    & ( op(op(e3,e2),e1) = op(e3,op(e2,e1)) )
    & ( op(op(e3,e2),e2) = op(e3,op(e2,e2)) )
    & ( op(op(e3,e2),e3) = op(e3,op(e2,e3)) )
    & ( op(op(e3,e3),e0) = op(e3,op(e3,e0)) )
    & ( op(op(e3,e3),e1) = op(e3,op(e3,e1)) )
    & ( op(op(e3,e3),e2) = op(e3,op(e3,e2)) )
    & ( op(op(e3,e3),e3) = op(e3,op(e3,e3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

tff(f_743,axiom,
    ~ ( ( e3 = op(op(e1,op(e1,e1)),e1) )
      & ( e0 = op(e1,op(e1,e1)) )
      & ( e2 = op(e1,e1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).

tff(f_437,axiom,
    ( ( inv(e0) != inv(e1) )
    & ( inv(e0) != inv(e2) )
    & ( inv(e0) != inv(e3) )
    & ( inv(e1) != inv(e2) )
    & ( inv(e1) != inv(e3) )
    & ( inv(e2) != inv(e3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8) ).

tff(f_707,axiom,
    ~ ( ( e2 = op(op(e1,op(e1,e1)),e1) )
      & ( e0 = op(e1,op(e1,e1)) )
      & ( e3 = op(e1,e1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).

tff(f_659,axiom,
    ~ ( ( e0 = op(op(e1,op(e1,e1)),e1) )
      & ( e3 = op(e1,op(e1,e1)) )
      & ( e2 = op(e1,e1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).

tff(f_737,axiom,
    ~ ( ( e2 = op(op(e1,op(e1,e1)),e1) )
      & ( e3 = op(e1,op(e1,e1)) )
      & ( e0 = op(e1,e1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).

tff(f_767,axiom,
    ~ ( ( e3 = op(op(e0,op(e0,e0)),e0) )
      & ( e2 = op(e0,op(e0,e0)) )
      & ( e1 = op(e0,e0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).

tff(f_671,axiom,
    ~ ( ( e1 = op(op(e2,op(e2,e2)),e2) )
      & ( e0 = op(e2,op(e2,e2)) )
      & ( e3 = op(e2,e2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).

tff(f_635,axiom,
    ~ ( ( e0 = op(op(e2,op(e2,e2)),e2) )
      & ( e1 = op(e2,op(e2,e2)) )
      & ( e3 = op(e2,e2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax12) ).

tff(f_761,axiom,
    ~ ( ( e3 = op(op(e2,op(e2,e2)),e2) )
      & ( e1 = op(e2,op(e2,e2)) )
      & ( e0 = op(e2,e2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).

tff(f_677,axiom,
    ~ ( ( e1 = op(op(e3,op(e3,e3)),e3) )
      & ( e0 = op(e3,op(e3,e3)) )
      & ( e2 = op(e3,e3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).

tff(f_713,axiom,
    ~ ( ( e2 = op(op(e3,op(e3,e3)),e3) )
      & ( e0 = op(e3,op(e3,e3)) )
      & ( e1 = op(e3,e3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).

tff(f_665,axiom,
    ~ ( ( e0 = op(op(e2,op(e2,e2)),e2) )
      & ( e3 = op(e2,op(e2,e2)) )
      & ( e1 = op(e2,e2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).

tff(f_689,axiom,
    ~ ( ( e1 = op(op(e3,op(e3,e3)),e3) )
      & ( e2 = op(e3,op(e3,e3)) )
      & ( e0 = op(e3,e3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).

tff(c_354,plain,
    e3 != e2,
    inference(cnfTransformation,[status(thm)],[f_597]) ).

tff(c_364,plain,
    e1 != e0,
    inference(cnfTransformation,[status(thm)],[f_597]) ).

tff(c_358,plain,
    e2 != e1,
    inference(cnfTransformation,[status(thm)],[f_597]) ).

tff(c_360,plain,
    e3 != e0,
    inference(cnfTransformation,[status(thm)],[f_597]) ).

tff(c_362,plain,
    e2 != e0,
    inference(cnfTransformation,[status(thm)],[f_597]) ).

tff(c_356,plain,
    e3 != e1,
    inference(cnfTransformation,[status(thm)],[f_597]) ).

tff(c_236,plain,
    ( ( inv(e0) = e1 )
    | ( inv(e1) != e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_513,plain,
    inv(e1) != e0,
    inference(splitLeft,[status(thm)],[c_236]) ).

tff(c_242,plain,
    ( ( inv(e1) = e0 )
    | ( inv(e0) != e1 ) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_516,plain,
    inv(e0) != e1,
    inference(negUnitSimplification,[status(thm)],[c_513,c_242]) ).

tff(c_228,plain,
    ( ( inv(e0) = e2 )
    | ( inv(e2) != e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_509,plain,
    inv(e2) != e0,
    inference(splitLeft,[status(thm)],[c_228]) ).

tff(c_240,plain,
    ( ( inv(e2) = e0 )
    | ( inv(e0) != e2 ) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_515,plain,
    inv(e0) != e2,
    inference(negUnitSimplification,[status(thm)],[c_509,c_240]) ).

tff(c_220,plain,
    ( ( inv(e0) = e3 )
    | ( inv(e3) != e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_506,plain,
    inv(e3) != e0,
    inference(splitLeft,[status(thm)],[c_220]) ).

tff(c_238,plain,
    ( ( inv(e3) = e0 )
    | ( inv(e0) != e3 ) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_512,plain,
    inv(e0) != e3,
    inference(negUnitSimplification,[status(thm)],[c_506,c_238]) ).

tff(c_186,plain,
    ( ( inv(e0) = e3 )
    | ( inv(e0) = e2 )
    | ( inv(e0) = e1 )
    | ( inv(e0) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_2795,plain,
    inv(e0) = e0,
    inference(negUnitSimplification,[status(thm)],[c_516,c_515,c_512,c_186]) ).

tff(c_2152,plain,
    inv(e0) = e0,
    inference(negUnitSimplification,[status(thm)],[c_516,c_515,c_512,c_186]) ).

tff(c_1494,plain,
    inv(e0) = e0,
    inference(negUnitSimplification,[status(thm)],[c_516,c_515,c_512,c_186]) ).

tff(c_162,plain,
    ( ( unit = e3 )
    | ( unit = e2 )
    | ( unit = e1 )
    | ( unit = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_302]) ).

tff(c_517,plain,
    unit = e0,
    inference(splitLeft,[status(thm)],[c_162]) ).

tff(c_176,plain,
    op(e0,unit) = e0,
    inference(cnfTransformation,[status(thm)],[f_302]) ).

tff(c_526,plain,
    op(e0,e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_517,c_176]) ).

tff(c_226,plain,
    ( ( inv(e1) = e2 )
    | ( inv(e2) != e1 ) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_507,plain,
    inv(e2) != e1,
    inference(splitLeft,[status(thm)],[c_226]) ).

tff(c_232,plain,
    ( ( inv(e2) = e1 )
    | ( inv(e1) != e2 ) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_511,plain,
    inv(e1) != e2,
    inference(negUnitSimplification,[status(thm)],[c_507,c_232]) ).

tff(c_230,plain,
    ( ( inv(e3) = e1 )
    | ( inv(e1) != e3 ) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_510,plain,
    inv(e1) != e3,
    inference(splitLeft,[status(thm)],[c_230]) ).

tff(c_184,plain,
    ( ( inv(e1) = e3 )
    | ( inv(e1) = e2 )
    | ( inv(e1) = e1 )
    | ( inv(e1) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_912,plain,
    inv(e1) = e1,
    inference(negUnitSimplification,[status(thm)],[c_513,c_511,c_510,c_184]) ).

tff(c_198,plain,
    op(e1,inv(e1)) = unit,
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_519,plain,
    op(e1,inv(e1)) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_517,c_198]) ).

tff(c_913,plain,
    op(e1,e1) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_912,c_519]) ).

tff(c_216,plain,
    ( ( inv(e2) = e3 )
    | ( inv(e3) != e2 ) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_505,plain,
    inv(e3) != e2,
    inference(splitLeft,[status(thm)],[c_216]) ).

tff(c_222,plain,
    ( ( inv(e3) = e2 )
    | ( inv(e2) != e3 ) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_508,plain,
    inv(e2) != e3,
    inference(negUnitSimplification,[status(thm)],[c_505,c_222]) ).

tff(c_182,plain,
    ( ( inv(e2) = e3 )
    | ( inv(e2) = e2 )
    | ( inv(e2) = e1 )
    | ( inv(e2) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_871,plain,
    inv(e2) = e2,
    inference(negUnitSimplification,[status(thm)],[c_509,c_507,c_508,c_182]) ).

tff(c_194,plain,
    op(e2,inv(e2)) = unit,
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_521,plain,
    op(e2,inv(e2)) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_517,c_194]) ).

tff(c_872,plain,
    op(e2,e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_871,c_521]) ).

tff(c_218,plain,
    ( ( inv(e1) = e3 )
    | ( inv(e3) != e1 ) ),
    inference(cnfTransformation,[status(thm)],[f_420]) ).

tff(c_514,plain,
    inv(e3) != e1,
    inference(negUnitSimplification,[status(thm)],[c_510,c_218]) ).

tff(c_180,plain,
    ( ( inv(e3) = e3 )
    | ( inv(e3) = e2 )
    | ( inv(e3) = e1 )
    | ( inv(e3) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_968,plain,
    inv(e3) = e3,
    inference(negUnitSimplification,[status(thm)],[c_506,c_514,c_505,c_180]) ).

tff(c_190,plain,
    op(e3,inv(e3)) = unit,
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_524,plain,
    op(e3,inv(e3)) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_517,c_190]) ).

tff(c_969,plain,
    op(e3,e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_968,c_524]) ).

tff(c_372,plain,
    ( ( op(e3,e3) != e0 )
    | ( op(e2,e2) != e0 )
    | ( op(e1,e1) != e0 )
    | ( op(e0,e0) != e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_1143,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_526,c_913,c_872,c_969,c_372]) ).

tff(c_1144,plain,
    ( ( unit = e1 )
    | ( unit = e2 )
    | ( unit = e3 ) ),
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_1146,plain,
    unit = e3,
    inference(splitLeft,[status(thm)],[c_1144]) ).

tff(c_200,plain,
    op(inv(e0),e0) = unit,
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_1150,plain,
    op(inv(e0),e0) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_1146,c_200]) ).

tff(c_1495,plain,
    op(e0,e0) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_1494,c_1150]) ).

tff(c_1535,plain,
    inv(e1) = e1,
    inference(negUnitSimplification,[status(thm)],[c_513,c_511,c_510,c_184]) ).

tff(c_1149,plain,
    op(e1,inv(e1)) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_1146,c_198]) ).

tff(c_1536,plain,
    op(e1,e1) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_1535,c_1149]) ).

tff(c_1591,plain,
    inv(e2) = e2,
    inference(negUnitSimplification,[status(thm)],[c_509,c_507,c_508,c_182]) ).

tff(c_192,plain,
    op(inv(e2),e2) = unit,
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_1152,plain,
    op(inv(e2),e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_1146,c_192]) ).

tff(c_1592,plain,
    op(e2,e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_1591,c_1152]) ).

tff(c_164,plain,
    op(e3,unit) = e3,
    inference(cnfTransformation,[status(thm)],[f_302]) ).

tff(c_1163,plain,
    op(e3,e3) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_1146,c_164]) ).

tff(c_366,plain,
    ( ( op(e3,e3) != e3 )
    | ( op(e2,e2) != e3 )
    | ( op(e1,e1) != e3 )
    | ( op(e0,e0) != e3 ) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_1792,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1495,c_1536,c_1592,c_1163,c_366]) ).

tff(c_1793,plain,
    ( ( unit = e2 )
    | ( unit = e1 ) ),
    inference(splitRight,[status(thm)],[c_1144]) ).

tff(c_1799,plain,
    unit = e1,
    inference(splitLeft,[status(thm)],[c_1793]) ).

tff(c_1804,plain,
    op(inv(e0),e0) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_1799,c_200]) ).

tff(c_2153,plain,
    op(e0,e0) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_2152,c_1804]) ).

tff(c_174,plain,
    op(unit,e1) = e1,
    inference(cnfTransformation,[status(thm)],[f_302]) ).

tff(c_1812,plain,
    op(e1,e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_1799,c_174]) ).

tff(c_2193,plain,
    inv(e2) = e2,
    inference(negUnitSimplification,[status(thm)],[c_509,c_507,c_508,c_182]) ).

tff(c_1805,plain,
    op(e2,inv(e2)) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_1799,c_194]) ).

tff(c_2194,plain,
    op(e2,e2) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_2193,c_1805]) ).

tff(c_2249,plain,
    inv(e3) = e3,
    inference(negUnitSimplification,[status(thm)],[c_506,c_514,c_505,c_180]) ).

tff(c_1808,plain,
    op(e3,inv(e3)) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_1799,c_190]) ).

tff(c_2250,plain,
    op(e3,e3) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_2249,c_1808]) ).

tff(c_370,plain,
    ( ( op(e3,e3) != e1 )
    | ( op(e2,e2) != e1 )
    | ( op(e1,e1) != e1 )
    | ( op(e0,e0) != e1 ) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_2437,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2153,c_1812,c_2194,c_2250,c_370]) ).

tff(c_2438,plain,
    unit = e2,
    inference(splitRight,[status(thm)],[c_1793]) ).

tff(c_202,plain,
    op(e0,inv(e0)) = unit,
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_2449,plain,
    op(e0,inv(e0)) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_2438,c_202]) ).

tff(c_2796,plain,
    op(e0,e0) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_2795,c_2449]) ).

tff(c_2832,plain,
    inv(e1) = e1,
    inference(negUnitSimplification,[status(thm)],[c_513,c_511,c_510,c_184]) ).

tff(c_196,plain,
    op(inv(e1),e1) = unit,
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_2442,plain,
    op(inv(e1),e1) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_2438,c_196]) ).

tff(c_2833,plain,
    op(e1,e1) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_2832,c_2442]) ).

tff(c_170,plain,
    op(unit,e2) = e2,
    inference(cnfTransformation,[status(thm)],[f_302]) ).

tff(c_2454,plain,
    op(e2,e2) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_2438,c_170]) ).

tff(c_2880,plain,
    inv(e3) = e3,
    inference(negUnitSimplification,[status(thm)],[c_506,c_514,c_505,c_180]) ).

tff(c_188,plain,
    op(inv(e3),e3) = unit,
    inference(cnfTransformation,[status(thm)],[f_349]) ).

tff(c_2447,plain,
    op(inv(e3),e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_2438,c_188]) ).

tff(c_2881,plain,
    op(e3,e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_2880,c_2447]) ).

tff(c_368,plain,
    ( ( op(e3,e3) != e2 )
    | ( op(e2,e2) != e2 )
    | ( op(e1,e1) != e2 )
    | ( op(e0,e0) != e2 ) ),
    inference(cnfTransformation,[status(thm)],[f_629]) ).

tff(c_3098,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2796,c_2833,c_2454,c_2881,c_368]) ).

tff(c_3100,plain,
    inv(e1) = e0,
    inference(splitRight,[status(thm)],[c_236]) ).

tff(c_3154,plain,
    unit = e0,
    inference(splitLeft,[status(thm)],[c_162]) ).

tff(c_204,plain,
    inv(unit) = unit,
    inference(cnfTransformation,[status(thm)],[f_350]) ).

tff(c_3179,plain,
    inv(e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_3154,c_3154,c_204]) ).

tff(c_3099,plain,
    inv(e0) = e1,
    inference(splitRight,[status(thm)],[c_236]) ).

tff(c_3184,plain,
    e1 = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_3179,c_3099]) ).

tff(c_3186,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_364,c_3184]) ).

tff(c_3187,plain,
    ( ( unit = e1 )
    | ( unit = e2 )
    | ( unit = e3 ) ),
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_3189,plain,
    unit = e3,
    inference(splitLeft,[status(thm)],[c_3187]) ).

tff(c_3103,plain,
    op(e0,e1) = unit,
    inference(demodulation,[status(thm),theory(equality)],[c_3099,c_202]) ).

tff(c_3202,plain,
    op(e0,e1) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_3189,c_3103]) ).

tff(c_178,plain,
    op(unit,e0) = e0,
    inference(cnfTransformation,[status(thm)],[f_302]) ).

tff(c_3208,plain,
    op(e3,e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_3189,c_178]) ).

tff(c_342,plain,
    op(e3,e0) != op(e2,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_3308,plain,
    op(e2,e0) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_3208,c_342]) ).

tff(c_168,plain,
    op(e2,unit) = e2,
    inference(cnfTransformation,[status(thm)],[f_302]) ).

tff(c_3212,plain,
    op(e2,e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_3189,c_168]) ).

tff(c_276,plain,
    op(e2,e3) != op(e2,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_3256,plain,
    op(e2,e0) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_3212,c_276]) ).

tff(c_3115,plain,
    op(e1,e0) = unit,
    inference(demodulation,[status(thm),theory(equality)],[c_3100,c_198]) ).

tff(c_346,plain,
    op(e2,e0) != op(e1,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_3147,plain,
    op(e2,e0) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_3115,c_346]) ).

tff(c_3195,plain,
    op(e2,e0) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_3189,c_3147]) ).

tff(c_16,plain,
    ( ( op(e2,e0) = e3 )
    | ( op(e2,e0) = e2 )
    | ( op(e2,e0) = e1 )
    | ( op(e2,e0) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_3587,plain,
    op(e2,e0) = e1,
    inference(negUnitSimplification,[status(thm)],[c_3308,c_3256,c_3195,c_16]) ).

tff(c_3530,plain,
    inv(e2) = e2,
    inference(negUnitSimplification,[status(thm)],[c_509,c_507,c_508,c_182]) ).

tff(c_3204,plain,
    op(inv(e2),e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_3189,c_192]) ).

tff(c_3531,plain,
    op(e2,e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_3530,c_3204]) ).

tff(c_80,plain,
    op(op(e2,e2),e0) = op(e2,op(e2,e0)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_3541,plain,
    op(e2,op(e2,e0)) = op(e3,e0),
    inference(demodulation,[status(thm),theory(equality)],[c_3531,c_80]) ).

tff(c_3553,plain,
    op(e2,op(e2,e0)) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_3208,c_3541]) ).

tff(c_3588,plain,
    op(e2,e1) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_3587,c_3553]) ).

tff(c_94,plain,
    op(op(e2,e0),e1) = op(e2,op(e0,e1)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_3463,plain,
    op(op(e2,e0),e1) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_3212,c_3202,c_94]) ).

tff(c_3591,plain,
    op(e1,e1) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_3587,c_3463]) ).

tff(c_118,plain,
    op(op(e1,e1),e1) = op(e1,op(e1,e1)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_3630,plain,
    op(e2,e1) = op(e1,e2),
    inference(demodulation,[status(thm),theory(equality)],[c_3591,c_3591,c_118]) ).

tff(c_3639,plain,
    op(e1,e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_3588,c_3630]) ).

tff(c_410,plain,
    ( ( op(e1,e1) != e2 )
    | ( op(e1,op(e1,e1)) != e0 )
    | ( op(op(e1,op(e1,e1)),e1) != e3 ) ),
    inference(cnfTransformation,[status(thm)],[f_743]) ).

tff(c_3766,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3202,c_3639,c_3591,c_3639,c_3591,c_3591,c_410]) ).

tff(c_3767,plain,
    ( ( unit = e2 )
    | ( unit = e1 ) ),
    inference(splitRight,[status(thm)],[c_3187]) ).

tff(c_3769,plain,
    unit = e1,
    inference(splitLeft,[status(thm)],[c_3767]) ).

tff(c_3796,plain,
    inv(e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_3769,c_3769,c_204]) ).

tff(c_3797,plain,
    e1 = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_3100,c_3796]) ).

tff(c_3799,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_364,c_3797]) ).

tff(c_3800,plain,
    unit = e2,
    inference(splitRight,[status(thm)],[c_3767]) ).

tff(c_3819,plain,
    op(e0,e1) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_3800,c_3103]) ).

tff(c_172,plain,
    op(e1,unit) = e1,
    inference(cnfTransformation,[status(thm)],[f_302]) ).

tff(c_3827,plain,
    op(e1,e2) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_3800,c_172]) ).

tff(c_286,plain,
    op(e1,e2) != op(e1,e1),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_3870,plain,
    op(e1,e1) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_3827,c_286]) ).

tff(c_292,plain,
    op(e1,e1) != op(e1,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_3135,plain,
    op(e1,e1) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_3115,c_292]) ).

tff(c_3815,plain,
    op(e1,e1) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_3800,c_3135]) ).

tff(c_22,plain,
    ( ( op(e1,e1) = e3 )
    | ( op(e1,e1) = e2 )
    | ( op(e1,e1) = e1 )
    | ( op(e1,e1) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_4198,plain,
    ( ( op(e1,e1) = e3 )
    | ( op(e1,e1) = e0 ) ),
    inference(negUnitSimplification,[status(thm)],[c_3870,c_3815,c_22]) ).

tff(c_4199,plain,
    op(e1,e1) = e0,
    inference(splitLeft,[status(thm)],[c_4198]) ).

tff(c_332,plain,
    op(e3,e1) != op(e1,e1),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_4209,plain,
    op(e3,e1) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_4199,c_332]) ).

tff(c_3826,plain,
    op(e2,e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_3800,c_174]) ).

tff(c_330,plain,
    op(e3,e1) != op(e2,e1),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_3911,plain,
    op(e3,e1) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_3826,c_330]) ).

tff(c_336,plain,
    op(e3,e1) != op(e0,e1),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_3148,plain,
    op(e3,e1) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_3103,c_336]) ).

tff(c_3811,plain,
    op(e3,e1) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_3800,c_3148]) ).

tff(c_3831,plain,
    op(e3,e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_3800,c_164]) ).

tff(c_262,plain,
    op(e3,e2) != op(e3,e1),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_3901,plain,
    op(e3,e1) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_3831,c_262]) ).

tff(c_6,plain,
    ( ( op(e3,e1) = e3 )
    | ( op(e3,e1) = e2 )
    | ( op(e3,e1) = e1 )
    | ( op(e3,e1) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_4262,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4209,c_3911,c_3811,c_3901,c_6]) ).

tff(c_4263,plain,
    op(e1,e1) = e3,
    inference(splitRight,[status(thm)],[c_4198]) ).

tff(c_150,plain,
    op(op(e0,e1),e1) = op(e0,op(e1,e1)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_4026,plain,
    op(e0,op(e1,e1)) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_3826,c_3819,c_150]) ).

tff(c_4267,plain,
    op(e0,e3) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_4263,c_4026]) ).

tff(c_3824,plain,
    op(e0,e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_3800,c_176]) ).

tff(c_252,plain,
    inv(e3) != inv(e0),
    inference(cnfTransformation,[status(thm)],[f_437]) ).

tff(c_3105,plain,
    inv(e3) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_3099,c_252]) ).

tff(c_4143,plain,
    inv(e3) = e3,
    inference(negUnitSimplification,[status(thm)],[c_506,c_3105,c_505,c_180]) ).

tff(c_3822,plain,
    op(inv(e3),e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_3800,c_188]) ).

tff(c_4144,plain,
    op(e3,e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_4143,c_3822]) ).

tff(c_130,plain,
    op(op(e0,e3),e3) = op(e0,op(e3,e3)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_4159,plain,
    op(op(e0,e3),e3) = op(e0,e2),
    inference(demodulation,[status(thm),theory(equality)],[c_4144,c_130]) ).

tff(c_4171,plain,
    op(op(e0,e3),e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_3824,c_4159]) ).

tff(c_4308,plain,
    op(e1,e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_4267,c_4171]) ).

tff(c_398,plain,
    ( ( op(e1,e1) != e3 )
    | ( op(e1,op(e1,e1)) != e0 )
    | ( op(op(e1,op(e1,e1)),e1) != e2 ) ),
    inference(cnfTransformation,[status(thm)],[f_707]) ).

tff(c_4452,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3819,c_4308,c_4263,c_4308,c_4263,c_4263,c_398]) ).

tff(c_4453,plain,
    inv(e3) = e1,
    inference(splitRight,[status(thm)],[c_230]) ).

tff(c_4512,plain,
    unit = e0,
    inference(splitLeft,[status(thm)],[c_162]) ).

tff(c_4454,plain,
    inv(e1) = e3,
    inference(splitRight,[status(thm)],[c_230]) ).

tff(c_4467,plain,
    op(e3,e1) = unit,
    inference(demodulation,[status(thm),theory(equality)],[c_4454,c_196]) ).

tff(c_4503,plain,
    op(e3,e2) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_4467,c_262]) ).

tff(c_4517,plain,
    op(e3,e2) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_4512,c_4503]) ).

tff(c_4523,plain,
    op(e3,e1) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_4512,c_4467]) ).

tff(c_4468,plain,
    op(e1,e3) = unit,
    inference(demodulation,[status(thm),theory(equality)],[c_4454,c_198]) ).

tff(c_284,plain,
    op(e1,e3) != op(e1,e1),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_4480,plain,
    op(e1,e1) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_4468,c_284]) ).

tff(c_4521,plain,
    op(e1,e1) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_4512,c_4480]) ).

tff(c_4531,plain,
    op(e0,e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_4512,c_174]) ).

tff(c_340,plain,
    op(e1,e1) != op(e0,e1),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_4612,plain,
    op(e1,e1) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_4531,c_340]) ).

tff(c_4905,plain,
    ( ( op(e1,e1) = e3 )
    | ( op(e1,e1) = e2 ) ),
    inference(negUnitSimplification,[status(thm)],[c_4521,c_4612,c_22]) ).

tff(c_4906,plain,
    op(e1,e1) = e2,
    inference(splitLeft,[status(thm)],[c_4905]) ).

tff(c_54,plain,
    op(op(e3,e1),e1) = op(e3,op(e1,e1)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_4670,plain,
    op(e3,op(e1,e1)) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_4531,c_4523,c_54]) ).

tff(c_4911,plain,
    op(e3,e2) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_4906,c_4670]) ).

tff(c_4536,plain,
    op(e3,e0) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_4512,c_164]) ).

tff(c_4848,plain,
    inv(e2) = e2,
    inference(negUnitSimplification,[status(thm)],[c_509,c_507,c_508,c_182]) ).

tff(c_4526,plain,
    op(e2,inv(e2)) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_4512,c_194]) ).

tff(c_4849,plain,
    op(e2,e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_4848,c_4526]) ).

tff(c_44,plain,
    op(op(e3,e2),e2) = op(e3,op(e2,e2)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_4865,plain,
    op(op(e3,e2),e2) = op(e3,e0),
    inference(demodulation,[status(thm),theory(equality)],[c_4849,c_44]) ).

tff(c_4877,plain,
    op(op(e3,e2),e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_4536,c_4865]) ).

tff(c_4949,plain,
    op(e1,e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_4911,c_4877]) ).

tff(c_382,plain,
    ( ( op(e1,e1) != e2 )
    | ( op(e1,op(e1,e1)) != e3 )
    | ( op(op(e1,op(e1,e1)),e1) != e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_659]) ).

tff(c_5068,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4523,c_4949,c_4906,c_4949,c_4906,c_4906,c_382]) ).

tff(c_5069,plain,
    op(e1,e1) = e3,
    inference(splitRight,[status(thm)],[c_4905]) ).

tff(c_4532,plain,
    op(e1,e0) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_4512,c_172]) ).

tff(c_4524,plain,
    op(e1,e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_4512,c_4468]) ).

tff(c_114,plain,
    op(op(e1,e1),e3) = op(e1,op(e1,e3)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_4783,plain,
    op(op(e1,e1),e3) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_4532,c_4524,c_114]) ).

tff(c_5072,plain,
    op(e3,e3) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_5069,c_4783]) ).

tff(c_258,plain,
    op(e3,e3) != op(e3,e2),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_5100,plain,
    op(e3,e2) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_5072,c_258]) ).

tff(c_4533,plain,
    op(e0,e2) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_4512,c_170]) ).

tff(c_324,plain,
    op(e3,e2) != op(e0,e2),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_4591,plain,
    op(e3,e2) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_4533,c_324]) ).

tff(c_266,plain,
    op(e3,e2) != op(e3,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_4557,plain,
    op(e3,e2) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_4536,c_266]) ).

tff(c_4,plain,
    ( ( op(e3,e2) = e3 )
    | ( op(e3,e2) = e2 )
    | ( op(e3,e2) = e1 )
    | ( op(e3,e2) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_5129,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4517,c_5100,c_4591,c_4557,c_4]) ).

tff(c_5130,plain,
    ( ( unit = e1 )
    | ( unit = e2 )
    | ( unit = e3 ) ),
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_5136,plain,
    unit = e3,
    inference(splitLeft,[status(thm)],[c_5130]) ).

tff(c_5162,plain,
    inv(e3) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_5136,c_5136,c_204]) ).

tff(c_5163,plain,
    e3 = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_4453,c_5162]) ).

tff(c_5165,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_356,c_5163]) ).

tff(c_5166,plain,
    ( ( unit = e2 )
    | ( unit = e1 ) ),
    inference(splitRight,[status(thm)],[c_5130]) ).

tff(c_5168,plain,
    unit = e1,
    inference(splitLeft,[status(thm)],[c_5166]) ).

tff(c_5195,plain,
    inv(e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_5168,c_5168,c_204]) ).

tff(c_5200,plain,
    e3 = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_5195,c_4454]) ).

tff(c_5202,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_356,c_5200]) ).

tff(c_5203,plain,
    unit = e2,
    inference(splitRight,[status(thm)],[c_5166]) ).

tff(c_5217,plain,
    op(e3,e1) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_5203,c_4467]) ).

tff(c_5224,plain,
    op(e2,e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5203,c_178]) ).

tff(c_5329,plain,
    op(e1,e0) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5224,c_346]) ).

tff(c_5226,plain,
    op(e1,e2) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_5203,c_172]) ).

tff(c_290,plain,
    op(e1,e2) != op(e1,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_5302,plain,
    op(e1,e0) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_5226,c_290]) ).

tff(c_288,plain,
    op(e1,e3) != op(e1,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_4481,plain,
    op(e1,e0) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_4468,c_288]) ).

tff(c_5216,plain,
    op(e1,e0) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_5203,c_4481]) ).

tff(c_24,plain,
    ( ( op(e1,e0) = e3 )
    | ( op(e1,e0) = e2 )
    | ( op(e1,e0) = e1 )
    | ( op(e1,e0) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_5603,plain,
    op(e1,e0) = e3,
    inference(negUnitSimplification,[status(thm)],[c_5329,c_5302,c_5216,c_24]) ).

tff(c_4462,plain,
    inv(e0) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_4453,c_252]) ).

tff(c_4492,plain,
    inv(e0) != e2,
    inference(negUnitSimplification,[status(thm)],[c_509,c_240]) ).

tff(c_256,plain,
    inv(e1) != inv(e0),
    inference(cnfTransformation,[status(thm)],[f_437]) ).

tff(c_4471,plain,
    inv(e0) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_4454,c_256]) ).

tff(c_5550,plain,
    inv(e0) = e0,
    inference(negUnitSimplification,[status(thm)],[c_4462,c_4492,c_4471,c_186]) ).

tff(c_5219,plain,
    op(inv(e0),e0) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_5203,c_200]) ).

tff(c_5551,plain,
    op(e0,e0) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_5550,c_5219]) ).

tff(c_128,plain,
    op(op(e1,e0),e0) = op(e1,op(e0,e0)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_5567,plain,
    op(op(e1,e0),e0) = op(e1,e2),
    inference(demodulation,[status(thm),theory(equality)],[c_5551,c_128]) ).

tff(c_5579,plain,
    op(op(e1,e0),e0) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_5226,c_5567]) ).

tff(c_5604,plain,
    op(e3,e0) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_5603,c_5579]) ).

tff(c_5218,plain,
    op(e1,e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_5203,c_4468]) ).

tff(c_104,plain,
    op(op(e1,e3),e0) = op(e1,op(e3,e0)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_5436,plain,
    op(e1,op(e3,e0)) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5224,c_5218,c_104]) ).

tff(c_5629,plain,
    op(e1,e1) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5604,c_5436]) ).

tff(c_408,plain,
    ( ( op(e1,e1) != e0 )
    | ( op(e1,op(e1,e1)) != e3 )
    | ( op(op(e1,op(e1,e1)),e1) != e2 ) ),
    inference(cnfTransformation,[status(thm)],[f_737]) ).

tff(c_5771,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5217,c_5603,c_5629,c_5603,c_5629,c_5629,c_408]) ).

tff(c_5773,plain,
    inv(e2) = e0,
    inference(splitRight,[status(thm)],[c_228]) ).

tff(c_5832,plain,
    unit = e0,
    inference(splitLeft,[status(thm)],[c_162]) ).

tff(c_5857,plain,
    inv(e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5832,c_5832,c_204]) ).

tff(c_5772,plain,
    inv(e0) = e2,
    inference(splitRight,[status(thm)],[c_228]) ).

tff(c_5862,plain,
    e2 = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5857,c_5772]) ).

tff(c_5864,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_362,c_5862]) ).

tff(c_5865,plain,
    ( ( unit = e1 )
    | ( unit = e2 )
    | ( unit = e3 ) ),
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_5867,plain,
    unit = e3,
    inference(splitLeft,[status(thm)],[c_5865]) ).

tff(c_5885,plain,
    op(e0,e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5867,c_176]) ).

tff(c_296,plain,
    op(e0,e3) != op(e0,e1),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_5947,plain,
    op(e0,e1) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5885,c_296]) ).

tff(c_5887,plain,
    op(e3,e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_5867,c_174]) ).

tff(c_5978,plain,
    op(e0,e1) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_5887,c_336]) ).

tff(c_5786,plain,
    op(e2,e0) = unit,
    inference(demodulation,[status(thm),theory(equality)],[c_5773,c_194]) ).

tff(c_5880,plain,
    op(e2,e0) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_5867,c_5786]) ).

tff(c_5886,plain,
    op(e3,e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5867,c_178]) ).

tff(c_348,plain,
    op(e3,e0) != op(e0,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_5966,plain,
    op(e0,e0) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5886,c_348]) ).

tff(c_350,plain,
    op(e2,e0) != op(e0,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_5803,plain,
    op(e0,e0) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_5786,c_350]) ).

tff(c_5879,plain,
    op(e0,e0) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_5867,c_5803]) ).

tff(c_32,plain,
    ( ( op(e0,e0) = e3 )
    | ( op(e0,e0) = e2 )
    | ( op(e0,e0) = e1 )
    | ( op(e0,e0) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_6264,plain,
    ( ( op(e0,e0) = e2 )
    | ( op(e0,e0) = e1 ) ),
    inference(negUnitSimplification,[status(thm)],[c_5966,c_5879,c_32]) ).

tff(c_6265,plain,
    op(e0,e0) = e1,
    inference(splitLeft,[status(thm)],[c_6264]) ).

tff(c_96,plain,
    op(op(e2,e0),e0) = op(e2,op(e0,e0)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_6175,plain,
    op(e2,op(e0,e0)) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5886,c_5880,c_96]) ).

tff(c_6266,plain,
    op(e2,e1) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_6265,c_6175]) ).

tff(c_5890,plain,
    op(e2,e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_5867,c_168]) ).

tff(c_250,plain,
    inv(e2) != inv(e1),
    inference(cnfTransformation,[status(thm)],[f_437]) ).

tff(c_5790,plain,
    inv(e1) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5773,c_250]) ).

tff(c_5779,plain,
    inv(e1) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_5772,c_256]) ).

tff(c_5812,plain,
    inv(e1) != e3,
    inference(splitLeft,[status(thm)],[c_230]) ).

tff(c_6207,plain,
    inv(e1) = e1,
    inference(negUnitSimplification,[status(thm)],[c_5790,c_5779,c_5812,c_184]) ).

tff(c_5881,plain,
    op(inv(e1),e1) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_5867,c_196]) ).

tff(c_6208,plain,
    op(e1,e1) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_6207,c_5881]) ).

tff(c_86,plain,
    op(op(e2,e1),e1) = op(e2,op(e1,e1)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_6224,plain,
    op(op(e2,e1),e1) = op(e2,e3),
    inference(demodulation,[status(thm),theory(equality)],[c_6208,c_86]) ).

tff(c_6236,plain,
    op(op(e2,e1),e1) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_5890,c_6224]) ).

tff(c_6285,plain,
    op(e0,e1) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_6266,c_6236]) ).

tff(c_418,plain,
    ( ( op(e0,e0) != e1 )
    | ( op(e0,op(e0,e0)) != e2 )
    | ( op(op(e0,op(e0,e0)),e0) != e3 ) ),
    inference(cnfTransformation,[status(thm)],[f_767]) ).

tff(c_6437,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5880,c_6285,c_6265,c_6285,c_6265,c_6265,c_418]) ).

tff(c_6438,plain,
    op(e0,e0) = e2,
    inference(splitRight,[status(thm)],[c_6264]) ).

tff(c_304,plain,
    op(e0,e1) != op(e0,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_6449,plain,
    op(e0,e1) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_6438,c_304]) ).

tff(c_5775,plain,
    op(e0,e2) = unit,
    inference(demodulation,[status(thm),theory(equality)],[c_5772,c_202]) ).

tff(c_298,plain,
    op(e0,e2) != op(e0,e1),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_5831,plain,
    op(e0,e1) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_5775,c_298]) ).

tff(c_5869,plain,
    op(e0,e1) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_5867,c_5831]) ).

tff(c_30,plain,
    ( ( op(e0,e1) = e3 )
    | ( op(e0,e1) = e2 )
    | ( op(e0,e1) = e1 )
    | ( op(e0,e1) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_6500,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5947,c_5978,c_6449,c_5869,c_30]) ).

tff(c_6501,plain,
    ( ( unit = e2 )
    | ( unit = e1 ) ),
    inference(splitRight,[status(thm)],[c_5865]) ).

tff(c_6503,plain,
    unit = e1,
    inference(splitLeft,[status(thm)],[c_6501]) ).

tff(c_6519,plain,
    op(e0,e2) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_6503,c_5775]) ).

tff(c_6526,plain,
    op(e0,e1) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_6503,c_176]) ).

tff(c_6549,plain,
    op(e0,e3) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_6526,c_296]) ).

tff(c_294,plain,
    op(e0,e3) != op(e0,e2),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_5805,plain,
    op(e0,e3) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_5775,c_294]) ).

tff(c_6516,plain,
    op(e0,e3) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_6503,c_5805]) ).

tff(c_6527,plain,
    op(e1,e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_6503,c_178]) ).

tff(c_352,plain,
    op(e1,e0) != op(e0,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_6559,plain,
    op(e0,e0) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_6527,c_352]) ).

tff(c_6520,plain,
    op(e0,e0) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_6503,c_5803]) ).

tff(c_6917,plain,
    ( ( op(e0,e0) = e3 )
    | ( op(e0,e0) = e2 ) ),
    inference(negUnitSimplification,[status(thm)],[c_6559,c_6520,c_32]) ).

tff(c_6918,plain,
    op(e0,e0) = e2,
    inference(splitLeft,[status(thm)],[c_6917]) ).

tff(c_300,plain,
    op(e0,e3) != op(e0,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_6930,plain,
    op(e0,e3) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_6918,c_300]) ).

tff(c_166,plain,
    op(unit,e3) = e3,
    inference(cnfTransformation,[status(thm)],[f_302]) ).

tff(c_6532,plain,
    op(e1,e3) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_6503,c_166]) ).

tff(c_316,plain,
    op(e1,e3) != op(e0,e3),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_6610,plain,
    op(e0,e3) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_6532,c_316]) ).

tff(c_26,plain,
    ( ( op(e0,e3) = e3 )
    | ( op(e0,e3) = e2 )
    | ( op(e0,e3) = e1 )
    | ( op(e0,e3) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_6968,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6549,c_6516,c_6930,c_6610,c_26]) ).

tff(c_6969,plain,
    op(e0,e0) = e3,
    inference(splitRight,[status(thm)],[c_6917]) ).

tff(c_6521,plain,
    op(e2,e0) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_6503,c_5786]) ).

tff(c_6816,plain,
    op(e2,op(e0,e0)) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_6527,c_6521,c_96]) ).

tff(c_6971,plain,
    op(e2,e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_6969,c_6816]) ).

tff(c_156,plain,
    op(op(e0,e0),e2) = op(e0,op(e0,e2)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_6807,plain,
    op(op(e0,e0),e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_6526,c_6519,c_156]) ).

tff(c_6972,plain,
    op(e3,e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_6969,c_6807]) ).

tff(c_6530,plain,
    op(e1,e2) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_6503,c_170]) ).

tff(c_5823,plain,
    inv(e3) != e1,
    inference(negUnitSimplification,[status(thm)],[c_5812,c_218]) ).

tff(c_6859,plain,
    inv(e3) = e3,
    inference(negUnitSimplification,[status(thm)],[c_506,c_5823,c_505,c_180]) ).

tff(c_6525,plain,
    op(e3,inv(e3)) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_6503,c_190]) ).

tff(c_6860,plain,
    op(e3,e3) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_6859,c_6525]) ).

tff(c_36,plain,
    op(op(e3,e3),e2) = op(e3,op(e3,e2)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_6875,plain,
    op(e3,op(e3,e2)) = op(e1,e2),
    inference(demodulation,[status(thm),theory(equality)],[c_6860,c_36]) ).

tff(c_6887,plain,
    op(e3,op(e3,e2)) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_6530,c_6875]) ).

tff(c_7014,plain,
    op(e3,e0) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_6972,c_6887]) ).

tff(c_6533,plain,
    op(e3,e1) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_6503,c_164]) ).

tff(c_60,plain,
    op(op(e3,e0),e2) = op(e3,op(e0,e2)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_6822,plain,
    op(op(e3,e0),e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_6533,c_6519,c_60]) ).

tff(c_7036,plain,
    op(e2,e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_7014,c_6822]) ).

tff(c_386,plain,
    ( ( op(e2,e2) != e3 )
    | ( op(e2,op(e2,e2)) != e0 )
    | ( op(op(e2,op(e2,e2)),e2) != e1 ) ),
    inference(cnfTransformation,[status(thm)],[f_671]) ).

tff(c_7130,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6519,c_6971,c_7036,c_6971,c_7036,c_7036,c_386]) ).

tff(c_7131,plain,
    unit = e2,
    inference(splitRight,[status(thm)],[c_6501]) ).

tff(c_7159,plain,
    inv(e2) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_7131,c_7131,c_204]) ).

tff(c_7160,plain,
    e2 = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5773,c_7159]) ).

tff(c_7162,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_362,c_7160]) ).

tff(c_7163,plain,
    inv(e3) = e1,
    inference(splitRight,[status(thm)],[c_230]) ).

tff(c_7229,plain,
    unit = e0,
    inference(splitLeft,[status(thm)],[c_162]) ).

tff(c_7254,plain,
    inv(e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_7229,c_7229,c_204]) ).

tff(c_7259,plain,
    e2 = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_7254,c_5772]) ).

tff(c_7261,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_362,c_7259]) ).

tff(c_7262,plain,
    ( ( unit = e1 )
    | ( unit = e2 )
    | ( unit = e3 ) ),
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_7269,plain,
    unit = e3,
    inference(splitLeft,[status(thm)],[c_7262]) ).

tff(c_7295,plain,
    inv(e3) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_7269,c_7269,c_204]) ).

tff(c_7296,plain,
    e3 = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_7163,c_7295]) ).

tff(c_7298,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_356,c_7296]) ).

tff(c_7299,plain,
    ( ( unit = e2 )
    | ( unit = e1 ) ),
    inference(splitRight,[status(thm)],[c_7262]) ).

tff(c_7301,plain,
    unit = e1,
    inference(splitLeft,[status(thm)],[c_7299]) ).

tff(c_7328,plain,
    inv(e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_7301,c_7301,c_204]) ).

tff(c_7164,plain,
    inv(e1) = e3,
    inference(splitRight,[status(thm)],[c_230]) ).

tff(c_7333,plain,
    e3 = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_7328,c_7164]) ).

tff(c_7335,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_356,c_7333]) ).

tff(c_7336,plain,
    unit = e2,
    inference(splitRight,[status(thm)],[c_7299]) ).

tff(c_7364,plain,
    inv(e2) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_7336,c_7336,c_204]) ).

tff(c_7365,plain,
    e2 = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_5773,c_7364]) ).

tff(c_7367,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_362,c_7365]) ).

tff(c_7369,plain,
    inv(e2) = e1,
    inference(splitRight,[status(thm)],[c_226]) ).

tff(c_7431,plain,
    unit = e0,
    inference(splitLeft,[status(thm)],[c_162]) ).

tff(c_7368,plain,
    inv(e1) = e2,
    inference(splitRight,[status(thm)],[c_226]) ).

tff(c_7371,plain,
    op(e1,e2) = unit,
    inference(demodulation,[status(thm),theory(equality)],[c_7368,c_198]) ).

tff(c_7443,plain,
    op(e1,e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_7431,c_7371]) ).

tff(c_7380,plain,
    op(e2,e1) = unit,
    inference(demodulation,[status(thm),theory(equality)],[c_7369,c_194]) ).

tff(c_7412,plain,
    op(e3,e1) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_7380,c_330]) ).

tff(c_7437,plain,
    op(e3,e1) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_7431,c_7412]) ).

tff(c_7450,plain,
    op(e0,e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_7431,c_174]) ).

tff(c_7484,plain,
    op(e3,e1) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_7450,c_336]) ).

tff(c_7455,plain,
    op(e3,e0) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_7431,c_164]) ).

tff(c_268,plain,
    op(e3,e1) != op(e3,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_7545,plain,
    op(e3,e1) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_7455,c_268]) ).

tff(c_7830,plain,
    op(e3,e1) = e2,
    inference(negUnitSimplification,[status(thm)],[c_7437,c_7484,c_7545,c_6]) ).

tff(c_52,plain,
    op(op(e3,e1),e2) = op(e3,op(e1,e2)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_7722,plain,
    op(op(e3,e1),e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_7455,c_7443,c_52]) ).

tff(c_7833,plain,
    op(e2,e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_7830,c_7722]) ).

tff(c_7452,plain,
    op(e0,e2) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_7431,c_170]) ).

tff(c_108,plain,
    op(op(e1,e2),e2) = op(e1,op(e2,e2)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_7614,plain,
    op(e1,op(e2,e2)) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_7452,c_7443,c_108]) ).

tff(c_7858,plain,
    op(e1,e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_7833,c_7614]) ).

tff(c_7451,plain,
    op(e1,e0) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_7431,c_172]) ).

tff(c_246,plain,
    inv(e3) != inv(e2),
    inference(cnfTransformation,[status(thm)],[f_437]) ).

tff(c_7383,plain,
    inv(e3) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_7369,c_246]) ).

tff(c_7777,plain,
    inv(e3) = e3,
    inference(negUnitSimplification,[status(thm)],[c_506,c_7383,c_505,c_180]) ).

tff(c_7446,plain,
    op(e3,inv(e3)) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_7431,c_190]) ).

tff(c_7778,plain,
    op(e3,e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_7777,c_7446]) ).

tff(c_98,plain,
    op(op(e1,e3),e3) = op(e1,op(e3,e3)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_7795,plain,
    op(op(e1,e3),e3) = op(e1,e0),
    inference(demodulation,[status(thm),theory(equality)],[c_7778,c_98]) ).

tff(c_7806,plain,
    op(op(e1,e3),e3) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_7451,c_7795]) ).

tff(c_7892,plain,
    op(e2,e3) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_7858,c_7806]) ).

tff(c_374,plain,
    ( ( op(e2,e2) != e3 )
    | ( op(e2,op(e2,e2)) != e1 )
    | ( op(op(e2,op(e2,e2)),e2) != e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_635]) ).

tff(c_7992,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_7443,c_7892,c_7833,c_7892,c_7833,c_7833,c_374]) ).

tff(c_7993,plain,
    ( ( unit = e1 )
    | ( unit = e2 )
    | ( unit = e3 ) ),
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_7995,plain,
    unit = e3,
    inference(splitLeft,[status(thm)],[c_7993]) ).

tff(c_8008,plain,
    op(e1,e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_7995,c_7371]) ).

tff(c_8013,plain,
    op(e0,e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_7995,c_176]) ).

tff(c_8039,plain,
    op(e0,e1) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8013,c_296]) ).

tff(c_8015,plain,
    op(e3,e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_7995,c_174]) ).

tff(c_8065,plain,
    op(e0,e1) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_8015,c_336]) ).

tff(c_338,plain,
    op(e2,e1) != op(e0,e1),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_7428,plain,
    op(e0,e1) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_7380,c_338]) ).

tff(c_7998,plain,
    op(e0,e1) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_7995,c_7428]) ).

tff(c_8402,plain,
    op(e0,e1) = e2,
    inference(negUnitSimplification,[status(thm)],[c_8039,c_8065,c_7998,c_30]) ).

tff(c_254,plain,
    inv(e2) != inv(e0),
    inference(cnfTransformation,[status(thm)],[f_437]) ).

tff(c_7384,plain,
    inv(e0) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_7369,c_254]) ).

tff(c_7375,plain,
    inv(e0) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_7368,c_256]) ).

tff(c_7421,plain,
    inv(e0) != e3,
    inference(negUnitSimplification,[status(thm)],[c_506,c_238]) ).

tff(c_8348,plain,
    inv(e0) = e0,
    inference(negUnitSimplification,[status(thm)],[c_7384,c_7375,c_7421,c_186]) ).

tff(c_8012,plain,
    op(e0,inv(e0)) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_7995,c_202]) ).

tff(c_8349,plain,
    op(e0,e0) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_8348,c_8012]) ).

tff(c_158,plain,
    op(op(e0,e0),e1) = op(e0,op(e0,e1)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_8361,plain,
    op(e0,op(e0,e1)) = op(e3,e1),
    inference(demodulation,[status(thm),theory(equality)],[c_8349,c_158]) ).

tff(c_8373,plain,
    op(e0,op(e0,e1)) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_8015,c_8361]) ).

tff(c_8403,plain,
    op(e0,e2) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_8402,c_8373]) ).

tff(c_8007,plain,
    op(e2,e1) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_7995,c_7380]) ).

tff(c_142,plain,
    op(op(e0,e2),e1) = op(e0,op(e2,e1)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_8173,plain,
    op(op(e0,e2),e1) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8013,c_8007,c_142]) ).

tff(c_8431,plain,
    op(e1,e1) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8403,c_8173]) ).

tff(c_8240,plain,
    op(e2,op(e1,e1)) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_8015,c_8007,c_86]) ).

tff(c_8467,plain,
    op(e2,e0) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_8431,c_8240]) ).

tff(c_148,plain,
    op(op(e0,e1),e2) = op(e0,op(e1,e2)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_8278,plain,
    op(op(e0,e1),e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8013,c_8008,c_148]) ).

tff(c_8406,plain,
    op(e2,e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8402,c_8278]) ).

tff(c_416,plain,
    ( ( op(e2,e2) != e0 )
    | ( op(e2,op(e2,e2)) != e1 )
    | ( op(op(e2,op(e2,e2)),e2) != e3 ) ),
    inference(cnfTransformation,[status(thm)],[f_761]) ).

tff(c_8582,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8008,c_8467,c_8406,c_8467,c_8406,c_8406,c_416]) ).

tff(c_8583,plain,
    ( ( unit = e2 )
    | ( unit = e1 ) ),
    inference(splitRight,[status(thm)],[c_7993]) ).

tff(c_8585,plain,
    unit = e1,
    inference(splitLeft,[status(thm)],[c_8583]) ).

tff(c_8612,plain,
    inv(e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_8585,c_8585,c_204]) ).

tff(c_8617,plain,
    e2 = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_8612,c_7368]) ).

tff(c_8619,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_358,c_8617]) ).

tff(c_8620,plain,
    unit = e2,
    inference(splitRight,[status(thm)],[c_8583]) ).

tff(c_8652,plain,
    inv(e2) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_8620,c_8620,c_204]) ).

tff(c_8653,plain,
    e2 = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_7369,c_8652]) ).

tff(c_8655,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_358,c_8653]) ).

tff(c_8657,plain,
    inv(e3) = e0,
    inference(splitRight,[status(thm)],[c_220]) ).

tff(c_8721,plain,
    unit = e0,
    inference(splitLeft,[status(thm)],[c_162]) ).

tff(c_8746,plain,
    inv(e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8721,c_8721,c_204]) ).

tff(c_8656,plain,
    inv(e0) = e3,
    inference(splitRight,[status(thm)],[c_220]) ).

tff(c_8755,plain,
    e3 = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8746,c_8656]) ).

tff(c_8757,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_360,c_8755]) ).

tff(c_8758,plain,
    ( ( unit = e1 )
    | ( unit = e2 )
    | ( unit = e3 ) ),
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_8760,plain,
    unit = e3,
    inference(splitLeft,[status(thm)],[c_8758]) ).

tff(c_8786,plain,
    inv(e3) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_8760,c_8760,c_204]) ).

tff(c_8787,plain,
    e3 = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8657,c_8786]) ).

tff(c_8789,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_360,c_8787]) ).

tff(c_8790,plain,
    ( ( unit = e2 )
    | ( unit = e1 ) ),
    inference(splitRight,[status(thm)],[c_8758]) ).

tff(c_8792,plain,
    unit = e1,
    inference(splitLeft,[status(thm)],[c_8790]) ).

tff(c_8659,plain,
    op(e0,e3) = unit,
    inference(demodulation,[status(thm),theory(equality)],[c_8656,c_202]) ).

tff(c_8806,plain,
    op(e0,e3) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_8792,c_8659]) ).

tff(c_8812,plain,
    op(e1,e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8792,c_178]) ).

tff(c_8863,plain,
    op(e2,e0) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8812,c_346]) ).

tff(c_8658,plain,
    op(e3,e0) = unit,
    inference(demodulation,[status(thm),theory(equality)],[c_8656,c_200]) ).

tff(c_8711,plain,
    op(e2,e0) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_8658,c_342]) ).

tff(c_8800,plain,
    op(e2,e0) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_8792,c_8711]) ).

tff(c_8816,plain,
    op(e2,e1) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_8792,c_168]) ).

tff(c_280,plain,
    op(e2,e1) != op(e2,e0),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_8895,plain,
    op(e2,e0) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_8816,c_280]) ).

tff(c_9201,plain,
    op(e2,e0) = e3,
    inference(negUnitSimplification,[status(thm)],[c_8863,c_8800,c_8895,c_16]) ).

tff(c_90,plain,
    op(op(e2,e0),e3) = op(e2,op(e0,e3)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_8973,plain,
    op(op(e2,e0),e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_8816,c_8806,c_90]) ).

tff(c_9208,plain,
    op(e3,e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_9201,c_8973]) ).

tff(c_8817,plain,
    op(e1,e3) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_8792,c_166]) ).

tff(c_9092,plain,
    op(e0,op(e3,e3)) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_8817,c_8806,c_130]) ).

tff(c_9225,plain,
    op(e0,e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_9208,c_9092]) ).

tff(c_8811,plain,
    op(e0,e1) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8792,c_176]) ).

tff(c_8672,plain,
    inv(e2) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8657,c_246]) ).

tff(c_8694,plain,
    inv(e2) != e1,
    inference(splitLeft,[status(thm)],[c_226]) ).

tff(c_8662,plain,
    inv(e2) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_8656,c_254]) ).

tff(c_9146,plain,
    inv(e2) = e2,
    inference(negUnitSimplification,[status(thm)],[c_8672,c_8694,c_8662,c_182]) ).

tff(c_8810,plain,
    op(inv(e2),e2) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_8792,c_192]) ).

tff(c_9147,plain,
    op(e2,e2) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_9146,c_8810]) ).

tff(c_140,plain,
    op(op(e0,e2),e2) = op(e0,op(e2,e2)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_9164,plain,
    op(op(e0,e2),e2) = op(e0,e1),
    inference(demodulation,[status(thm),theory(equality)],[c_9147,c_140]) ).

tff(c_9175,plain,
    op(op(e0,e2),e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8811,c_9164]) ).

tff(c_9243,plain,
    op(e3,e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_9225,c_9175]) ).

tff(c_388,plain,
    ( ( op(e3,e3) != e2 )
    | ( op(e3,op(e3,e3)) != e0 )
    | ( op(op(e3,op(e3,e3)),e3) != e1 ) ),
    inference(cnfTransformation,[status(thm)],[f_677]) ).

tff(c_9367,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8806,c_9243,c_9208,c_9243,c_9208,c_9208,c_388]) ).

tff(c_9368,plain,
    unit = e2,
    inference(splitRight,[status(thm)],[c_8790]) ).

tff(c_9383,plain,
    op(e0,e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_9368,c_8659]) ).

tff(c_9389,plain,
    op(e2,e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_9368,c_178]) ).

tff(c_9417,plain,
    op(e0,e0) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_9389,c_350]) ).

tff(c_8697,plain,
    op(e0,e0) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_8658,c_348]) ).

tff(c_9380,plain,
    op(e0,e0) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_9368,c_8697]) ).

tff(c_9783,plain,
    ( ( op(e0,e0) = e3 )
    | ( op(e0,e0) = e1 ) ),
    inference(negUnitSimplification,[status(thm)],[c_9417,c_9380,c_32]) ).

tff(c_9784,plain,
    op(e0,e0) = e1,
    inference(splitLeft,[status(thm)],[c_9783]) ).

tff(c_9382,plain,
    op(e3,e0) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_9368,c_8658]) ).

tff(c_64,plain,
    op(op(e3,e0),e0) = op(e3,op(e0,e0)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_9513,plain,
    op(e3,op(e0,e0)) = op(e2,e0),
    inference(demodulation,[status(thm),theory(equality)],[c_9382,c_64]) ).

tff(c_9514,plain,
    op(e3,op(e0,e0)) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_9389,c_9513]) ).

tff(c_9791,plain,
    op(e3,e1) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_9784,c_9514]) ).

tff(c_9388,plain,
    op(e0,e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_9368,c_176]) ).

tff(c_154,plain,
    op(op(e0,e0),e3) = op(e0,op(e0,e3)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_9711,plain,
    op(op(e0,e0),e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_9388,c_9383,c_154]) ).

tff(c_9785,plain,
    op(e1,e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_9784,c_9711]) ).

tff(c_9394,plain,
    op(e2,e3) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_9368,c_166]) ).

tff(c_248,plain,
    inv(e3) != inv(e1),
    inference(cnfTransformation,[status(thm)],[f_437]) ).

tff(c_8673,plain,
    inv(e1) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8657,c_248]) ).

tff(c_8700,plain,
    inv(e1) != e2,
    inference(negUnitSimplification,[status(thm)],[c_8694,c_232]) ).

tff(c_8663,plain,
    inv(e1) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_8656,c_256]) ).

tff(c_9728,plain,
    inv(e1) = e1,
    inference(negUnitSimplification,[status(thm)],[c_8673,c_8700,c_8663,c_184]) ).

tff(c_9385,plain,
    op(e1,inv(e1)) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_9368,c_198]) ).

tff(c_9729,plain,
    op(e1,e1) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_9728,c_9385]) ).

tff(c_9739,plain,
    op(e1,op(e1,e3)) = op(e2,e3),
    inference(demodulation,[status(thm),theory(equality)],[c_9729,c_114]) ).

tff(c_9751,plain,
    op(e1,op(e1,e3)) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_9394,c_9739]) ).

tff(c_9804,plain,
    op(e1,e0) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_9785,c_9751]) ).

tff(c_9391,plain,
    op(e1,e2) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_9368,c_172]) ).

tff(c_122,plain,
    op(op(e1,e0),e3) = op(e1,op(e0,e3)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_9633,plain,
    op(op(e1,e0),e3) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_9391,c_9383,c_122]) ).

tff(c_9850,plain,
    op(e3,e3) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_9804,c_9633]) ).

tff(c_400,plain,
    ( ( op(e3,e3) != e1 )
    | ( op(e3,op(e3,e3)) != e0 )
    | ( op(op(e3,op(e3,e3)),e3) != e2 ) ),
    inference(cnfTransformation,[status(thm)],[f_713]) ).

tff(c_9948,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_9383,c_9791,c_9850,c_9791,c_9850,c_9850,c_400]) ).

tff(c_9949,plain,
    op(e0,e0) = e3,
    inference(splitRight,[status(thm)],[c_9783]) ).

tff(c_9951,plain,
    op(e3,e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_9949,c_9711]) ).

tff(c_260,plain,
    op(e3,e3) != op(e3,e1),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_9980,plain,
    op(e3,e1) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_9951,c_260]) ).

tff(c_9390,plain,
    op(e2,e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_9368,c_174]) ).

tff(c_9465,plain,
    op(e3,e1) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_9390,c_330]) ).

tff(c_8705,plain,
    op(e3,e1) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_8658,c_268]) ).

tff(c_9379,plain,
    op(e3,e1) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_9368,c_8705]) ).

tff(c_9395,plain,
    op(e3,e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_9368,c_164]) ).

tff(c_9428,plain,
    op(e3,e1) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_9395,c_262]) ).

tff(c_10017,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_9980,c_9465,c_9379,c_9428,c_6]) ).

tff(c_10019,plain,
    inv(e2) = e1,
    inference(splitRight,[status(thm)],[c_226]) ).

tff(c_10091,plain,
    unit = e0,
    inference(splitLeft,[status(thm)],[c_162]) ).

tff(c_10116,plain,
    inv(e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_10091,c_10091,c_204]) ).

tff(c_10121,plain,
    e3 = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_10116,c_8656]) ).

tff(c_10123,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_360,c_10121]) ).

tff(c_10124,plain,
    ( ( unit = e1 )
    | ( unit = e2 )
    | ( unit = e3 ) ),
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_10126,plain,
    unit = e3,
    inference(splitLeft,[status(thm)],[c_10124]) ).

tff(c_10152,plain,
    inv(e3) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_10126,c_10126,c_204]) ).

tff(c_10153,plain,
    e3 = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_8657,c_10152]) ).

tff(c_10155,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_360,c_10153]) ).

tff(c_10156,plain,
    ( ( unit = e2 )
    | ( unit = e1 ) ),
    inference(splitRight,[status(thm)],[c_10124]) ).

tff(c_10158,plain,
    unit = e1,
    inference(splitLeft,[status(thm)],[c_10156]) ).

tff(c_10185,plain,
    inv(e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_10158,c_10158,c_204]) ).

tff(c_10018,plain,
    inv(e1) = e2,
    inference(splitRight,[status(thm)],[c_226]) ).

tff(c_10190,plain,
    e2 = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_10185,c_10018]) ).

tff(c_10192,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_358,c_10190]) ).

tff(c_10193,plain,
    unit = e2,
    inference(splitRight,[status(thm)],[c_10156]) ).

tff(c_10222,plain,
    inv(e2) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10193,c_10193,c_204]) ).

tff(c_10223,plain,
    e2 = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_10019,c_10222]) ).

tff(c_10225,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_358,c_10223]) ).

tff(c_10227,plain,
    inv(e3) = e2,
    inference(splitRight,[status(thm)],[c_216]) ).

tff(c_10292,plain,
    unit = e0,
    inference(splitLeft,[status(thm)],[c_162]) ).

tff(c_10239,plain,
    op(e3,e2) = unit,
    inference(demodulation,[status(thm),theory(equality)],[c_10227,c_190]) ).

tff(c_10285,plain,
    op(e3,e1) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_10239,c_262]) ).

tff(c_10297,plain,
    op(e3,e1) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_10292,c_10285]) ).

tff(c_10311,plain,
    op(e0,e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_10292,c_174]) ).

tff(c_10400,plain,
    op(e3,e1) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_10311,c_336]) ).

tff(c_10304,plain,
    op(e3,e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_10292,c_10239]) ).

tff(c_10226,plain,
    inv(e2) = e3,
    inference(splitRight,[status(thm)],[c_216]) ).

tff(c_10228,plain,
    op(e2,e3) = unit,
    inference(demodulation,[status(thm),theory(equality)],[c_10226,c_194]) ).

tff(c_270,plain,
    op(e2,e3) != op(e2,e2),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_10283,plain,
    op(e2,e2) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_10228,c_270]) ).

tff(c_10299,plain,
    op(e2,e2) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_10292,c_10283]) ).

tff(c_10313,plain,
    op(e0,e2) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10292,c_170]) ).

tff(c_326,plain,
    op(e2,e2) != op(e0,e2),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_10373,plain,
    op(e2,e2) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10313,c_326]) ).

tff(c_12,plain,
    ( ( op(e2,e2) = e3 )
    | ( op(e2,e2) = e2 )
    | ( op(e2,e2) = e1 )
    | ( op(e2,e2) = e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_10698,plain,
    ( ( op(e2,e2) = e3 )
    | ( op(e2,e2) = e1 ) ),
    inference(negUnitSimplification,[status(thm)],[c_10299,c_10373,c_12]) ).

tff(c_10699,plain,
    op(e2,e2) = e1,
    inference(splitLeft,[status(thm)],[c_10698]) ).

tff(c_10597,plain,
    op(e3,op(e2,e2)) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10313,c_10304,c_44]) ).

tff(c_10703,plain,
    op(e3,e1) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10699,c_10597]) ).

tff(c_10316,plain,
    op(e3,e0) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_10292,c_164]) ).

tff(c_10275,plain,
    inv(e1) != e0,
    inference(splitLeft,[status(thm)],[c_236]) ).

tff(c_10241,plain,
    inv(e1) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10227,c_248]) ).

tff(c_10232,plain,
    inv(e1) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_10226,c_250]) ).

tff(c_10633,plain,
    inv(e1) = e1,
    inference(negUnitSimplification,[status(thm)],[c_10275,c_10241,c_10232,c_184]) ).

tff(c_10306,plain,
    op(e1,inv(e1)) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_10292,c_198]) ).

tff(c_10634,plain,
    op(e1,e1) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_10633,c_10306]) ).

tff(c_10650,plain,
    op(op(e3,e1),e1) = op(e3,e0),
    inference(demodulation,[status(thm),theory(equality)],[c_10634,c_54]) ).

tff(c_10662,plain,
    op(op(e3,e1),e1) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_10316,c_10650]) ).

tff(c_10742,plain,
    op(e2,e1) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_10703,c_10662]) ).

tff(c_384,plain,
    ( ( op(e2,e2) != e1 )
    | ( op(e2,op(e2,e2)) != e3 )
    | ( op(op(e2,op(e2,e2)),e2) != e0 ) ),
    inference(cnfTransformation,[status(thm)],[f_665]) ).

tff(c_10874,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_10304,c_10742,c_10699,c_10742,c_10699,c_10699,c_384]) ).

tff(c_10875,plain,
    op(e2,e2) = e3,
    inference(splitRight,[status(thm)],[c_10698]) ).

tff(c_10314,plain,
    op(e2,e0) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10292,c_168]) ).

tff(c_10303,plain,
    op(e2,e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_10292,c_10228]) ).

tff(c_74,plain,
    op(op(e2,e2),e3) = op(e2,op(e2,e3)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_10616,plain,
    op(op(e2,e2),e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10314,c_10303,c_74]) ).

tff(c_10878,plain,
    op(e3,e3) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10875,c_10616]) ).

tff(c_10906,plain,
    op(e3,e1) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10878,c_260]) ).

tff(c_10359,plain,
    op(e3,e1) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_10316,c_268]) ).

tff(c_10917,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10297,c_10400,c_10906,c_10359,c_6]) ).

tff(c_10918,plain,
    ( ( unit = e1 )
    | ( unit = e2 )
    | ( unit = e3 ) ),
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_10920,plain,
    unit = e3,
    inference(splitLeft,[status(thm)],[c_10918]) ).

tff(c_10946,plain,
    inv(e3) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_10920,c_10920,c_204]) ).

tff(c_10947,plain,
    e3 = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10227,c_10946]) ).

tff(c_10949,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_354,c_10947]) ).

tff(c_10950,plain,
    ( ( unit = e2 )
    | ( unit = e1 ) ),
    inference(splitRight,[status(thm)],[c_10918]) ).

tff(c_10952,plain,
    unit = e1,
    inference(splitLeft,[status(thm)],[c_10950]) ).

tff(c_10965,plain,
    op(e2,e3) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_10952,c_10228]) ).

tff(c_10971,plain,
    op(e0,e1) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_10952,c_176]) ).

tff(c_10995,plain,
    op(e0,e3) != e0,
    inference(demodulation,[status(thm),theory(equality)],[c_10971,c_296]) ).

tff(c_314,plain,
    op(e2,e3) != op(e0,e3),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_10289,plain,
    op(e0,e3) != unit,
    inference(demodulation,[status(thm),theory(equality)],[c_10228,c_314]) ).

tff(c_10956,plain,
    op(e0,e3) != e1,
    inference(demodulation,[status(thm),theory(equality)],[c_10952,c_10289]) ).

tff(c_10977,plain,
    op(e1,e3) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_10952,c_166]) ).

tff(c_11033,plain,
    op(e0,e3) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_10977,c_316]) ).

tff(c_11357,plain,
    op(e0,e3) = e2,
    inference(negUnitSimplification,[status(thm)],[c_10995,c_10956,c_11033,c_26]) ).

tff(c_10966,plain,
    op(e3,e2) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_10952,c_10239]) ).

tff(c_132,plain,
    op(op(e0,e3),e2) = op(e0,op(e3,e2)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_11237,plain,
    op(op(e0,e3),e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_10971,c_10966,c_132]) ).

tff(c_11360,plain,
    op(e2,e2) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_11357,c_11237]) ).

tff(c_10975,plain,
    op(e1,e2) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10952,c_170]) ).

tff(c_11141,plain,
    op(e3,op(e2,e2)) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10975,c_10966,c_44]) ).

tff(c_11385,plain,
    op(e3,e0) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_11360,c_11141]) ).

tff(c_10281,plain,
    inv(e0) != e1,
    inference(negUnitSimplification,[status(thm)],[c_10275,c_242]) ).

tff(c_10242,plain,
    inv(e0) != e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10227,c_252]) ).

tff(c_10233,plain,
    inv(e0) != e3,
    inference(demodulation,[status(thm),theory(equality)],[c_10226,c_254]) ).

tff(c_11306,plain,
    inv(e0) = e0,
    inference(negUnitSimplification,[status(thm)],[c_10281,c_10242,c_10233,c_186]) ).

tff(c_10969,plain,
    op(inv(e0),e0) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_10952,c_200]) ).

tff(c_11307,plain,
    op(e0,e0) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_11306,c_10969]) ).

tff(c_11323,plain,
    op(e0,op(e0,e3)) = op(e1,e3),
    inference(demodulation,[status(thm),theory(equality)],[c_11307,c_154]) ).

tff(c_11335,plain,
    op(e0,op(e0,e3)) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_10977,c_11323]) ).

tff(c_11358,plain,
    op(e0,e2) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_11357,c_11335]) ).

tff(c_138,plain,
    op(op(e0,e2),e3) = op(e0,op(e2,e3)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_11165,plain,
    op(op(e0,e2),e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_10971,c_10965,c_138]) ).

tff(c_11422,plain,
    op(e3,e3) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_11358,c_11165]) ).

tff(c_392,plain,
    ( ( op(e3,e3) != e0 )
    | ( op(e3,op(e3,e3)) != e2 )
    | ( op(op(e3,op(e3,e3)),e3) != e1 ) ),
    inference(cnfTransformation,[status(thm)],[f_689]) ).

tff(c_11548,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_10965,c_11385,c_11422,c_11385,c_11422,c_11422,c_392]) ).

tff(c_11549,plain,
    unit = e2,
    inference(splitRight,[status(thm)],[c_10950]) ).

tff(c_11582,plain,
    inv(e2) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_11549,c_11549,c_204]) ).

tff(c_11588,plain,
    e3 = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_11582,c_10226]) ).

tff(c_11590,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_354,c_11588]) ).

tff(c_11592,plain,
    inv(e1) = e0,
    inference(splitRight,[status(thm)],[c_236]) ).

tff(c_11654,plain,
    unit = e0,
    inference(splitLeft,[status(thm)],[c_162]) ).

tff(c_11679,plain,
    inv(e0) = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_11654,c_11654,c_204]) ).

tff(c_11591,plain,
    inv(e0) = e1,
    inference(splitRight,[status(thm)],[c_236]) ).

tff(c_11684,plain,
    e1 = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_11679,c_11591]) ).

tff(c_11686,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_364,c_11684]) ).

tff(c_11687,plain,
    ( ( unit = e1 )
    | ( unit = e2 )
    | ( unit = e3 ) ),
    inference(splitRight,[status(thm)],[c_162]) ).

tff(c_11689,plain,
    unit = e3,
    inference(splitLeft,[status(thm)],[c_11687]) ).

tff(c_11715,plain,
    inv(e3) = e3,
    inference(demodulation,[status(thm),theory(equality)],[c_11689,c_11689,c_204]) ).

tff(c_11716,plain,
    e3 = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_10227,c_11715]) ).

tff(c_11718,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_354,c_11716]) ).

tff(c_11719,plain,
    ( ( unit = e2 )
    | ( unit = e1 ) ),
    inference(splitRight,[status(thm)],[c_11687]) ).

tff(c_11721,plain,
    unit = e1,
    inference(splitLeft,[status(thm)],[c_11719]) ).

tff(c_11753,plain,
    inv(e1) = e1,
    inference(demodulation,[status(thm),theory(equality)],[c_11721,c_11721,c_204]) ).

tff(c_11754,plain,
    e1 = e0,
    inference(demodulation,[status(thm),theory(equality)],[c_11592,c_11753]) ).

tff(c_11756,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_364,c_11754]) ).

tff(c_11757,plain,
    unit = e2,
    inference(splitRight,[status(thm)],[c_11719]) ).

tff(c_11785,plain,
    inv(e2) = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_11757,c_11757,c_204]) ).

tff(c_11791,plain,
    e3 = e2,
    inference(demodulation,[status(thm),theory(equality)],[c_11785,c_10226]) ).

tff(c_11793,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_354,c_11791]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : ALG024+1 : TPTP v8.1.2. Released v2.7.0.
% 0.13/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36  % Computer : n031.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % 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 : Thu Aug  3 20:37:29 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 14.00/4.56  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.12/4.63  
% 14.12/4.63  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.55/4.70  
% 14.55/4.70  Inference rules
% 14.55/4.70  ----------------------
% 14.55/4.70  #Ref     : 0
% 14.55/4.70  #Sup     : 2482
% 14.55/4.70  #Fact    : 0
% 14.55/4.70  #Define  : 0
% 14.55/4.70  #Split   : 45
% 14.55/4.70  #Chain   : 0
% 14.55/4.70  #Close   : 0
% 14.55/4.70  
% 14.55/4.70  Ordering : KBO
% 14.55/4.70  
% 14.55/4.70  Simplification rules
% 14.55/4.70  ----------------------
% 14.55/4.70  #Subsume      : 1291
% 14.55/4.70  #Demod        : 8788
% 14.55/4.70  #Tautology    : 3880
% 14.55/4.70  #SimpNegUnit  : 370
% 14.55/4.70  #BackRed      : 3302
% 14.55/4.70  
% 14.55/4.70  #Partial instantiations: 0
% 14.55/4.70  #Strategies tried      : 1
% 14.55/4.70  
% 14.55/4.70  Timing (in seconds)
% 14.55/4.70  ----------------------
% 14.55/4.71  Preprocessing        : 0.75
% 14.55/4.71  Parsing              : 0.40
% 14.55/4.71  CNF conversion       : 0.04
% 14.55/4.71  Main loop            : 2.70
% 14.55/4.71  Inferencing          : 0.72
% 14.55/4.71  Reduction            : 1.08
% 14.55/4.71  Demodulation         : 0.73
% 14.55/4.71  BG Simplification    : 0.07
% 14.55/4.71  Subsumption          : 0.58
% 14.55/4.71  Abstraction          : 0.05
% 14.55/4.71  MUC search           : 0.00
% 14.55/4.71  Cooper               : 0.00
% 14.55/4.71  Total                : 3.61
% 14.55/4.71  Index Insertion      : 0.00
% 14.55/4.71  Index Deletion       : 0.00
% 14.55/4.71  Index Matching       : 0.00
% 14.55/4.71  BG Taut test         : 0.00
%------------------------------------------------------------------------------