TSTP Solution File: ALG085+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : ALG085+1 : TPTP v8.2.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 18:15:56 EDT 2024

% Result   : Theorem 170.57s 25.26s
% Output   : Refutation 170.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   50
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  222 (  94 unt;  14 typ;   0 def)
%            Number of atoms       :  831 ( 830 equ;   0 cnn)
%            Maximal formula atoms :  110 (   3 avg)
%            Number of connectives : 2891 ( 170   ~; 284   |; 336   &;2098   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   63 (   4 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;  11 con; 0-2 aty)
%            Number of variables   :    0 (   0   ^   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
thf(h_type,type,
    h: $i > $i ).

thf(e10_type,type,
    e10: $i ).

thf(e20_type,type,
    e20: $i ).

thf(e21_type,type,
    e21: $i ).

thf(e22_type,type,
    e22: $i ).

thf(e23_type,type,
    e23: $i ).

thf(e24_type,type,
    e24: $i ).

thf(e11_type,type,
    e11: $i ).

thf(e12_type,type,
    e12: $i ).

thf(e13_type,type,
    e13: $i ).

thf(e14_type,type,
    e14: $i ).

thf(j_type,type,
    j: $i > $i ).

thf(op1_type,type,
    op1: $i > $i > $i ).

thf(op2_type,type,
    op2: $i > $i > $i ).

thf(1,conjecture,
    ( ( ( ( ( h @ e10 )
          = e20 )
        | ( ( h @ e10 )
          = e21 )
        | ( ( h @ e10 )
          = e22 )
        | ( ( h @ e10 )
          = e23 )
        | ( ( h @ e10 )
          = e24 ) )
      & ( ( ( h @ e11 )
          = e20 )
        | ( ( h @ e11 )
          = e21 )
        | ( ( h @ e11 )
          = e22 )
        | ( ( h @ e11 )
          = e23 )
        | ( ( h @ e11 )
          = e24 ) )
      & ( ( ( h @ e12 )
          = e20 )
        | ( ( h @ e12 )
          = e21 )
        | ( ( h @ e12 )
          = e22 )
        | ( ( h @ e12 )
          = e23 )
        | ( ( h @ e12 )
          = e24 ) )
      & ( ( ( h @ e13 )
          = e20 )
        | ( ( h @ e13 )
          = e21 )
        | ( ( h @ e13 )
          = e22 )
        | ( ( h @ e13 )
          = e23 )
        | ( ( h @ e13 )
          = e24 ) )
      & ( ( ( h @ e14 )
          = e20 )
        | ( ( h @ e14 )
          = e21 )
        | ( ( h @ e14 )
          = e22 )
        | ( ( h @ e14 )
          = e23 )
        | ( ( h @ e14 )
          = e24 ) )
      & ( ( ( j @ e20 )
          = e10 )
        | ( ( j @ e20 )
          = e11 )
        | ( ( j @ e20 )
          = e12 )
        | ( ( j @ e20 )
          = e13 )
        | ( ( j @ e20 )
          = e14 ) )
      & ( ( ( j @ e21 )
          = e10 )
        | ( ( j @ e21 )
          = e11 )
        | ( ( j @ e21 )
          = e12 )
        | ( ( j @ e21 )
          = e13 )
        | ( ( j @ e21 )
          = e14 ) )
      & ( ( ( j @ e22 )
          = e10 )
        | ( ( j @ e22 )
          = e11 )
        | ( ( j @ e22 )
          = e12 )
        | ( ( j @ e22 )
          = e13 )
        | ( ( j @ e22 )
          = e14 ) )
      & ( ( ( j @ e23 )
          = e10 )
        | ( ( j @ e23 )
          = e11 )
        | ( ( j @ e23 )
          = e12 )
        | ( ( j @ e23 )
          = e13 )
        | ( ( j @ e23 )
          = e14 ) )
      & ( ( ( j @ e24 )
          = e10 )
        | ( ( j @ e24 )
          = e11 )
        | ( ( j @ e24 )
          = e12 )
        | ( ( j @ e24 )
          = e13 )
        | ( ( j @ e24 )
          = e14 ) ) )
   => ~ ( ( ( h @ ( op1 @ e10 @ e10 ) )
          = ( op2 @ ( h @ e10 ) @ ( h @ e10 ) ) )
        & ( ( h @ ( op1 @ e10 @ e11 ) )
          = ( op2 @ ( h @ e10 ) @ ( h @ e11 ) ) )
        & ( ( h @ ( op1 @ e10 @ e12 ) )
          = ( op2 @ ( h @ e10 ) @ ( h @ e12 ) ) )
        & ( ( h @ ( op1 @ e10 @ e13 ) )
          = ( op2 @ ( h @ e10 ) @ ( h @ e13 ) ) )
        & ( ( h @ ( op1 @ e10 @ e14 ) )
          = ( op2 @ ( h @ e10 ) @ ( h @ e14 ) ) )
        & ( ( h @ ( op1 @ e11 @ e10 ) )
          = ( op2 @ ( h @ e11 ) @ ( h @ e10 ) ) )
        & ( ( h @ ( op1 @ e11 @ e11 ) )
          = ( op2 @ ( h @ e11 ) @ ( h @ e11 ) ) )
        & ( ( h @ ( op1 @ e11 @ e12 ) )
          = ( op2 @ ( h @ e11 ) @ ( h @ e12 ) ) )
        & ( ( h @ ( op1 @ e11 @ e13 ) )
          = ( op2 @ ( h @ e11 ) @ ( h @ e13 ) ) )
        & ( ( h @ ( op1 @ e11 @ e14 ) )
          = ( op2 @ ( h @ e11 ) @ ( h @ e14 ) ) )
        & ( ( h @ ( op1 @ e12 @ e10 ) )
          = ( op2 @ ( h @ e12 ) @ ( h @ e10 ) ) )
        & ( ( h @ ( op1 @ e12 @ e11 ) )
          = ( op2 @ ( h @ e12 ) @ ( h @ e11 ) ) )
        & ( ( h @ ( op1 @ e12 @ e12 ) )
          = ( op2 @ ( h @ e12 ) @ ( h @ e12 ) ) )
        & ( ( h @ ( op1 @ e12 @ e13 ) )
          = ( op2 @ ( h @ e12 ) @ ( h @ e13 ) ) )
        & ( ( h @ ( op1 @ e12 @ e14 ) )
          = ( op2 @ ( h @ e12 ) @ ( h @ e14 ) ) )
        & ( ( h @ ( op1 @ e13 @ e10 ) )
          = ( op2 @ ( h @ e13 ) @ ( h @ e10 ) ) )
        & ( ( h @ ( op1 @ e13 @ e11 ) )
          = ( op2 @ ( h @ e13 ) @ ( h @ e11 ) ) )
        & ( ( h @ ( op1 @ e13 @ e12 ) )
          = ( op2 @ ( h @ e13 ) @ ( h @ e12 ) ) )
        & ( ( h @ ( op1 @ e13 @ e13 ) )
          = ( op2 @ ( h @ e13 ) @ ( h @ e13 ) ) )
        & ( ( h @ ( op1 @ e13 @ e14 ) )
          = ( op2 @ ( h @ e13 ) @ ( h @ e14 ) ) )
        & ( ( h @ ( op1 @ e14 @ e10 ) )
          = ( op2 @ ( h @ e14 ) @ ( h @ e10 ) ) )
        & ( ( h @ ( op1 @ e14 @ e11 ) )
          = ( op2 @ ( h @ e14 ) @ ( h @ e11 ) ) )
        & ( ( h @ ( op1 @ e14 @ e12 ) )
          = ( op2 @ ( h @ e14 ) @ ( h @ e12 ) ) )
        & ( ( h @ ( op1 @ e14 @ e13 ) )
          = ( op2 @ ( h @ e14 ) @ ( h @ e13 ) ) )
        & ( ( h @ ( op1 @ e14 @ e14 ) )
          = ( op2 @ ( h @ e14 ) @ ( h @ e14 ) ) )
        & ( ( j @ ( op2 @ e20 @ e20 ) )
          = ( op1 @ ( j @ e20 ) @ ( j @ e20 ) ) )
        & ( ( j @ ( op2 @ e20 @ e21 ) )
          = ( op1 @ ( j @ e20 ) @ ( j @ e21 ) ) )
        & ( ( j @ ( op2 @ e20 @ e22 ) )
          = ( op1 @ ( j @ e20 ) @ ( j @ e22 ) ) )
        & ( ( j @ ( op2 @ e20 @ e23 ) )
          = ( op1 @ ( j @ e20 ) @ ( j @ e23 ) ) )
        & ( ( j @ ( op2 @ e20 @ e24 ) )
          = ( op1 @ ( j @ e20 ) @ ( j @ e24 ) ) )
        & ( ( j @ ( op2 @ e21 @ e20 ) )
          = ( op1 @ ( j @ e21 ) @ ( j @ e20 ) ) )
        & ( ( j @ ( op2 @ e21 @ e21 ) )
          = ( op1 @ ( j @ e21 ) @ ( j @ e21 ) ) )
        & ( ( j @ ( op2 @ e21 @ e22 ) )
          = ( op1 @ ( j @ e21 ) @ ( j @ e22 ) ) )
        & ( ( j @ ( op2 @ e21 @ e23 ) )
          = ( op1 @ ( j @ e21 ) @ ( j @ e23 ) ) )
        & ( ( j @ ( op2 @ e21 @ e24 ) )
          = ( op1 @ ( j @ e21 ) @ ( j @ e24 ) ) )
        & ( ( j @ ( op2 @ e22 @ e20 ) )
          = ( op1 @ ( j @ e22 ) @ ( j @ e20 ) ) )
        & ( ( j @ ( op2 @ e22 @ e21 ) )
          = ( op1 @ ( j @ e22 ) @ ( j @ e21 ) ) )
        & ( ( j @ ( op2 @ e22 @ e22 ) )
          = ( op1 @ ( j @ e22 ) @ ( j @ e22 ) ) )
        & ( ( j @ ( op2 @ e22 @ e23 ) )
          = ( op1 @ ( j @ e22 ) @ ( j @ e23 ) ) )
        & ( ( j @ ( op2 @ e22 @ e24 ) )
          = ( op1 @ ( j @ e22 ) @ ( j @ e24 ) ) )
        & ( ( j @ ( op2 @ e23 @ e20 ) )
          = ( op1 @ ( j @ e23 ) @ ( j @ e20 ) ) )
        & ( ( j @ ( op2 @ e23 @ e21 ) )
          = ( op1 @ ( j @ e23 ) @ ( j @ e21 ) ) )
        & ( ( j @ ( op2 @ e23 @ e22 ) )
          = ( op1 @ ( j @ e23 ) @ ( j @ e22 ) ) )
        & ( ( j @ ( op2 @ e23 @ e23 ) )
          = ( op1 @ ( j @ e23 ) @ ( j @ e23 ) ) )
        & ( ( j @ ( op2 @ e23 @ e24 ) )
          = ( op1 @ ( j @ e23 ) @ ( j @ e24 ) ) )
        & ( ( j @ ( op2 @ e24 @ e20 ) )
          = ( op1 @ ( j @ e24 ) @ ( j @ e20 ) ) )
        & ( ( j @ ( op2 @ e24 @ e21 ) )
          = ( op1 @ ( j @ e24 ) @ ( j @ e21 ) ) )
        & ( ( j @ ( op2 @ e24 @ e22 ) )
          = ( op1 @ ( j @ e24 ) @ ( j @ e22 ) ) )
        & ( ( j @ ( op2 @ e24 @ e23 ) )
          = ( op1 @ ( j @ e24 ) @ ( j @ e23 ) ) )
        & ( ( j @ ( op2 @ e24 @ e24 ) )
          = ( op1 @ ( j @ e24 ) @ ( j @ e24 ) ) )
        & ( ( h @ ( j @ e20 ) )
          = e20 )
        & ( ( h @ ( j @ e21 ) )
          = e21 )
        & ( ( h @ ( j @ e22 ) )
          = e22 )
        & ( ( h @ ( j @ e23 ) )
          = e23 )
        & ( ( h @ ( j @ e24 ) )
          = e24 )
        & ( ( j @ ( h @ e10 ) )
          = e10 )
        & ( ( j @ ( h @ e11 ) )
          = e11 )
        & ( ( j @ ( h @ e12 ) )
          = e12 )
        & ( ( j @ ( h @ e13 ) )
          = e13 )
        & ( ( j @ ( h @ e14 ) )
          = e14 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

thf(2,negated_conjecture,
    ~ ( ( ( ( ( h @ e10 )
            = e20 )
          | ( ( h @ e10 )
            = e21 )
          | ( ( h @ e10 )
            = e22 )
          | ( ( h @ e10 )
            = e23 )
          | ( ( h @ e10 )
            = e24 ) )
        & ( ( ( h @ e11 )
            = e20 )
          | ( ( h @ e11 )
            = e21 )
          | ( ( h @ e11 )
            = e22 )
          | ( ( h @ e11 )
            = e23 )
          | ( ( h @ e11 )
            = e24 ) )
        & ( ( ( h @ e12 )
            = e20 )
          | ( ( h @ e12 )
            = e21 )
          | ( ( h @ e12 )
            = e22 )
          | ( ( h @ e12 )
            = e23 )
          | ( ( h @ e12 )
            = e24 ) )
        & ( ( ( h @ e13 )
            = e20 )
          | ( ( h @ e13 )
            = e21 )
          | ( ( h @ e13 )
            = e22 )
          | ( ( h @ e13 )
            = e23 )
          | ( ( h @ e13 )
            = e24 ) )
        & ( ( ( h @ e14 )
            = e20 )
          | ( ( h @ e14 )
            = e21 )
          | ( ( h @ e14 )
            = e22 )
          | ( ( h @ e14 )
            = e23 )
          | ( ( h @ e14 )
            = e24 ) )
        & ( ( ( j @ e20 )
            = e10 )
          | ( ( j @ e20 )
            = e11 )
          | ( ( j @ e20 )
            = e12 )
          | ( ( j @ e20 )
            = e13 )
          | ( ( j @ e20 )
            = e14 ) )
        & ( ( ( j @ e21 )
            = e10 )
          | ( ( j @ e21 )
            = e11 )
          | ( ( j @ e21 )
            = e12 )
          | ( ( j @ e21 )
            = e13 )
          | ( ( j @ e21 )
            = e14 ) )
        & ( ( ( j @ e22 )
            = e10 )
          | ( ( j @ e22 )
            = e11 )
          | ( ( j @ e22 )
            = e12 )
          | ( ( j @ e22 )
            = e13 )
          | ( ( j @ e22 )
            = e14 ) )
        & ( ( ( j @ e23 )
            = e10 )
          | ( ( j @ e23 )
            = e11 )
          | ( ( j @ e23 )
            = e12 )
          | ( ( j @ e23 )
            = e13 )
          | ( ( j @ e23 )
            = e14 ) )
        & ( ( ( j @ e24 )
            = e10 )
          | ( ( j @ e24 )
            = e11 )
          | ( ( j @ e24 )
            = e12 )
          | ( ( j @ e24 )
            = e13 )
          | ( ( j @ e24 )
            = e14 ) ) )
     => ~ ( ( ( h @ ( op1 @ e10 @ e10 ) )
            = ( op2 @ ( h @ e10 ) @ ( h @ e10 ) ) )
          & ( ( h @ ( op1 @ e10 @ e11 ) )
            = ( op2 @ ( h @ e10 ) @ ( h @ e11 ) ) )
          & ( ( h @ ( op1 @ e10 @ e12 ) )
            = ( op2 @ ( h @ e10 ) @ ( h @ e12 ) ) )
          & ( ( h @ ( op1 @ e10 @ e13 ) )
            = ( op2 @ ( h @ e10 ) @ ( h @ e13 ) ) )
          & ( ( h @ ( op1 @ e10 @ e14 ) )
            = ( op2 @ ( h @ e10 ) @ ( h @ e14 ) ) )
          & ( ( h @ ( op1 @ e11 @ e10 ) )
            = ( op2 @ ( h @ e11 ) @ ( h @ e10 ) ) )
          & ( ( h @ ( op1 @ e11 @ e11 ) )
            = ( op2 @ ( h @ e11 ) @ ( h @ e11 ) ) )
          & ( ( h @ ( op1 @ e11 @ e12 ) )
            = ( op2 @ ( h @ e11 ) @ ( h @ e12 ) ) )
          & ( ( h @ ( op1 @ e11 @ e13 ) )
            = ( op2 @ ( h @ e11 ) @ ( h @ e13 ) ) )
          & ( ( h @ ( op1 @ e11 @ e14 ) )
            = ( op2 @ ( h @ e11 ) @ ( h @ e14 ) ) )
          & ( ( h @ ( op1 @ e12 @ e10 ) )
            = ( op2 @ ( h @ e12 ) @ ( h @ e10 ) ) )
          & ( ( h @ ( op1 @ e12 @ e11 ) )
            = ( op2 @ ( h @ e12 ) @ ( h @ e11 ) ) )
          & ( ( h @ ( op1 @ e12 @ e12 ) )
            = ( op2 @ ( h @ e12 ) @ ( h @ e12 ) ) )
          & ( ( h @ ( op1 @ e12 @ e13 ) )
            = ( op2 @ ( h @ e12 ) @ ( h @ e13 ) ) )
          & ( ( h @ ( op1 @ e12 @ e14 ) )
            = ( op2 @ ( h @ e12 ) @ ( h @ e14 ) ) )
          & ( ( h @ ( op1 @ e13 @ e10 ) )
            = ( op2 @ ( h @ e13 ) @ ( h @ e10 ) ) )
          & ( ( h @ ( op1 @ e13 @ e11 ) )
            = ( op2 @ ( h @ e13 ) @ ( h @ e11 ) ) )
          & ( ( h @ ( op1 @ e13 @ e12 ) )
            = ( op2 @ ( h @ e13 ) @ ( h @ e12 ) ) )
          & ( ( h @ ( op1 @ e13 @ e13 ) )
            = ( op2 @ ( h @ e13 ) @ ( h @ e13 ) ) )
          & ( ( h @ ( op1 @ e13 @ e14 ) )
            = ( op2 @ ( h @ e13 ) @ ( h @ e14 ) ) )
          & ( ( h @ ( op1 @ e14 @ e10 ) )
            = ( op2 @ ( h @ e14 ) @ ( h @ e10 ) ) )
          & ( ( h @ ( op1 @ e14 @ e11 ) )
            = ( op2 @ ( h @ e14 ) @ ( h @ e11 ) ) )
          & ( ( h @ ( op1 @ e14 @ e12 ) )
            = ( op2 @ ( h @ e14 ) @ ( h @ e12 ) ) )
          & ( ( h @ ( op1 @ e14 @ e13 ) )
            = ( op2 @ ( h @ e14 ) @ ( h @ e13 ) ) )
          & ( ( h @ ( op1 @ e14 @ e14 ) )
            = ( op2 @ ( h @ e14 ) @ ( h @ e14 ) ) )
          & ( ( j @ ( op2 @ e20 @ e20 ) )
            = ( op1 @ ( j @ e20 ) @ ( j @ e20 ) ) )
          & ( ( j @ ( op2 @ e20 @ e21 ) )
            = ( op1 @ ( j @ e20 ) @ ( j @ e21 ) ) )
          & ( ( j @ ( op2 @ e20 @ e22 ) )
            = ( op1 @ ( j @ e20 ) @ ( j @ e22 ) ) )
          & ( ( j @ ( op2 @ e20 @ e23 ) )
            = ( op1 @ ( j @ e20 ) @ ( j @ e23 ) ) )
          & ( ( j @ ( op2 @ e20 @ e24 ) )
            = ( op1 @ ( j @ e20 ) @ ( j @ e24 ) ) )
          & ( ( j @ ( op2 @ e21 @ e20 ) )
            = ( op1 @ ( j @ e21 ) @ ( j @ e20 ) ) )
          & ( ( j @ ( op2 @ e21 @ e21 ) )
            = ( op1 @ ( j @ e21 ) @ ( j @ e21 ) ) )
          & ( ( j @ ( op2 @ e21 @ e22 ) )
            = ( op1 @ ( j @ e21 ) @ ( j @ e22 ) ) )
          & ( ( j @ ( op2 @ e21 @ e23 ) )
            = ( op1 @ ( j @ e21 ) @ ( j @ e23 ) ) )
          & ( ( j @ ( op2 @ e21 @ e24 ) )
            = ( op1 @ ( j @ e21 ) @ ( j @ e24 ) ) )
          & ( ( j @ ( op2 @ e22 @ e20 ) )
            = ( op1 @ ( j @ e22 ) @ ( j @ e20 ) ) )
          & ( ( j @ ( op2 @ e22 @ e21 ) )
            = ( op1 @ ( j @ e22 ) @ ( j @ e21 ) ) )
          & ( ( j @ ( op2 @ e22 @ e22 ) )
            = ( op1 @ ( j @ e22 ) @ ( j @ e22 ) ) )
          & ( ( j @ ( op2 @ e22 @ e23 ) )
            = ( op1 @ ( j @ e22 ) @ ( j @ e23 ) ) )
          & ( ( j @ ( op2 @ e22 @ e24 ) )
            = ( op1 @ ( j @ e22 ) @ ( j @ e24 ) ) )
          & ( ( j @ ( op2 @ e23 @ e20 ) )
            = ( op1 @ ( j @ e23 ) @ ( j @ e20 ) ) )
          & ( ( j @ ( op2 @ e23 @ e21 ) )
            = ( op1 @ ( j @ e23 ) @ ( j @ e21 ) ) )
          & ( ( j @ ( op2 @ e23 @ e22 ) )
            = ( op1 @ ( j @ e23 ) @ ( j @ e22 ) ) )
          & ( ( j @ ( op2 @ e23 @ e23 ) )
            = ( op1 @ ( j @ e23 ) @ ( j @ e23 ) ) )
          & ( ( j @ ( op2 @ e23 @ e24 ) )
            = ( op1 @ ( j @ e23 ) @ ( j @ e24 ) ) )
          & ( ( j @ ( op2 @ e24 @ e20 ) )
            = ( op1 @ ( j @ e24 ) @ ( j @ e20 ) ) )
          & ( ( j @ ( op2 @ e24 @ e21 ) )
            = ( op1 @ ( j @ e24 ) @ ( j @ e21 ) ) )
          & ( ( j @ ( op2 @ e24 @ e22 ) )
            = ( op1 @ ( j @ e24 ) @ ( j @ e22 ) ) )
          & ( ( j @ ( op2 @ e24 @ e23 ) )
            = ( op1 @ ( j @ e24 ) @ ( j @ e23 ) ) )
          & ( ( j @ ( op2 @ e24 @ e24 ) )
            = ( op1 @ ( j @ e24 ) @ ( j @ e24 ) ) )
          & ( ( h @ ( j @ e20 ) )
            = e20 )
          & ( ( h @ ( j @ e21 ) )
            = e21 )
          & ( ( h @ ( j @ e22 ) )
            = e22 )
          & ( ( h @ ( j @ e23 ) )
            = e23 )
          & ( ( h @ ( j @ e24 ) )
            = e24 )
          & ( ( j @ ( h @ e10 ) )
            = e10 )
          & ( ( j @ ( h @ e11 ) )
            = e11 )
          & ( ( j @ ( h @ e12 ) )
            = e12 )
          & ( ( j @ ( h @ e13 ) )
            = e13 )
          & ( ( j @ ( h @ e14 ) )
            = e14 ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(8,plain,
    ~ ( ( ( ( ( h @ e10 )
            = e20 )
          | ( ( h @ e10 )
            = e21 )
          | ( ( h @ e10 )
            = e22 )
          | ( ( h @ e10 )
            = e23 )
          | ( ( h @ e10 )
            = e24 ) )
        & ( ( ( h @ e11 )
            = e20 )
          | ( ( h @ e11 )
            = e21 )
          | ( ( h @ e11 )
            = e22 )
          | ( ( h @ e11 )
            = e23 )
          | ( ( h @ e11 )
            = e24 ) )
        & ( ( ( h @ e12 )
            = e20 )
          | ( ( h @ e12 )
            = e21 )
          | ( ( h @ e12 )
            = e22 )
          | ( ( h @ e12 )
            = e23 )
          | ( ( h @ e12 )
            = e24 ) )
        & ( ( ( h @ e13 )
            = e20 )
          | ( ( h @ e13 )
            = e21 )
          | ( ( h @ e13 )
            = e22 )
          | ( ( h @ e13 )
            = e23 )
          | ( ( h @ e13 )
            = e24 ) )
        & ( ( ( h @ e14 )
            = e20 )
          | ( ( h @ e14 )
            = e21 )
          | ( ( h @ e14 )
            = e22 )
          | ( ( h @ e14 )
            = e23 )
          | ( ( h @ e14 )
            = e24 ) )
        & ( ( ( j @ e20 )
            = e10 )
          | ( ( j @ e20 )
            = e11 )
          | ( ( j @ e20 )
            = e12 )
          | ( ( j @ e20 )
            = e13 )
          | ( ( j @ e20 )
            = e14 ) )
        & ( ( ( j @ e21 )
            = e10 )
          | ( ( j @ e21 )
            = e11 )
          | ( ( j @ e21 )
            = e12 )
          | ( ( j @ e21 )
            = e13 )
          | ( ( j @ e21 )
            = e14 ) )
        & ( ( ( j @ e22 )
            = e10 )
          | ( ( j @ e22 )
            = e11 )
          | ( ( j @ e22 )
            = e12 )
          | ( ( j @ e22 )
            = e13 )
          | ( ( j @ e22 )
            = e14 ) )
        & ( ( ( j @ e23 )
            = e10 )
          | ( ( j @ e23 )
            = e11 )
          | ( ( j @ e23 )
            = e12 )
          | ( ( j @ e23 )
            = e13 )
          | ( ( j @ e23 )
            = e14 ) )
        & ( ( ( j @ e24 )
            = e10 )
          | ( ( j @ e24 )
            = e11 )
          | ( ( j @ e24 )
            = e12 )
          | ( ( j @ e24 )
            = e13 )
          | ( ( j @ e24 )
            = e14 ) ) )
     => ~ ( ( ( h @ ( op1 @ e10 @ e10 ) )
            = ( op2 @ ( h @ e10 ) @ ( h @ e10 ) ) )
          & ( ( h @ ( op1 @ e10 @ e11 ) )
            = ( op2 @ ( h @ e10 ) @ ( h @ e11 ) ) )
          & ( ( h @ ( op1 @ e10 @ e12 ) )
            = ( op2 @ ( h @ e10 ) @ ( h @ e12 ) ) )
          & ( ( h @ ( op1 @ e10 @ e13 ) )
            = ( op2 @ ( h @ e10 ) @ ( h @ e13 ) ) )
          & ( ( h @ ( op1 @ e10 @ e14 ) )
            = ( op2 @ ( h @ e10 ) @ ( h @ e14 ) ) )
          & ( ( h @ ( op1 @ e11 @ e10 ) )
            = ( op2 @ ( h @ e11 ) @ ( h @ e10 ) ) )
          & ( ( h @ ( op1 @ e11 @ e11 ) )
            = ( op2 @ ( h @ e11 ) @ ( h @ e11 ) ) )
          & ( ( h @ ( op1 @ e11 @ e12 ) )
            = ( op2 @ ( h @ e11 ) @ ( h @ e12 ) ) )
          & ( ( h @ ( op1 @ e11 @ e13 ) )
            = ( op2 @ ( h @ e11 ) @ ( h @ e13 ) ) )
          & ( ( h @ ( op1 @ e11 @ e14 ) )
            = ( op2 @ ( h @ e11 ) @ ( h @ e14 ) ) )
          & ( ( h @ ( op1 @ e12 @ e10 ) )
            = ( op2 @ ( h @ e12 ) @ ( h @ e10 ) ) )
          & ( ( h @ ( op1 @ e12 @ e11 ) )
            = ( op2 @ ( h @ e12 ) @ ( h @ e11 ) ) )
          & ( ( h @ ( op1 @ e12 @ e12 ) )
            = ( op2 @ ( h @ e12 ) @ ( h @ e12 ) ) )
          & ( ( h @ ( op1 @ e12 @ e13 ) )
            = ( op2 @ ( h @ e12 ) @ ( h @ e13 ) ) )
          & ( ( h @ ( op1 @ e12 @ e14 ) )
            = ( op2 @ ( h @ e12 ) @ ( h @ e14 ) ) )
          & ( ( h @ ( op1 @ e13 @ e10 ) )
            = ( op2 @ ( h @ e13 ) @ ( h @ e10 ) ) )
          & ( ( h @ ( op1 @ e13 @ e11 ) )
            = ( op2 @ ( h @ e13 ) @ ( h @ e11 ) ) )
          & ( ( h @ ( op1 @ e13 @ e12 ) )
            = ( op2 @ ( h @ e13 ) @ ( h @ e12 ) ) )
          & ( ( h @ ( op1 @ e13 @ e13 ) )
            = ( op2 @ ( h @ e13 ) @ ( h @ e13 ) ) )
          & ( ( h @ ( op1 @ e13 @ e14 ) )
            = ( op2 @ ( h @ e13 ) @ ( h @ e14 ) ) )
          & ( ( h @ ( op1 @ e14 @ e10 ) )
            = ( op2 @ ( h @ e14 ) @ ( h @ e10 ) ) )
          & ( ( h @ ( op1 @ e14 @ e11 ) )
            = ( op2 @ ( h @ e14 ) @ ( h @ e11 ) ) )
          & ( ( h @ ( op1 @ e14 @ e12 ) )
            = ( op2 @ ( h @ e14 ) @ ( h @ e12 ) ) )
          & ( ( h @ ( op1 @ e14 @ e13 ) )
            = ( op2 @ ( h @ e14 ) @ ( h @ e13 ) ) )
          & ( ( h @ ( op1 @ e14 @ e14 ) )
            = ( op2 @ ( h @ e14 ) @ ( h @ e14 ) ) )
          & ( ( j @ ( op2 @ e20 @ e20 ) )
            = ( op1 @ ( j @ e20 ) @ ( j @ e20 ) ) )
          & ( ( j @ ( op2 @ e20 @ e21 ) )
            = ( op1 @ ( j @ e20 ) @ ( j @ e21 ) ) )
          & ( ( j @ ( op2 @ e20 @ e22 ) )
            = ( op1 @ ( j @ e20 ) @ ( j @ e22 ) ) )
          & ( ( j @ ( op2 @ e20 @ e23 ) )
            = ( op1 @ ( j @ e20 ) @ ( j @ e23 ) ) )
          & ( ( j @ ( op2 @ e20 @ e24 ) )
            = ( op1 @ ( j @ e20 ) @ ( j @ e24 ) ) )
          & ( ( j @ ( op2 @ e21 @ e20 ) )
            = ( op1 @ ( j @ e21 ) @ ( j @ e20 ) ) )
          & ( ( j @ ( op2 @ e21 @ e21 ) )
            = ( op1 @ ( j @ e21 ) @ ( j @ e21 ) ) )
          & ( ( j @ ( op2 @ e21 @ e22 ) )
            = ( op1 @ ( j @ e21 ) @ ( j @ e22 ) ) )
          & ( ( j @ ( op2 @ e21 @ e23 ) )
            = ( op1 @ ( j @ e21 ) @ ( j @ e23 ) ) )
          & ( ( j @ ( op2 @ e21 @ e24 ) )
            = ( op1 @ ( j @ e21 ) @ ( j @ e24 ) ) )
          & ( ( j @ ( op2 @ e22 @ e20 ) )
            = ( op1 @ ( j @ e22 ) @ ( j @ e20 ) ) )
          & ( ( j @ ( op2 @ e22 @ e21 ) )
            = ( op1 @ ( j @ e22 ) @ ( j @ e21 ) ) )
          & ( ( j @ ( op2 @ e22 @ e22 ) )
            = ( op1 @ ( j @ e22 ) @ ( j @ e22 ) ) )
          & ( ( j @ ( op2 @ e22 @ e23 ) )
            = ( op1 @ ( j @ e22 ) @ ( j @ e23 ) ) )
          & ( ( j @ ( op2 @ e22 @ e24 ) )
            = ( op1 @ ( j @ e22 ) @ ( j @ e24 ) ) )
          & ( ( j @ ( op2 @ e23 @ e20 ) )
            = ( op1 @ ( j @ e23 ) @ ( j @ e20 ) ) )
          & ( ( j @ ( op2 @ e23 @ e21 ) )
            = ( op1 @ ( j @ e23 ) @ ( j @ e21 ) ) )
          & ( ( j @ ( op2 @ e23 @ e22 ) )
            = ( op1 @ ( j @ e23 ) @ ( j @ e22 ) ) )
          & ( ( j @ ( op2 @ e23 @ e23 ) )
            = ( op1 @ ( j @ e23 ) @ ( j @ e23 ) ) )
          & ( ( j @ ( op2 @ e23 @ e24 ) )
            = ( op1 @ ( j @ e23 ) @ ( j @ e24 ) ) )
          & ( ( j @ ( op2 @ e24 @ e20 ) )
            = ( op1 @ ( j @ e24 ) @ ( j @ e20 ) ) )
          & ( ( j @ ( op2 @ e24 @ e21 ) )
            = ( op1 @ ( j @ e24 ) @ ( j @ e21 ) ) )
          & ( ( j @ ( op2 @ e24 @ e22 ) )
            = ( op1 @ ( j @ e24 ) @ ( j @ e22 ) ) )
          & ( ( j @ ( op2 @ e24 @ e23 ) )
            = ( op1 @ ( j @ e24 ) @ ( j @ e23 ) ) )
          & ( ( j @ ( op2 @ e24 @ e24 ) )
            = ( op1 @ ( j @ e24 ) @ ( j @ e24 ) ) )
          & ( ( h @ ( j @ e20 ) )
            = e20 )
          & ( ( h @ ( j @ e21 ) )
            = e21 )
          & ( ( h @ ( j @ e22 ) )
            = e22 )
          & ( ( h @ ( j @ e23 ) )
            = e23 )
          & ( ( h @ ( j @ e24 ) )
            = e24 )
          & ( ( j @ ( h @ e10 ) )
            = e10 )
          & ( ( j @ ( h @ e11 ) )
            = e11 )
          & ( ( j @ ( h @ e12 ) )
            = e12 )
          & ( ( j @ ( h @ e13 ) )
            = e13 )
          & ( ( j @ ( h @ e14 ) )
            = e14 ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(45,plain,
    ( ( h @ ( op1 @ e12 @ e12 ) )
    = ( op2 @ ( h @ e12 ) @ ( h @ e12 ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(110,plain,
    ( ( op2 @ ( h @ e12 ) @ ( h @ e12 ) )
    = ( h @ ( op1 @ e12 @ e12 ) ) ),
    inference(lifteq,[status(thm)],[45]) ).

thf(6,axiom,
    ( ( ( op1 @ e10 @ e10 )
      = e10 )
    & ( ( op1 @ e10 @ e11 )
      = e11 )
    & ( ( op1 @ e10 @ e12 )
      = e12 )
    & ( ( op1 @ e10 @ e13 )
      = e13 )
    & ( ( op1 @ e10 @ e14 )
      = e14 )
    & ( ( op1 @ e11 @ e10 )
      = e11 )
    & ( ( op1 @ e11 @ e11 )
      = e14 )
    & ( ( op1 @ e11 @ e12 )
      = e10 )
    & ( ( op1 @ e11 @ e13 )
      = e12 )
    & ( ( op1 @ e11 @ e14 )
      = e13 )
    & ( ( op1 @ e12 @ e10 )
      = e12 )
    & ( ( op1 @ e12 @ e11 )
      = e10 )
    & ( ( op1 @ e12 @ e12 )
      = e13 )
    & ( ( op1 @ e12 @ e13 )
      = e14 )
    & ( ( op1 @ e12 @ e14 )
      = e11 )
    & ( ( op1 @ e13 @ e10 )
      = e13 )
    & ( ( op1 @ e13 @ e11 )
      = e12 )
    & ( ( op1 @ e13 @ e12 )
      = e14 )
    & ( ( op1 @ e13 @ e13 )
      = e11 )
    & ( ( op1 @ e13 @ e14 )
      = e10 )
    & ( ( op1 @ e14 @ e10 )
      = e14 )
    & ( ( op1 @ e14 @ e11 )
      = e13 )
    & ( ( op1 @ e14 @ e12 )
      = e11 )
    & ( ( op1 @ e14 @ e13 )
      = e10 )
    & ( ( op1 @ e14 @ e14 )
      = e12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

thf(242,plain,
    ( ( ( op1 @ e10 @ e10 )
      = e10 )
    & ( ( op1 @ e10 @ e11 )
      = e11 )
    & ( ( op1 @ e10 @ e12 )
      = e12 )
    & ( ( op1 @ e10 @ e13 )
      = e13 )
    & ( ( op1 @ e10 @ e14 )
      = e14 )
    & ( ( op1 @ e11 @ e10 )
      = e11 )
    & ( ( op1 @ e11 @ e11 )
      = e14 )
    & ( ( op1 @ e11 @ e12 )
      = e10 )
    & ( ( op1 @ e11 @ e13 )
      = e12 )
    & ( ( op1 @ e11 @ e14 )
      = e13 )
    & ( ( op1 @ e12 @ e10 )
      = e12 )
    & ( ( op1 @ e12 @ e11 )
      = e10 )
    & ( ( op1 @ e12 @ e12 )
      = e13 )
    & ( ( op1 @ e12 @ e13 )
      = e14 )
    & ( ( op1 @ e12 @ e14 )
      = e11 )
    & ( ( op1 @ e13 @ e10 )
      = e13 )
    & ( ( op1 @ e13 @ e11 )
      = e12 )
    & ( ( op1 @ e13 @ e12 )
      = e14 )
    & ( ( op1 @ e13 @ e13 )
      = e11 )
    & ( ( op1 @ e13 @ e14 )
      = e10 )
    & ( ( op1 @ e14 @ e10 )
      = e14 )
    & ( ( op1 @ e14 @ e11 )
      = e13 )
    & ( ( op1 @ e14 @ e12 )
      = e11 )
    & ( ( op1 @ e14 @ e13 )
      = e10 )
    & ( ( op1 @ e14 @ e14 )
      = e12 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(251,plain,
    ( ( op1 @ e12 @ e12 )
    = e13 ),
    inference(cnf,[status(esa)],[242]) ).

thf(280,plain,
    ( ( op1 @ e12 @ e12 )
    = e13 ),
    inference(lifteq,[status(thm)],[251]) ).

thf(7995,plain,
    ( ( op2 @ ( h @ e12 ) @ ( h @ e12 ) )
    = ( h @ e13 ) ),
    inference(rewrite,[status(thm)],[110,280]) ).

thf(7,axiom,
    ( ( ( op2 @ e20 @ e20 )
      = e20 )
    & ( ( op2 @ e20 @ e21 )
      = e21 )
    & ( ( op2 @ e20 @ e22 )
      = e22 )
    & ( ( op2 @ e20 @ e23 )
      = e23 )
    & ( ( op2 @ e20 @ e24 )
      = e24 )
    & ( ( op2 @ e21 @ e20 )
      = e21 )
    & ( ( op2 @ e21 @ e21 )
      = e22 )
    & ( ( op2 @ e21 @ e22 )
      = e24 )
    & ( ( op2 @ e21 @ e23 )
      = e20 )
    & ( ( op2 @ e21 @ e24 )
      = e23 )
    & ( ( op2 @ e22 @ e20 )
      = e22 )
    & ( ( op2 @ e22 @ e21 )
      = e20 )
    & ( ( op2 @ e22 @ e22 )
      = e23 )
    & ( ( op2 @ e22 @ e23 )
      = e24 )
    & ( ( op2 @ e22 @ e24 )
      = e21 )
    & ( ( op2 @ e23 @ e20 )
      = e23 )
    & ( ( op2 @ e23 @ e21 )
      = e24 )
    & ( ( op2 @ e23 @ e22 )
      = e20 )
    & ( ( op2 @ e23 @ e23 )
      = e21 )
    & ( ( op2 @ e23 @ e24 )
      = e22 )
    & ( ( op2 @ e24 @ e20 )
      = e24 )
    & ( ( op2 @ e24 @ e21 )
      = e23 )
    & ( ( op2 @ e24 @ e22 )
      = e21 )
    & ( ( op2 @ e24 @ e23 )
      = e22 )
    & ( ( op2 @ e24 @ e24 )
      = e20 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

thf(293,plain,
    ( ( ( op2 @ e20 @ e20 )
      = e20 )
    & ( ( op2 @ e20 @ e21 )
      = e21 )
    & ( ( op2 @ e20 @ e22 )
      = e22 )
    & ( ( op2 @ e20 @ e23 )
      = e23 )
    & ( ( op2 @ e20 @ e24 )
      = e24 )
    & ( ( op2 @ e21 @ e20 )
      = e21 )
    & ( ( op2 @ e21 @ e21 )
      = e22 )
    & ( ( op2 @ e21 @ e22 )
      = e24 )
    & ( ( op2 @ e21 @ e23 )
      = e20 )
    & ( ( op2 @ e21 @ e24 )
      = e23 )
    & ( ( op2 @ e22 @ e20 )
      = e22 )
    & ( ( op2 @ e22 @ e21 )
      = e20 )
    & ( ( op2 @ e22 @ e22 )
      = e23 )
    & ( ( op2 @ e22 @ e23 )
      = e24 )
    & ( ( op2 @ e22 @ e24 )
      = e21 )
    & ( ( op2 @ e23 @ e20 )
      = e23 )
    & ( ( op2 @ e23 @ e21 )
      = e24 )
    & ( ( op2 @ e23 @ e22 )
      = e20 )
    & ( ( op2 @ e23 @ e23 )
      = e21 )
    & ( ( op2 @ e23 @ e24 )
      = e22 )
    & ( ( op2 @ e24 @ e20 )
      = e24 )
    & ( ( op2 @ e24 @ e21 )
      = e23 )
    & ( ( op2 @ e24 @ e22 )
      = e21 )
    & ( ( op2 @ e24 @ e23 )
      = e22 )
    & ( ( op2 @ e24 @ e24 )
      = e20 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(307,plain,
    ( ( op2 @ e23 @ e23 )
    = e21 ),
    inference(cnf,[status(esa)],[293]) ).

thf(323,plain,
    ( ( op2 @ e23 @ e23 )
    = e21 ),
    inference(lifteq,[status(thm)],[307]) ).

thf(8030,plain,
    ( ( ( h @ e13 )
      = e21 )
    | ( ( op2 @ ( h @ e12 ) @ ( h @ e12 ) )
     != ( op2 @ e23 @ e23 ) ) ),
    inference(paramod_ordered,[status(thm)],[7995,323]) ).

thf(8089,plain,
    ( ( ( h @ e13 )
      = e21 )
    | ( ( h @ e12 )
     != e23 )
    | ( ( h @ e12 )
     != e23 ) ),
    inference(simp,[status(thm)],[8030]) ).

thf(8171,plain,
    ( ( ( h @ e13 )
      = e21 )
    | ( ( h @ e12 )
     != e23 ) ),
    inference(simp,[status(thm)],[8089]) ).

thf(13,plain,
    ( ( j @ ( h @ e13 ) )
    = e13 ),
    inference(cnf,[status(esa)],[8]) ).

thf(108,plain,
    ( ( j @ ( h @ e13 ) )
    = e13 ),
    inference(lifteq,[status(thm)],[13]) ).

thf(9,plain,
    ( ( j @ ( h @ e11 ) )
    = e11 ),
    inference(cnf,[status(esa)],[8]) ).

thf(106,plain,
    ( ( j @ ( h @ e11 ) )
    = e11 ),
    inference(lifteq,[status(thm)],[9]) ).

thf(376,plain,
    ( ( e13 = e11 )
    | ( ( j @ ( h @ e13 ) )
     != ( j @ ( h @ e11 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[108,106]) ).

thf(382,plain,
    ( ( e13 = e11 )
    | ( ( h @ e13 )
     != ( h @ e11 ) ) ),
    inference(simp,[status(thm)],[376]) ).

thf(3,axiom,
    ( ( e10 != e11 )
    & ( e10 != e12 )
    & ( e10 != e13 )
    & ( e10 != e14 )
    & ( e11 != e12 )
    & ( e11 != e13 )
    & ( e11 != e14 )
    & ( e12 != e13 )
    & ( e12 != e14 )
    & ( e13 != e14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

thf(149,plain,
    ( ( e10 != e11 )
    & ( e10 != e12 )
    & ( e10 != e13 )
    & ( e10 != e14 )
    & ( e11 != e12 )
    & ( e11 != e13 )
    & ( e11 != e14 )
    & ( e12 != e13 )
    & ( e12 != e14 )
    & ( e13 != e14 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(157,plain,
    e11 != e13,
    inference(cnf,[status(esa)],[149]) ).

thf(161,plain,
    e13 != e11,
    inference(lifteq,[status(thm)],[157]) ).

thf(933,plain,
    ( ( h @ e13 )
   != ( h @ e11 ) ),
    inference(simplifyReflect,[status(thm)],[382,161]) ).

thf(51,plain,
    ( ( ( h @ e11 )
      = e20 )
    | ( ( h @ e11 )
      = e21 )
    | ( ( h @ e11 )
      = e22 )
    | ( ( h @ e11 )
      = e23 )
    | ( ( h @ e11 )
      = e24 ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(143,plain,
    ( ( ( h @ e11 )
      = e20 )
    | ( ( h @ e11 )
      = e21 )
    | ( ( h @ e11 )
      = e22 )
    | ( ( h @ e11 )
      = e23 )
    | ( ( h @ e11 )
      = e24 ) ),
    inference(lifteq,[status(thm)],[51]) ).

thf(317,plain,
    ( ( op2 @ e20 @ e20 )
    = e20 ),
    inference(cnf,[status(esa)],[293]) ).

thf(324,plain,
    ( ( op2 @ e20 @ e20 )
    = e20 ),
    inference(lifteq,[status(thm)],[317]) ).

thf(28,plain,
    ( ( h @ ( op1 @ e11 @ e11 ) )
    = ( op2 @ ( h @ e11 ) @ ( h @ e11 ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(104,plain,
    ( ( op2 @ ( h @ e11 ) @ ( h @ e11 ) )
    = ( h @ ( op1 @ e11 @ e11 ) ) ),
    inference(lifteq,[status(thm)],[28]) ).

thf(267,plain,
    ( ( op1 @ e11 @ e11 )
    = e14 ),
    inference(cnf,[status(esa)],[242]) ).

thf(281,plain,
    ( ( op1 @ e11 @ e11 )
    = e14 ),
    inference(lifteq,[status(thm)],[267]) ).

thf(7216,plain,
    ( ( op2 @ ( h @ e11 ) @ ( h @ e11 ) )
    = ( h @ e14 ) ),
    inference(rewrite,[status(thm)],[104,281]) ).

thf(7240,plain,
    ( ( ( h @ e14 )
      = e20 )
    | ( ( op2 @ ( h @ e11 ) @ ( h @ e11 ) )
     != ( op2 @ e20 @ e20 ) ) ),
    inference(paramod_ordered,[status(thm)],[324,7216]) ).

thf(7311,plain,
    ( ( ( h @ e14 )
      = e20 )
    | ( ( h @ e11 )
     != e20 )
    | ( ( h @ e11 )
     != e20 ) ),
    inference(simp,[status(thm)],[7240]) ).

thf(7385,plain,
    ( ( ( h @ e14 )
      = e20 )
    | ( ( h @ e11 )
     != e20 ) ),
    inference(simp,[status(thm)],[7311]) ).

thf(62,plain,
    ( ( j @ ( h @ e14 ) )
    = e14 ),
    inference(cnf,[status(esa)],[8]) ).

thf(148,plain,
    ( ( j @ ( h @ e14 ) )
    = e14 ),
    inference(lifteq,[status(thm)],[62]) ).

thf(566,plain,
    ( ( e14 = e11 )
    | ( ( j @ ( h @ e14 ) )
     != ( j @ ( h @ e11 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[148,106]) ).

thf(583,plain,
    ( ( e14 = e11 )
    | ( ( h @ e14 )
     != ( h @ e11 ) ) ),
    inference(simp,[status(thm)],[566]) ).

thf(150,plain,
    e11 != e14,
    inference(cnf,[status(esa)],[149]) ).

thf(166,plain,
    e14 != e11,
    inference(lifteq,[status(thm)],[150]) ).

thf(9170,plain,
    ( ( h @ e14 )
   != ( h @ e11 ) ),
    inference(simplifyReflect,[status(thm)],[583,166]) ).

thf(62543,plain,
    ( ( ( h @ e11 )
     != e20 )
    | ( ( h @ e14 )
     != ( h @ e14 ) ) ),
    inference(paramod_ordered,[status(thm)],[7385,9170]) ).

thf(62544,plain,
    ( ( h @ e11 )
   != e20 ),
    inference(pattern_uni,[status(thm)],[62543:[]]) ).

thf(63318,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e11 )
      = e22 )
    | ( ( h @ e11 )
      = e23 )
    | ( ( h @ e11 )
      = e24 ) ),
    inference(simplifyReflect,[status(thm)],[143,62544]) ).

thf(303,plain,
    ( ( op2 @ e24 @ e24 )
    = e20 ),
    inference(cnf,[status(esa)],[293]) ).

thf(335,plain,
    ( ( op2 @ e24 @ e24 )
    = e20 ),
    inference(lifteq,[status(thm)],[303]) ).

thf(7249,plain,
    ( ( ( h @ e14 )
      = e20 )
    | ( ( op2 @ ( h @ e11 ) @ ( h @ e11 ) )
     != ( op2 @ e24 @ e24 ) ) ),
    inference(paramod_ordered,[status(thm)],[7216,335]) ).

thf(7334,plain,
    ( ( ( h @ e14 )
      = e20 )
    | ( ( h @ e11 )
     != e24 )
    | ( ( h @ e11 )
     != e24 ) ),
    inference(simp,[status(thm)],[7249]) ).

thf(7390,plain,
    ( ( ( h @ e14 )
      = e20 )
    | ( ( h @ e11 )
     != e24 ) ),
    inference(simp,[status(thm)],[7334]) ).

thf(24,plain,
    ( ( j @ ( h @ e10 ) )
    = e10 ),
    inference(cnf,[status(esa)],[8]) ).

thf(89,plain,
    ( ( j @ ( h @ e10 ) )
    = e10 ),
    inference(lifteq,[status(thm)],[24]) ).

thf(570,plain,
    ( ( e14 = e10 )
    | ( ( j @ ( h @ e14 ) )
     != ( j @ ( h @ e10 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[148,89]) ).

thf(581,plain,
    ( ( e14 = e10 )
    | ( ( h @ e14 )
     != ( h @ e10 ) ) ),
    inference(simp,[status(thm)],[570]) ).

thf(159,plain,
    e10 != e14,
    inference(cnf,[status(esa)],[149]) ).

thf(164,plain,
    e14 != e10,
    inference(lifteq,[status(thm)],[159]) ).

thf(7977,plain,
    ( ( h @ e14 )
   != ( h @ e10 ) ),
    inference(simplifyReflect,[status(thm)],[581,164]) ).

thf(76,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( h @ e10 )
      = e21 )
    | ( ( h @ e10 )
      = e22 )
    | ( ( h @ e10 )
      = e23 )
    | ( ( h @ e10 )
      = e24 ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(123,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( h @ e10 )
      = e21 )
    | ( ( h @ e10 )
      = e22 )
    | ( ( h @ e10 )
      = e23 )
    | ( ( h @ e10 )
      = e24 ) ),
    inference(lifteq,[status(thm)],[76]) ).

thf(10401,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( h @ e10 )
      = e21 )
    | ( ( h @ e10 )
      = e22 )
    | ( ( h @ e10 )
      = e23 )
    | ( ( j @ e24 )
      = e10 )
    | ( ( h @ e10 )
     != ( h @ e10 ) ) ),
    inference(paramod_ordered,[status(thm)],[123,89]) ).

thf(10402,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( h @ e10 )
      = e21 )
    | ( ( h @ e10 )
      = e22 )
    | ( ( h @ e10 )
      = e23 )
    | ( ( j @ e24 )
      = e10 ) ),
    inference(pattern_uni,[status(thm)],[10401:[]]) ).

thf(262,plain,
    ( ( op1 @ e10 @ e10 )
    = e10 ),
    inference(cnf,[status(esa)],[242]) ).

thf(287,plain,
    ( ( op1 @ e10 @ e10 )
    = e10 ),
    inference(lifteq,[status(thm)],[262]) ).

thf(29,plain,
    ( ( j @ ( op2 @ e21 @ e21 ) )
    = ( op1 @ ( j @ e21 ) @ ( j @ e21 ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(98,plain,
    ( ( j @ ( op2 @ e21 @ e21 ) )
    = ( op1 @ ( j @ e21 ) @ ( j @ e21 ) ) ),
    inference(lifteq,[status(thm)],[29]) ).

thf(308,plain,
    ( ( op2 @ e21 @ e21 )
    = e22 ),
    inference(cnf,[status(esa)],[293]) ).

thf(319,plain,
    ( ( op2 @ e21 @ e21 )
    = e22 ),
    inference(lifteq,[status(thm)],[308]) ).

thf(5070,plain,
    ( ( op1 @ ( j @ e21 ) @ ( j @ e21 ) )
    = ( j @ e22 ) ),
    inference(rewrite,[status(thm)],[98,319]) ).

thf(5126,plain,
    ( ( ( j @ e22 )
      = e10 )
    | ( ( op1 @ ( j @ e21 ) @ ( j @ e21 ) )
     != ( op1 @ e10 @ e10 ) ) ),
    inference(paramod_ordered,[status(thm)],[287,5070]) ).

thf(5175,plain,
    ( ( ( j @ e22 )
      = e10 )
    | ( ( j @ e21 )
     != e10 )
    | ( ( j @ e21 )
     != e10 ) ),
    inference(simp,[status(thm)],[5126]) ).

thf(5218,plain,
    ( ( ( j @ e22 )
      = e10 )
    | ( ( j @ e21 )
     != e10 ) ),
    inference(simp,[status(thm)],[5175]) ).

thf(52,plain,
    ( ( h @ ( j @ e21 ) )
    = e21 ),
    inference(cnf,[status(esa)],[8]) ).

thf(92,plain,
    ( ( h @ ( j @ e21 ) )
    = e21 ),
    inference(lifteq,[status(thm)],[52]) ).

thf(34,plain,
    ( ( h @ ( j @ e22 ) )
    = e22 ),
    inference(cnf,[status(esa)],[8]) ).

thf(114,plain,
    ( ( h @ ( j @ e22 ) )
    = e22 ),
    inference(lifteq,[status(thm)],[34]) ).

thf(391,plain,
    ( ( e22 = e21 )
    | ( ( h @ ( j @ e22 ) )
     != ( h @ ( j @ e21 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,114]) ).

thf(405,plain,
    ( ( e22 = e21 )
    | ( ( j @ e22 )
     != ( j @ e21 ) ) ),
    inference(simp,[status(thm)],[391]) ).

thf(4,axiom,
    ( ( e20 != e21 )
    & ( e20 != e22 )
    & ( e20 != e23 )
    & ( e20 != e24 )
    & ( e21 != e22 )
    & ( e21 != e23 )
    & ( e21 != e24 )
    & ( e22 != e23 )
    & ( e22 != e24 )
    & ( e23 != e24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

thf(170,plain,
    ( ( e20 != e21 )
    & ( e20 != e22 )
    & ( e20 != e23 )
    & ( e20 != e24 )
    & ( e21 != e22 )
    & ( e21 != e23 )
    & ( e21 != e24 )
    & ( e22 != e23 )
    & ( e22 != e24 )
    & ( e23 != e24 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(179,plain,
    e21 != e22,
    inference(cnf,[status(esa)],[170]) ).

thf(182,plain,
    e22 != e21,
    inference(lifteq,[status(thm)],[179]) ).

thf(1570,plain,
    ( ( j @ e22 )
   != ( j @ e21 ) ),
    inference(simplifyReflect,[status(thm)],[405,182]) ).

thf(49721,plain,
    ( ( ( j @ e21 )
     != e10 )
    | ( ( j @ e22 )
     != ( j @ e22 ) ) ),
    inference(paramod_ordered,[status(thm)],[5218,1570]) ).

thf(49722,plain,
    ( ( j @ e21 )
   != e10 ),
    inference(pattern_uni,[status(thm)],[49721:[]]) ).

thf(50247,plain,
    ( ( j @ ( h @ e10 ) )
   != ( j @ e21 ) ),
    inference(paramod_ordered,[status(thm)],[89,49722]) ).

thf(50305,plain,
    ( ( h @ e10 )
   != e21 ),
    inference(simp,[status(thm)],[50247]) ).

thf(50768,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( h @ e10 )
      = e22 )
    | ( ( h @ e10 )
      = e23 )
    | ( ( j @ e24 )
      = e10 ) ),
    inference(simplifyReflect,[status(thm)],[10402,50305]) ).

thf(21,plain,
    ( ( j @ ( op2 @ e22 @ e22 ) )
    = ( op1 @ ( j @ e22 ) @ ( j @ e22 ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(102,plain,
    ( ( j @ ( op2 @ e22 @ e22 ) )
    = ( op1 @ ( j @ e22 ) @ ( j @ e22 ) ) ),
    inference(lifteq,[status(thm)],[21]) ).

thf(299,plain,
    ( ( op2 @ e22 @ e22 )
    = e23 ),
    inference(cnf,[status(esa)],[293]) ).

thf(337,plain,
    ( ( op2 @ e22 @ e22 )
    = e23 ),
    inference(lifteq,[status(thm)],[299]) ).

thf(6872,plain,
    ( ( op1 @ ( j @ e22 ) @ ( j @ e22 ) )
    = ( j @ e23 ) ),
    inference(rewrite,[status(thm)],[102,337]) ).

thf(6936,plain,
    ( ( ( j @ e23 )
      = e10 )
    | ( ( op1 @ ( j @ e22 ) @ ( j @ e22 ) )
     != ( op1 @ e10 @ e10 ) ) ),
    inference(paramod_ordered,[status(thm)],[287,6872]) ).

thf(6972,plain,
    ( ( ( j @ e23 )
      = e10 )
    | ( ( j @ e22 )
     != e10 )
    | ( ( j @ e22 )
     != e10 ) ),
    inference(simp,[status(thm)],[6936]) ).

thf(7033,plain,
    ( ( ( j @ e23 )
      = e10 )
    | ( ( j @ e22 )
     != e10 ) ),
    inference(simp,[status(thm)],[6972]) ).

thf(40,plain,
    ( ( h @ ( j @ e23 ) )
    = e23 ),
    inference(cnf,[status(esa)],[8]) ).

thf(135,plain,
    ( ( h @ ( j @ e23 ) )
    = e23 ),
    inference(lifteq,[status(thm)],[40]) ).

thf(440,plain,
    ( ( e23 = e22 )
    | ( ( h @ ( j @ e23 ) )
     != ( h @ ( j @ e22 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[135,114]) ).

thf(442,plain,
    ( ( e23 = e22 )
    | ( ( j @ e23 )
     != ( j @ e22 ) ) ),
    inference(simp,[status(thm)],[440]) ).

thf(176,plain,
    e22 != e23,
    inference(cnf,[status(esa)],[170]) ).

thf(185,plain,
    e23 != e22,
    inference(lifteq,[status(thm)],[176]) ).

thf(2060,plain,
    ( ( j @ e23 )
   != ( j @ e22 ) ),
    inference(simplifyReflect,[status(thm)],[442,185]) ).

thf(58249,plain,
    ( ( ( j @ e22 )
     != e10 )
    | ( ( j @ e23 )
     != ( j @ e23 ) ) ),
    inference(paramod_ordered,[status(thm)],[7033,2060]) ).

thf(58250,plain,
    ( ( j @ e22 )
   != e10 ),
    inference(pattern_uni,[status(thm)],[58249:[]]) ).

thf(58638,plain,
    ( ( j @ ( h @ e10 ) )
   != ( j @ e22 ) ),
    inference(paramod_ordered,[status(thm)],[89,58250]) ).

thf(58688,plain,
    ( ( h @ e10 )
   != e22 ),
    inference(simp,[status(thm)],[58638]) ).

thf(58705,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( h @ e10 )
      = e23 )
    | ( ( j @ e24 )
      = e10 ) ),
    inference(simplifyReflect,[status(thm)],[50768,58688]) ).

thf(41,plain,
    ( ( j @ ( op2 @ e24 @ e24 ) )
    = ( op1 @ ( j @ e24 ) @ ( j @ e24 ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(109,plain,
    ( ( j @ ( op2 @ e24 @ e24 ) )
    = ( op1 @ ( j @ e24 ) @ ( j @ e24 ) ) ),
    inference(lifteq,[status(thm)],[41]) ).

thf(7782,plain,
    ( ( op1 @ ( j @ e24 ) @ ( j @ e24 ) )
    = ( j @ e20 ) ),
    inference(rewrite,[status(thm)],[109,335]) ).

thf(7848,plain,
    ( ( ( j @ e20 )
      = e10 )
    | ( ( op1 @ ( j @ e24 ) @ ( j @ e24 ) )
     != ( op1 @ e10 @ e10 ) ) ),
    inference(paramod_ordered,[status(thm)],[287,7782]) ).

thf(7939,plain,
    ( ( ( j @ e20 )
      = e10 )
    | ( ( j @ e24 )
     != e10 )
    | ( ( j @ e24 )
     != e10 ) ),
    inference(simp,[status(thm)],[7848]) ).

thf(7945,plain,
    ( ( ( j @ e20 )
      = e10 )
    | ( ( j @ e24 )
     != e10 ) ),
    inference(simp,[status(thm)],[7939]) ).

thf(72537,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( h @ e10 )
      = e23 )
    | ( ( j @ e20 )
      = e10 )
    | ( ( j @ e24 )
     != ( j @ e24 ) ) ),
    inference(paramod_ordered,[status(thm)],[58705,7945]) ).

thf(72538,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( h @ e10 )
      = e23 )
    | ( ( j @ e20 )
      = e10 ) ),
    inference(pattern_uni,[status(thm)],[72537:[]]) ).

thf(75,plain,
    ( ( h @ ( j @ e20 ) )
    = e20 ),
    inference(cnf,[status(esa)],[8]) ).

thf(139,plain,
    ( ( h @ ( j @ e20 ) )
    = e20 ),
    inference(lifteq,[status(thm)],[75]) ).

thf(73575,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( h @ e10 )
      = e23 )
    | ( ( j @ e20 )
     != ( j @ e20 ) ) ),
    inference(paramod_ordered,[status(thm)],[72538,139]) ).

thf(73576,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( h @ e10 )
      = e23 ) ),
    inference(pattern_uni,[status(thm)],[73575:[]]) ).

thf(48,plain,
    ( ( h @ ( op1 @ e10 @ e10 ) )
    = ( op2 @ ( h @ e10 ) @ ( h @ e10 ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(125,plain,
    ( ( op2 @ ( h @ e10 ) @ ( h @ e10 ) )
    = ( h @ ( op1 @ e10 @ e10 ) ) ),
    inference(lifteq,[status(thm)],[48]) ).

thf(10730,plain,
    ( ( op2 @ ( h @ e10 ) @ ( h @ e10 ) )
    = ( h @ e10 ) ),
    inference(rewrite,[status(thm)],[125,287]) ).

thf(74066,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( op2 @ e23 @ ( h @ e10 ) )
      = ( h @ e10 ) )
    | ( ( h @ e10 )
     != ( h @ e10 ) ) ),
    inference(paramod_ordered,[status(thm)],[73576,10730]) ).

thf(74067,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( op2 @ e23 @ ( h @ e10 ) )
      = ( h @ e10 ) ) ),
    inference(pattern_uni,[status(thm)],[74066:[]]) ).

thf(75353,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( op2 @ e23 @ e23 )
      = ( h @ e10 ) )
    | ( ( h @ e10 )
     != ( h @ e10 ) ) ),
    inference(paramod_ordered,[status(thm)],[73576,74067]) ).

thf(75354,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( op2 @ e23 @ e23 )
      = ( h @ e10 ) ) ),
    inference(pattern_uni,[status(thm)],[75353:[]]) ).

thf(75891,plain,
    ( ( ( h @ e10 )
      = e20 )
    | ( ( h @ e10 )
      = e21 ) ),
    inference(rewrite,[status(thm)],[75354,323]) ).

thf(75892,plain,
    ( ( h @ e10 )
    = e20 ),
    inference(simplifyReflect,[status(thm)],[75891,50305]) ).

thf(75923,plain,
    ( ( h @ e14 )
   != e20 ),
    inference(rewrite,[status(thm)],[7977,75892]) ).

thf(76739,plain,
    ( ( h @ e11 )
   != e24 ),
    inference(simplifyReflect,[status(thm)],[7390,75923]) ).

thf(96304,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e11 )
      = e22 )
    | ( ( h @ e11 )
      = e23 ) ),
    inference(simplifyReflect,[status(thm)],[63318,76739]) ).

thf(7251,plain,
    ( ( ( h @ e14 )
      = e21 )
    | ( ( op2 @ ( h @ e11 ) @ ( h @ e11 ) )
     != ( op2 @ e23 @ e23 ) ) ),
    inference(paramod_ordered,[status(thm)],[7216,323]) ).

thf(7360,plain,
    ( ( ( h @ e14 )
      = e21 )
    | ( ( h @ e11 )
     != e23 )
    | ( ( h @ e11 )
     != e23 ) ),
    inference(simp,[status(thm)],[7251]) ).

thf(7397,plain,
    ( ( ( h @ e14 )
      = e21 )
    | ( ( h @ e11 )
     != e23 ) ),
    inference(simp,[status(thm)],[7360]) ).

thf(96405,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e11 )
      = e22 )
    | ( ( h @ e14 )
      = e21 )
    | ( ( h @ e11 )
     != ( h @ e11 ) ) ),
    inference(paramod_ordered,[status(thm)],[96304,7397]) ).

thf(96406,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e11 )
      = e22 )
    | ( ( h @ e14 )
      = e21 ) ),
    inference(pattern_uni,[status(thm)],[96405:[]]) ).

thf(25,plain,
    ( ( h @ ( op1 @ e14 @ e14 ) )
    = ( op2 @ ( h @ e14 ) @ ( h @ e14 ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(91,plain,
    ( ( op2 @ ( h @ e14 ) @ ( h @ e14 ) )
    = ( h @ ( op1 @ e14 @ e14 ) ) ),
    inference(lifteq,[status(thm)],[25]) ).

thf(247,plain,
    ( ( op1 @ e14 @ e14 )
    = e12 ),
    inference(cnf,[status(esa)],[242]) ).

thf(269,plain,
    ( ( op1 @ e14 @ e14 )
    = e12 ),
    inference(lifteq,[status(thm)],[247]) ).

thf(2096,plain,
    ( ( op2 @ ( h @ e14 ) @ ( h @ e14 ) )
    = ( h @ e12 ) ),
    inference(rewrite,[status(thm)],[91,269]) ).

thf(2863,plain,
    ( ( ( h @ e12 )
      = e22 )
    | ( ( op2 @ ( h @ e14 ) @ ( h @ e14 ) )
     != ( op2 @ e21 @ e21 ) ) ),
    inference(paramod_ordered,[status(thm)],[319,2096]) ).

thf(2867,plain,
    ( ( ( h @ e12 )
      = e22 )
    | ( ( h @ e14 )
     != e21 )
    | ( ( h @ e14 )
     != e21 ) ),
    inference(simp,[status(thm)],[2863]) ).

thf(2869,plain,
    ( ( ( h @ e12 )
      = e22 )
    | ( ( h @ e14 )
     != e21 ) ),
    inference(simp,[status(thm)],[2867]) ).

thf(97255,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e11 )
      = e22 )
    | ( ( h @ e12 )
      = e22 )
    | ( ( h @ e14 )
     != ( h @ e14 ) ) ),
    inference(paramod_ordered,[status(thm)],[96406,2869]) ).

thf(97256,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e11 )
      = e22 )
    | ( ( h @ e12 )
      = e22 ) ),
    inference(pattern_uni,[status(thm)],[97255:[]]) ).

thf(8085,plain,
    ( ( ( h @ e13 )
      = e23 )
    | ( ( op2 @ ( h @ e12 ) @ ( h @ e12 ) )
     != ( op2 @ e22 @ e22 ) ) ),
    inference(paramod_ordered,[status(thm)],[337,7995]) ).

thf(8116,plain,
    ( ( ( h @ e13 )
      = e23 )
    | ( ( h @ e12 )
     != e22 )
    | ( ( h @ e12 )
     != e22 ) ),
    inference(simp,[status(thm)],[8085]) ).

thf(8180,plain,
    ( ( ( h @ e13 )
      = e23 )
    | ( ( h @ e12 )
     != e22 ) ),
    inference(simp,[status(thm)],[8116]) ).

thf(98364,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e11 )
      = e22 )
    | ( ( h @ e13 )
      = e23 )
    | ( ( h @ e12 )
     != ( h @ e12 ) ) ),
    inference(paramod_ordered,[status(thm)],[97256,8180]) ).

thf(98365,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e11 )
      = e22 )
    | ( ( h @ e13 )
      = e23 ) ),
    inference(pattern_uni,[status(thm)],[98364:[]]) ).

thf(44,plain,
    ( ( h @ ( op1 @ e13 @ e13 ) )
    = ( op2 @ ( h @ e13 ) @ ( h @ e13 ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(116,plain,
    ( ( op2 @ ( h @ e13 ) @ ( h @ e13 ) )
    = ( h @ ( op1 @ e13 @ e13 ) ) ),
    inference(lifteq,[status(thm)],[44]) ).

thf(255,plain,
    ( ( op1 @ e13 @ e13 )
    = e11 ),
    inference(cnf,[status(esa)],[242]) ).

thf(282,plain,
    ( ( op1 @ e13 @ e13 )
    = e11 ),
    inference(lifteq,[status(thm)],[255]) ).

thf(8949,plain,
    ( ( op2 @ ( h @ e13 ) @ ( h @ e13 ) )
    = ( h @ e11 ) ),
    inference(rewrite,[status(thm)],[116,282]) ).

thf(8986,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( op2 @ ( h @ e13 ) @ ( h @ e13 ) )
     != ( op2 @ e23 @ e23 ) ) ),
    inference(paramod_ordered,[status(thm)],[8949,323]) ).

thf(9095,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e13 )
     != e23 )
    | ( ( h @ e13 )
     != e23 ) ),
    inference(simp,[status(thm)],[8986]) ).

thf(9132,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e13 )
     != e23 ) ),
    inference(simp,[status(thm)],[9095]) ).

thf(102585,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e11 )
      = e22 )
    | ( ( h @ e13 )
     != ( h @ e13 ) ) ),
    inference(paramod_ordered,[status(thm)],[98365,9132]) ).

thf(102586,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e11 )
      = e22 ) ),
    inference(pattern_uni,[status(thm)],[102585:[]]) ).

thf(7300,plain,
    ( ( ( h @ e14 )
      = e23 )
    | ( ( op2 @ ( h @ e11 ) @ ( h @ e11 ) )
     != ( op2 @ e22 @ e22 ) ) ),
    inference(paramod_ordered,[status(thm)],[337,7216]) ).

thf(7323,plain,
    ( ( ( h @ e14 )
      = e23 )
    | ( ( h @ e11 )
     != e22 )
    | ( ( h @ e11 )
     != e22 ) ),
    inference(simp,[status(thm)],[7300]) ).

thf(7388,plain,
    ( ( ( h @ e14 )
      = e23 )
    | ( ( h @ e11 )
     != e22 ) ),
    inference(simp,[status(thm)],[7323]) ).

thf(103111,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e14 )
      = e23 )
    | ( ( h @ e11 )
     != ( h @ e11 ) ) ),
    inference(paramod_ordered,[status(thm)],[102586,7388]) ).

thf(103112,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e14 )
      = e23 ) ),
    inference(pattern_uni,[status(thm)],[103111:[]]) ).

thf(2959,plain,
    ( ( ( h @ e12 )
      = e21 )
    | ( ( op2 @ ( h @ e14 ) @ ( h @ e14 ) )
     != ( op2 @ e23 @ e23 ) ) ),
    inference(paramod_ordered,[status(thm)],[323,2096]) ).

thf(2971,plain,
    ( ( ( h @ e12 )
      = e21 )
    | ( ( h @ e14 )
     != e23 )
    | ( ( h @ e14 )
     != e23 ) ),
    inference(simp,[status(thm)],[2959]) ).

thf(2982,plain,
    ( ( ( h @ e12 )
      = e21 )
    | ( ( h @ e14 )
     != e23 ) ),
    inference(simp,[status(thm)],[2971]) ).

thf(104032,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e12 )
      = e21 )
    | ( ( h @ e14 )
     != ( h @ e14 ) ) ),
    inference(paramod_ordered,[status(thm)],[103112,2982]) ).

thf(104033,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( h @ e12 )
      = e21 ) ),
    inference(pattern_uni,[status(thm)],[104032:[]]) ).

thf(60,plain,
    ( ( j @ ( h @ e12 ) )
    = e12 ),
    inference(cnf,[status(esa)],[8]) ).

thf(80,plain,
    ( ( j @ ( h @ e12 ) )
    = e12 ),
    inference(lifteq,[status(thm)],[60]) ).

thf(5085,plain,
    ( ( ( j @ e22 )
      = e13 )
    | ( ( op1 @ ( j @ e21 ) @ ( j @ e21 ) )
     != ( op1 @ e12 @ e12 ) ) ),
    inference(paramod_ordered,[status(thm)],[5070,280]) ).

thf(5166,plain,
    ( ( ( j @ e22 )
      = e13 )
    | ( ( j @ e21 )
     != e12 )
    | ( ( j @ e21 )
     != e12 ) ),
    inference(simp,[status(thm)],[5085]) ).

thf(5216,plain,
    ( ( ( j @ e22 )
      = e13 )
    | ( ( j @ e21 )
     != e12 ) ),
    inference(simp,[status(thm)],[5166]) ).

thf(48251,plain,
    ( ( ( j @ e22 )
      = e13 )
    | ( ( j @ ( h @ e12 ) )
     != ( j @ e21 ) ) ),
    inference(paramod_ordered,[status(thm)],[80,5216]) ).

thf(48527,plain,
    ( ( ( j @ e22 )
      = e13 )
    | ( ( h @ e12 )
     != e21 ) ),
    inference(simp,[status(thm)],[48251]) ).

thf(106711,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( j @ e22 )
      = e13 )
    | ( ( h @ e12 )
     != ( h @ e12 ) ) ),
    inference(paramod_ordered,[status(thm)],[104033,48527]) ).

thf(106712,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( j @ e22 )
      = e13 ) ),
    inference(pattern_uni,[status(thm)],[106711:[]]) ).

thf(102967,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( j @ e22 )
      = e11 )
    | ( ( h @ e11 )
     != ( h @ e11 ) ) ),
    inference(paramod_ordered,[status(thm)],[102586,106]) ).

thf(102968,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( ( j @ e22 )
      = e11 ) ),
    inference(pattern_uni,[status(thm)],[102967:[]]) ).

thf(111923,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( e13 = e11 )
    | ( ( j @ e22 )
     != ( j @ e22 ) ) ),
    inference(paramod_ordered,[status(thm)],[106712,102968]) ).

thf(111924,plain,
    ( ( ( h @ e11 )
      = e21 )
    | ( e13 = e11 ) ),
    inference(pattern_uni,[status(thm)],[111923:[]]) ).

thf(112377,plain,
    ( ( h @ e11 )
    = e21 ),
    inference(simplifyReflect,[status(thm)],[111924,161]) ).

thf(112408,plain,
    ( ( h @ e13 )
   != e21 ),
    inference(rewrite,[status(thm)],[933,112377]) ).

thf(113300,plain,
    ( ( h @ e12 )
   != e23 ),
    inference(simplifyReflect,[status(thm)],[8171,112408]) ).

thf(4103,plain,
    ( ( ( h @ e12 )
      = e23 )
    | ( ( op2 @ ( h @ e14 ) @ ( h @ e14 ) )
     != ( op2 @ e22 @ e22 ) ) ),
    inference(paramod_ordered,[status(thm)],[337,2096]) ).

thf(4126,plain,
    ( ( ( h @ e12 )
      = e23 )
    | ( ( h @ e14 )
     != e22 )
    | ( ( h @ e14 )
     != e22 ) ),
    inference(simp,[status(thm)],[4103]) ).

thf(4158,plain,
    ( ( ( h @ e12 )
      = e23 )
    | ( ( h @ e14 )
     != e22 ) ),
    inference(simp,[status(thm)],[4126]) ).

thf(36656,plain,
    ( ( ( h @ e12 )
      = e23 )
    | ( ( h @ ( j @ e22 ) )
     != ( h @ e14 ) ) ),
    inference(paramod_ordered,[status(thm)],[114,4158]) ).

thf(36662,plain,
    ( ( ( h @ e12 )
      = e23 )
    | ( ( j @ e22 )
     != e14 ) ),
    inference(simp,[status(thm)],[36656]) ).

thf(5108,plain,
    ( ( ( j @ e22 )
      = e14 )
    | ( ( op1 @ ( j @ e21 ) @ ( j @ e21 ) )
     != ( op1 @ e11 @ e11 ) ) ),
    inference(paramod_ordered,[status(thm)],[281,5070]) ).

thf(5154,plain,
    ( ( ( j @ e22 )
      = e14 )
    | ( ( j @ e21 )
     != e11 )
    | ( ( j @ e21 )
     != e11 ) ),
    inference(simp,[status(thm)],[5108]) ).

thf(5214,plain,
    ( ( ( j @ e22 )
      = e14 )
    | ( ( j @ e21 )
     != e11 ) ),
    inference(simp,[status(thm)],[5154]) ).

thf(46974,plain,
    ( ( ( j @ e22 )
      = e14 )
    | ( ( j @ ( h @ e11 ) )
     != ( j @ e21 ) ) ),
    inference(paramod_ordered,[status(thm)],[106,5214]) ).

thf(47503,plain,
    ( ( ( j @ e22 )
      = e14 )
    | ( ( h @ e11 )
     != e21 ) ),
    inference(simp,[status(thm)],[46974]) ).

thf(112397,plain,
    ( ( ( j @ e22 )
      = e14 )
    | ( e21 != e21 ) ),
    inference(rewrite,[status(thm)],[47503,112377]) ).

thf(112398,plain,
    ( ( j @ e22 )
    = e14 ),
    inference(simp,[status(thm)],[112397]) ).

thf(113181,plain,
    ( ( ( h @ e12 )
      = e23 )
    | ( e14 != e14 ) ),
    inference(rewrite,[status(thm)],[36662,112398]) ).

thf(113182,plain,
    ( ( h @ e12 )
    = e23 ),
    inference(simp,[status(thm)],[113181]) ).

thf(113593,plain,
    e23 != e23,
    inference(rewrite,[status(thm)],[113300,113182]) ).

thf(113594,plain,
    $false,
    inference(simp,[status(thm)],[113593]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ALG085+1 : TPTP v8.2.0. Released v2.7.0.
% 0.14/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n008.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Sat May 18 23:49:09 EDT 2024
% 0.16/0.36  % CPUTime  : 
% 0.97/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.25/0.98  % [INFO] 	 Parsing done (125ms). 
% 1.25/0.99  % [INFO] 	 Running in sequential loop mode. 
% 1.74/1.19  % [INFO] 	 nitpick registered as external prover. 
% 1.74/1.19  % [INFO] 	 Scanning for conjecture ... 
% 2.24/1.34  % [INFO] 	 Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ... 
% 2.24/1.39  % [INFO] 	 Axiom selection finished. Selected 5 axioms (removed 0 axioms). 
% 2.40/1.42  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.40/1.42  % [INFO] 	 Type checking passed. 
% 2.40/1.43  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 170.57/25.25  % [INFO] 	 Killing All external provers ... 
% 170.57/25.25  % Time passed: 24732ms (effective reasoning time: 24262ms)
% 170.57/25.26  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 170.57/25.26  % Axioms used in derivation (4): ax4, ax5, ax1, ax2
% 170.57/25.26  % No. of inferences in proof: 208
% 170.57/25.26  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 24732 ms resp. 24262 ms w/o parsing
% 170.57/25.31  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 170.57/25.31  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------