TSTP Solution File: ALG067+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : ALG067+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 15:42:28 EDT 2022

% Result   : Theorem 1.35s 0.53s
% Output   : Refutation 1.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   29
% Syntax   : Number of formulae    :  197 (   1 unt;   3 typ;   0 def)
%            Number of atoms       : 1019 ( 663 equ)
%            Maximal formula atoms :  125 (   5 avg)
%            Number of connectives : 1286 ( 461   ~; 476   |; 348   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   53 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   30 (  28 usr;  25 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :    2 (   2   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_26,type,
    sQ25_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_27,type,
    sQ26_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_28,type,
    sQ27_eqProxy: ( $real * $real ) > $o ).

fof(f976,plain,
    $false,
    inference(sat_instgen_refutation,[],[f711,f762,f865,f664,f879,f943,f846,f882,f852,f784,f683,f841,f693,f712,f804,f808,f717,f674,f761,f724,f729,f731,f893,f942,f853,f732,f713,f847,f756,f947,f798,f896,f817,f935,f686,f777,f785,f915,f715,f750,f916,f707,f741,f776,f930,f928,f679,f867,f838,f871,f688,f791,f922,f779,f828,f727,f807,f796,f780,f955,f789,f745,f716,f682,f735,f698,f902,f945,f913,f700]) ).

fof(f700,plain,
    ( ~ sQ24_eqProxy(e0,op(e1,e1))
    | sQ24_eqProxy(e1,op(e1,e0)) ),
    inference(equality_proxy_replacement,[],[f193,f657,f657]) ).

fof(f657,plain,
    ! [X0,X1] :
      ( sQ24_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ24_eqProxy])]) ).

fof(f193,plain,
    ( e1 = op(e1,e0)
    | e0 != op(e1,e1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ( ( e4 = op(e4,e1)
      | e1 != op(e4,e4) )
    & ( e3 = op(e3,e0)
      | e0 != op(e3,e3) )
    & ( e3 != op(e2,e2)
      | e2 = op(e2,e3) )
    & ( e3 != op(e4,e4)
      | e4 = op(e4,e3) )
    & ( e1 = op(e1,e4)
      | e4 != op(e1,e1) )
    & ( e3 != op(e1,e1)
      | e1 = op(e1,e3) )
    & ( e4 != op(e4,e4)
      | e4 = op(e4,e4) )
    & ( op(e0,e0) != e2
      | e0 = op(e0,e2) )
    & ( op(e0,e0) != e3
      | e0 = op(e0,e3) )
    & ( e0 != op(e2,e2)
      | e2 = op(e2,e0) )
    & ( e2 = op(e2,e1)
      | e1 != op(e2,e2) )
    & ( e2 != op(e2,e2)
      | e2 = op(e2,e2) )
    & ( e1 = op(e1,e2)
      | e2 != op(e1,e1) )
    & ( e1 != op(e1,e1)
      | e1 = op(e1,e1) )
    & ( e0 != op(e1,e1)
      | e1 = op(e1,e0) )
    & ( e4 != op(e3,e3)
      | e3 = op(e3,e4) )
    & ( e0 = op(e0,e0)
      | e0 != op(e0,e0) )
    & ( e3 = op(e3,e3)
      | e3 != op(e3,e3) )
    & ( e4 = op(e4,e2)
      | e2 != op(e4,e4) )
    & ( e4 != op(e2,e2)
      | e2 = op(e2,e4) )
    & ( e1 != op(e3,e3)
      | e3 = op(e3,e1) )
    & ( e4 = op(e4,e0)
      | e0 != op(e4,e4) )
    & ( ( e4 = op(e3,e3)
        & e3 = op(e4,e4)
        & e3 != op(e3,e4) )
      | sP23
      | sP22
      | sP21
      | sP20
      | sP19
      | sP18
      | sP17
      | sP16
      | sP15
      | sP14
      | sP13
      | sP12
      | sP11
      | sP10
      | sP9
      | sP8
      | sP7
      | sP6
      | sP5
      | sP4
      | sP3
      | sP2
      | sP1
      | sP0 )
    & ( op(e0,e0) != e1
      | e0 = op(e0,e1) )
    & ( e0 = op(e0,e4)
      | op(e0,e0) != e4 )
    & ( e2 != op(e3,e3)
      | e3 = op(e3,e2) ) ),
    inference(definition_folding,[],[f9,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16,f15,f14,f13,f12,f11,f10]) ).

fof(f10,plain,
    ( ( e0 = op(e2,e2)
      & op(e0,e0) = e2
      & e0 != op(e0,e2) )
    | ~ sP0 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f11,plain,
    ( ( e3 != op(e3,e0)
      & e0 = op(e3,e3)
      & op(e0,e0) = e3 )
    | ~ sP1 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f12,plain,
    ( ( e0 = op(e1,e1)
      & op(e0,e0) = e1
      & e1 != op(e1,e0) )
    | ~ sP2 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f13,plain,
    ( ( e1 = op(e4,e4)
      & e1 != op(e1,e4)
      & e4 = op(e1,e1) )
    | ~ sP3 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f14,plain,
    ( ( e2 = op(e3,e3)
      & e3 = op(e2,e2)
      & e2 != op(e2,e3) )
    | ~ sP4 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f15,plain,
    ( ( e2 = op(e3,e3)
      & e3 = op(e2,e2)
      & e3 != op(e3,e2) )
    | ~ sP5 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

fof(f16,plain,
    ( ( e4 != op(e4,e4)
      & e4 = op(e4,e4)
      & e4 = op(e4,e4) )
    | ~ sP6 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f17,plain,
    ( ( op(e0,e0) = e4
      & e0 != op(e0,e4)
      & e0 = op(e4,e4) )
    | ~ sP7 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f18,plain,
    ( ( e2 = op(e4,e4)
      & e4 = op(e2,e2)
      & e2 != op(e2,e4) )
    | ~ sP8 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f19,plain,
    ( ( e0 = op(e2,e2)
      & op(e0,e0) = e2
      & e2 != op(e2,e0) )
    | ~ sP9 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

fof(f20,plain,
    ( ( e1 = op(e2,e2)
      & e1 != op(e1,e2)
      & e2 = op(e1,e1) )
    | ~ sP10 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).

fof(f21,plain,
    ( ( e0 != op(e0,e3)
      & op(e0,e0) = e3
      & e0 = op(e3,e3) )
    | ~ sP11 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).

fof(f22,plain,
    ( ( op(e0,e0) = e4
      & e0 = op(e4,e4)
      & e4 != op(e4,e0) )
    | ~ sP12 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).

fof(f23,plain,
    ( ( e0 != op(e0,e0)
      & e0 = op(e0,e0)
      & e0 = op(e0,e0) )
    | ~ sP13 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).

fof(f24,plain,
    ( ( e1 != op(e1,e1)
      & e1 = op(e1,e1)
      & e1 = op(e1,e1) )
    | ~ sP14 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).

fof(f25,plain,
    ( ( e4 = op(e1,e1)
      & e4 != op(e4,e1)
      & e1 = op(e4,e4) )
    | ~ sP15 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).

fof(f26,plain,
    ( ( e3 = op(e4,e4)
      & e4 != op(e4,e3)
      & e4 = op(e3,e3) )
    | ~ sP16 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).

fof(f27,plain,
    ( ( e2 = op(e4,e4)
      & e4 != op(e4,e2)
      & e4 = op(e2,e2) )
    | ~ sP17 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).

fof(f28,plain,
    ( ( e2 = op(e2,e2)
      & e2 != op(e2,e2)
      & e2 = op(e2,e2) )
    | ~ sP18 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).

fof(f29,plain,
    ( ( e2 = op(e1,e1)
      & e2 != op(e2,e1)
      & e1 = op(e2,e2) )
    | ~ sP19 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).

fof(f30,plain,
    ( ( e0 != op(e0,e1)
      & e0 = op(e1,e1)
      & op(e0,e0) = e1 )
    | ~ sP20 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).

fof(f31,plain,
    ( ( e3 != op(e3,e1)
      & e1 = op(e3,e3)
      & e3 = op(e1,e1) )
    | ~ sP21 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).

fof(f32,plain,
    ( ( e3 != op(e3,e3)
      & e3 = op(e3,e3)
      & e3 = op(e3,e3) )
    | ~ sP22 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).

fof(f33,plain,
    ( ( e1 = op(e3,e3)
      & e1 != op(e1,e3)
      & e3 = op(e1,e1) )
    | ~ sP23 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).

fof(f9,plain,
    ( ( e4 = op(e4,e1)
      | e1 != op(e4,e4) )
    & ( e3 = op(e3,e0)
      | e0 != op(e3,e3) )
    & ( e3 != op(e2,e2)
      | e2 = op(e2,e3) )
    & ( e3 != op(e4,e4)
      | e4 = op(e4,e3) )
    & ( e1 = op(e1,e4)
      | e4 != op(e1,e1) )
    & ( e3 != op(e1,e1)
      | e1 = op(e1,e3) )
    & ( e4 != op(e4,e4)
      | e4 = op(e4,e4) )
    & ( op(e0,e0) != e2
      | e0 = op(e0,e2) )
    & ( op(e0,e0) != e3
      | e0 = op(e0,e3) )
    & ( e0 != op(e2,e2)
      | e2 = op(e2,e0) )
    & ( e2 = op(e2,e1)
      | e1 != op(e2,e2) )
    & ( e2 != op(e2,e2)
      | e2 = op(e2,e2) )
    & ( e1 = op(e1,e2)
      | e2 != op(e1,e1) )
    & ( e1 != op(e1,e1)
      | e1 = op(e1,e1) )
    & ( e0 != op(e1,e1)
      | e1 = op(e1,e0) )
    & ( e4 != op(e3,e3)
      | e3 = op(e3,e4) )
    & ( e0 = op(e0,e0)
      | e0 != op(e0,e0) )
    & ( e3 = op(e3,e3)
      | e3 != op(e3,e3) )
    & ( e4 = op(e4,e2)
      | e2 != op(e4,e4) )
    & ( e4 != op(e2,e2)
      | e2 = op(e2,e4) )
    & ( e1 != op(e3,e3)
      | e3 = op(e3,e1) )
    & ( e4 = op(e4,e0)
      | e0 != op(e4,e4) )
    & ( ( e4 = op(e3,e3)
        & e3 = op(e4,e4)
        & e3 != op(e3,e4) )
      | ( e1 = op(e3,e3)
        & e1 != op(e1,e3)
        & e3 = op(e1,e1) )
      | ( e3 != op(e3,e3)
        & e3 = op(e3,e3)
        & e3 = op(e3,e3) )
      | ( e3 != op(e3,e1)
        & e1 = op(e3,e3)
        & e3 = op(e1,e1) )
      | ( e0 != op(e0,e1)
        & e0 = op(e1,e1)
        & op(e0,e0) = e1 )
      | ( e2 = op(e1,e1)
        & e2 != op(e2,e1)
        & e1 = op(e2,e2) )
      | ( e2 = op(e2,e2)
        & e2 != op(e2,e2)
        & e2 = op(e2,e2) )
      | ( e2 = op(e4,e4)
        & e4 != op(e4,e2)
        & e4 = op(e2,e2) )
      | ( e3 = op(e4,e4)
        & e4 != op(e4,e3)
        & e4 = op(e3,e3) )
      | ( e4 = op(e1,e1)
        & e4 != op(e4,e1)
        & e1 = op(e4,e4) )
      | ( e1 != op(e1,e1)
        & e1 = op(e1,e1)
        & e1 = op(e1,e1) )
      | ( e0 != op(e0,e0)
        & e0 = op(e0,e0)
        & e0 = op(e0,e0) )
      | ( op(e0,e0) = e4
        & e0 = op(e4,e4)
        & e4 != op(e4,e0) )
      | ( e0 != op(e0,e3)
        & op(e0,e0) = e3
        & e0 = op(e3,e3) )
      | ( e1 = op(e2,e2)
        & e1 != op(e1,e2)
        & e2 = op(e1,e1) )
      | ( e0 = op(e2,e2)
        & op(e0,e0) = e2
        & e2 != op(e2,e0) )
      | ( e2 = op(e4,e4)
        & e4 = op(e2,e2)
        & e2 != op(e2,e4) )
      | ( op(e0,e0) = e4
        & e0 != op(e0,e4)
        & e0 = op(e4,e4) )
      | ( e4 != op(e4,e4)
        & e4 = op(e4,e4)
        & e4 = op(e4,e4) )
      | ( e2 = op(e3,e3)
        & e3 = op(e2,e2)
        & e3 != op(e3,e2) )
      | ( e2 = op(e3,e3)
        & e3 = op(e2,e2)
        & e2 != op(e2,e3) )
      | ( e1 = op(e4,e4)
        & e1 != op(e1,e4)
        & e4 = op(e1,e1) )
      | ( e0 = op(e1,e1)
        & op(e0,e0) = e1
        & e1 != op(e1,e0) )
      | ( e3 != op(e3,e0)
        & e0 = op(e3,e3)
        & op(e0,e0) = e3 )
      | ( e0 = op(e2,e2)
        & op(e0,e0) = e2
        & e0 != op(e0,e2) ) )
    & ( op(e0,e0) != e1
      | e0 = op(e0,e1) )
    & ( e0 = op(e0,e4)
      | op(e0,e0) != e4 )
    & ( e2 != op(e3,e3)
      | e3 = op(e3,e2) ) ),
    inference(flattening,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ~ ( ( e4 = op(e4,e1)
          | e1 != op(e4,e4) )
        & ( e3 = op(e3,e0)
          | e0 != op(e3,e3) )
        & ( e3 != op(e2,e2)
          | e2 = op(e2,e3) )
        & ( e3 != op(e4,e4)
          | e4 = op(e4,e3) )
        & ( e1 = op(e1,e4)
          | e4 != op(e1,e1) )
        & ( e3 != op(e1,e1)
          | e1 = op(e1,e3) )
        & ( e4 != op(e4,e4)
          | e4 = op(e4,e4) )
        & ( op(e0,e0) != e2
          | e0 = op(e0,e2) )
        & ( op(e0,e0) != e3
          | e0 = op(e0,e3) )
        & ( e0 != op(e2,e2)
          | e2 = op(e2,e0) )
        & ( e2 = op(e2,e1)
          | e1 != op(e2,e2) )
        & ( e2 != op(e2,e2)
          | e2 = op(e2,e2) )
        & ( e1 = op(e1,e2)
          | e2 != op(e1,e1) )
        & ( e1 != op(e1,e1)
          | e1 = op(e1,e1) )
        & ( e0 != op(e1,e1)
          | e1 = op(e1,e0) )
        & ( e4 != op(e3,e3)
          | e3 = op(e3,e4) )
        & ( e0 = op(e0,e0)
          | e0 != op(e0,e0) )
        & ( e3 = op(e3,e3)
          | e3 != op(e3,e3) )
        & ( e4 = op(e4,e2)
          | e2 != op(e4,e4) )
        & ( e4 != op(e2,e2)
          | e2 = op(e2,e4) )
        & ( e1 != op(e3,e3)
          | e3 = op(e3,e1) )
        & ( e4 = op(e4,e0)
          | e0 != op(e4,e4) )
        & ( ( e4 = op(e3,e3)
            & e3 = op(e4,e4)
            & e3 != op(e3,e4) )
          | ( e1 = op(e3,e3)
            & e1 != op(e1,e3)
            & e3 = op(e1,e1) )
          | ( e3 != op(e3,e3)
            & e3 = op(e3,e3)
            & e3 = op(e3,e3) )
          | ( e3 != op(e3,e1)
            & e1 = op(e3,e3)
            & e3 = op(e1,e1) )
          | ( e0 != op(e0,e1)
            & e0 = op(e1,e1)
            & op(e0,e0) = e1 )
          | ( e2 = op(e1,e1)
            & e2 != op(e2,e1)
            & e1 = op(e2,e2) )
          | ( e2 = op(e2,e2)
            & e2 != op(e2,e2)
            & e2 = op(e2,e2) )
          | ( e2 = op(e4,e4)
            & e4 != op(e4,e2)
            & e4 = op(e2,e2) )
          | ( e3 = op(e4,e4)
            & e4 != op(e4,e3)
            & e4 = op(e3,e3) )
          | ( e4 = op(e1,e1)
            & e4 != op(e4,e1)
            & e1 = op(e4,e4) )
          | ( e1 != op(e1,e1)
            & e1 = op(e1,e1)
            & e1 = op(e1,e1) )
          | ( e0 != op(e0,e0)
            & e0 = op(e0,e0)
            & e0 = op(e0,e0) )
          | ( op(e0,e0) = e4
            & e0 = op(e4,e4)
            & e4 != op(e4,e0) )
          | ( e0 != op(e0,e3)
            & op(e0,e0) = e3
            & e0 = op(e3,e3) )
          | ( e1 = op(e2,e2)
            & e1 != op(e1,e2)
            & e2 = op(e1,e1) )
          | ( e0 = op(e2,e2)
            & op(e0,e0) = e2
            & e2 != op(e2,e0) )
          | ( e2 = op(e4,e4)
            & e4 = op(e2,e2)
            & e2 != op(e2,e4) )
          | ( op(e0,e0) = e4
            & e0 != op(e0,e4)
            & e0 = op(e4,e4) )
          | ( e4 != op(e4,e4)
            & e4 = op(e4,e4)
            & e4 = op(e4,e4) )
          | ( e2 = op(e3,e3)
            & e3 = op(e2,e2)
            & e3 != op(e3,e2) )
          | ( e2 = op(e3,e3)
            & e3 = op(e2,e2)
            & e2 != op(e2,e3) )
          | ( e1 = op(e4,e4)
            & e1 != op(e1,e4)
            & e4 = op(e1,e1) )
          | ( e0 = op(e1,e1)
            & op(e0,e0) = e1
            & e1 != op(e1,e0) )
          | ( e3 != op(e3,e0)
            & e0 = op(e3,e3)
            & op(e0,e0) = e3 )
          | ( e0 = op(e2,e2)
            & op(e0,e0) = e2
            & e0 != op(e0,e2) ) )
        & ( op(e0,e0) != e1
          | e0 = op(e0,e1) )
        & ( e0 = op(e0,e4)
          | op(e0,e0) != e4 )
        & ( e2 != op(e3,e3)
          | e3 = op(e3,e2) ) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ~ ( ( e4 = op(e4,e1)
        | e1 != op(e4,e4) )
      & ( e3 = op(e3,e0)
        | e0 != op(e3,e3) )
      & ( e3 != op(e2,e2)
        | e2 = op(e2,e3) )
      & ( e3 != op(e4,e4)
        | e4 = op(e4,e3) )
      & ( e1 = op(e1,e4)
        | e4 != op(e1,e1) )
      & ( e3 != op(e1,e1)
        | e1 = op(e1,e3) )
      & ( e4 != op(e4,e4)
        | e4 = op(e4,e4) )
      & ( op(e0,e0) != e2
        | e0 = op(e0,e2) )
      & ( op(e0,e0) != e3
        | e0 = op(e0,e3) )
      & ( e0 != op(e2,e2)
        | e2 = op(e2,e0) )
      & ( e2 = op(e2,e1)
        | e1 != op(e2,e2) )
      & ( e2 != op(e2,e2)
        | e2 = op(e2,e2) )
      & ( e1 = op(e1,e2)
        | e2 != op(e1,e1) )
      & ( e1 != op(e1,e1)
        | e1 = op(e1,e1) )
      & ( e0 != op(e1,e1)
        | e1 = op(e1,e0) )
      & ( e4 != op(e3,e3)
        | e3 = op(e3,e4) )
      & ( e0 = op(e0,e0)
        | e0 != op(e0,e0) )
      & ( e3 = op(e3,e3)
        | e3 != op(e3,e3) )
      & ( e4 = op(e4,e2)
        | e2 != op(e4,e4) )
      & ( e4 != op(e2,e2)
        | e2 = op(e2,e4) )
      & ( e1 != op(e3,e3)
        | e3 = op(e3,e1) )
      & ( e4 = op(e4,e0)
        | e0 != op(e4,e4) )
      & ( ( e4 = op(e3,e3)
          & e3 = op(e4,e4)
          & e3 != op(e3,e4) )
        | ( e1 = op(e3,e3)
          & e1 != op(e1,e3)
          & e3 = op(e1,e1) )
        | ( e3 != op(e3,e3)
          & e3 = op(e3,e3)
          & e3 = op(e3,e3) )
        | ( e3 != op(e3,e1)
          & e1 = op(e3,e3)
          & e3 = op(e1,e1) )
        | ( e0 != op(e0,e1)
          & e0 = op(e1,e1)
          & op(e0,e0) = e1 )
        | ( e2 = op(e1,e1)
          & e2 != op(e2,e1)
          & e1 = op(e2,e2) )
        | ( e2 = op(e2,e2)
          & e2 != op(e2,e2)
          & e2 = op(e2,e2) )
        | ( e2 = op(e4,e4)
          & e4 != op(e4,e2)
          & e4 = op(e2,e2) )
        | ( e3 = op(e4,e4)
          & e4 != op(e4,e3)
          & e4 = op(e3,e3) )
        | ( e4 = op(e1,e1)
          & e4 != op(e4,e1)
          & e1 = op(e4,e4) )
        | ( e1 != op(e1,e1)
          & e1 = op(e1,e1)
          & e1 = op(e1,e1) )
        | ( e0 != op(e0,e0)
          & e0 = op(e0,e0)
          & e0 = op(e0,e0) )
        | ( op(e0,e0) = e4
          & e0 = op(e4,e4)
          & e4 != op(e4,e0) )
        | ( e0 != op(e0,e3)
          & op(e0,e0) = e3
          & e0 = op(e3,e3) )
        | ( e1 = op(e2,e2)
          & e1 != op(e1,e2)
          & e2 = op(e1,e1) )
        | ( e0 = op(e2,e2)
          & op(e0,e0) = e2
          & e2 != op(e2,e0) )
        | ( e2 = op(e4,e4)
          & e4 = op(e2,e2)
          & e2 != op(e2,e4) )
        | ( op(e0,e0) = e4
          & e0 != op(e0,e4)
          & e0 = op(e4,e4) )
        | ( e4 != op(e4,e4)
          & e4 = op(e4,e4)
          & e4 = op(e4,e4) )
        | ( e2 = op(e3,e3)
          & e3 = op(e2,e2)
          & e3 != op(e3,e2) )
        | ( e2 = op(e3,e3)
          & e3 = op(e2,e2)
          & e2 != op(e2,e3) )
        | ( e1 = op(e4,e4)
          & e1 != op(e1,e4)
          & e4 = op(e1,e1) )
        | ( e0 = op(e1,e1)
          & op(e0,e0) = e1
          & e1 != op(e1,e0) )
        | ( e3 != op(e3,e0)
          & e0 = op(e3,e3)
          & op(e0,e0) = e3 )
        | ( e0 = op(e2,e2)
          & op(e0,e0) = e2
          & e0 != op(e0,e2) ) )
      & ( op(e0,e0) != e1
        | e0 = op(e0,e1) )
      & ( e0 = op(e0,e4)
        | op(e0,e0) != e4 )
      & ( e2 != op(e3,e3)
        | e3 = op(e3,e2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f913,plain,
    ( sQ24_eqProxy(e4,op(e4,e1))
    | ~ sQ24_eqProxy(e1,op(e4,e4)) ),
    inference(equality_proxy_replacement,[],[f207,f657,f657]) ).

fof(f207,plain,
    ( e1 != op(e4,e4)
    | e4 = op(e4,e1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f945,plain,
    ( ~ sQ24_eqProxy(e4,op(e4,e3))
    | ~ sP16 ),
    inference(equality_proxy_replacement,[],[f130,f657]) ).

fof(f130,plain,
    ( ~ sP16
    | e4 != op(e4,e3) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ( ( e3 = op(e4,e4)
      & e4 != op(e4,e3)
      & e4 = op(e3,e3) )
    | ~ sP16 ),
    inference(nnf_transformation,[],[f26]) ).

fof(f902,plain,
    ( ~ sQ24_eqProxy(e1,op(e1,e2))
    | ~ sP10 ),
    inference(equality_proxy_replacement,[],[f148,f657]) ).

fof(f148,plain,
    ( ~ sP10
    | e1 != op(e1,e2) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ( ( e1 = op(e2,e2)
      & e1 != op(e1,e2)
      & e2 = op(e1,e1) )
    | ~ sP10 ),
    inference(nnf_transformation,[],[f20]) ).

fof(f698,plain,
    ( ~ sQ24_eqProxy(e0,op(e3,e3))
    | sQ24_eqProxy(e3,op(e3,e0)) ),
    inference(equality_proxy_replacement,[],[f206,f657,f657]) ).

fof(f206,plain,
    ( e3 = op(e3,e0)
    | e0 != op(e3,e3) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f735,plain,
    ( ~ sQ24_eqProxy(e0,op(e0,e0))
    | ~ sP13 ),
    inference(equality_proxy_replacement,[],[f140,f657]) ).

fof(f140,plain,
    ( ~ sP13
    | e0 != op(e0,e0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ( ( e0 != op(e0,e0)
      & e0 = op(e0,e0)
      & e0 = op(e0,e0) )
    | ~ sP13 ),
    inference(nnf_transformation,[],[f23]) ).

fof(f682,plain,
    ( sQ24_eqProxy(op(e0,e0),e4)
    | ~ sP7 ),
    inference(equality_proxy_replacement,[],[f158,f657]) ).

fof(f158,plain,
    ( op(e0,e0) = e4
    | ~ sP7 ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ( ( op(e0,e0) = e4
      & e0 != op(e0,e4)
      & e0 = op(e4,e4) )
    | ~ sP7 ),
    inference(nnf_transformation,[],[f17]) ).

fof(f716,plain,
    ( ~ sQ24_eqProxy(e1,op(e2,e2))
    | sQ24_eqProxy(e2,op(e2,e1)) ),
    inference(equality_proxy_replacement,[],[f197,f657,f657]) ).

fof(f197,plain,
    ( e2 = op(e2,e1)
    | e1 != op(e2,e2) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f745,plain,
    ( ~ sQ24_eqProxy(e4,op(e2,e2))
    | sQ24_eqProxy(e2,op(e2,e4)) ),
    inference(equality_proxy_replacement,[],[f188,f657,f657]) ).

fof(f188,plain,
    ( e4 != op(e2,e2)
    | e2 = op(e2,e4) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f789,plain,
    ( ~ sP6
    | ~ sQ24_eqProxy(e4,op(e4,e4)) ),
    inference(equality_proxy_replacement,[],[f161,f657]) ).

fof(f161,plain,
    ( ~ sP6
    | e4 != op(e4,e4) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ( ( e4 != op(e4,e4)
      & e4 = op(e4,e4)
      & e4 = op(e4,e4) )
    | ~ sP6 ),
    inference(nnf_transformation,[],[f16]) ).

fof(f955,plain,
    ( sQ24_eqProxy(e4,op(e1,e1))
    | ~ sP3 ),
    inference(equality_proxy_replacement,[],[f168,f657]) ).

fof(f168,plain,
    ( ~ sP3
    | e4 = op(e1,e1) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ( ( e1 = op(e4,e4)
      & e1 != op(e1,e4)
      & e4 = op(e1,e1) )
    | ~ sP3 ),
    inference(nnf_transformation,[],[f13]) ).

fof(f780,plain,
    ( ~ sP21
    | sQ24_eqProxy(e1,op(e3,e3)) ),
    inference(equality_proxy_replacement,[],[f115,f657]) ).

fof(f115,plain,
    ( ~ sP21
    | e1 = op(e3,e3) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ( ( e3 != op(e3,e1)
      & e1 = op(e3,e3)
      & e3 = op(e1,e1) )
    | ~ sP21 ),
    inference(nnf_transformation,[],[f31]) ).

fof(f796,plain,
    ( ~ sQ24_eqProxy(e4,op(e4,e0))
    | ~ sP12 ),
    inference(equality_proxy_replacement,[],[f141,f657]) ).

fof(f141,plain,
    ( e4 != op(e4,e0)
    | ~ sP12 ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ( ( op(e0,e0) = e4
      & e0 = op(e4,e4)
      & e4 != op(e4,e0) )
    | ~ sP12 ),
    inference(nnf_transformation,[],[f22]) ).

fof(f807,plain,
    ( ~ sP9
    | sQ24_eqProxy(e0,op(e2,e2)) ),
    inference(equality_proxy_replacement,[],[f152,f657]) ).

fof(f152,plain,
    ( e0 = op(e2,e2)
    | ~ sP9 ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ( ( e0 = op(e2,e2)
      & op(e0,e0) = e2
      & e2 != op(e2,e0) )
    | ~ sP9 ),
    inference(nnf_transformation,[],[f19]) ).

fof(f727,plain,
    ( sQ24_eqProxy(e4,op(e4,e3))
    | ~ sQ24_eqProxy(e3,op(e4,e4)) ),
    inference(equality_proxy_replacement,[],[f204,f657,f657]) ).

fof(f204,plain,
    ( e3 != op(e4,e4)
    | e4 = op(e4,e3) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f828,plain,
    ( ~ sP1
    | ~ sQ24_eqProxy(e3,op(e3,e0)) ),
    inference(equality_proxy_replacement,[],[f176,f657]) ).

fof(f176,plain,
    ( ~ sP1
    | e3 != op(e3,e0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ( ( e3 != op(e3,e0)
      & e0 = op(e3,e3)
      & op(e0,e0) = e3 )
    | ~ sP1 ),
    inference(nnf_transformation,[],[f11]) ).

fof(f779,plain,
    ( sQ24_eqProxy(e1,op(e1,e1))
    | ~ sP14 ),
    inference(equality_proxy_replacement,[],[f135,f657]) ).

fof(f135,plain,
    ( ~ sP14
    | e1 = op(e1,e1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ( ( e1 != op(e1,e1)
      & e1 = op(e1,e1)
      & e1 = op(e1,e1) )
    | ~ sP14 ),
    inference(nnf_transformation,[],[f24]) ).

fof(f922,plain,
    ( ~ sP14
    | ~ sQ24_eqProxy(e1,op(e1,e1)) ),
    inference(equality_proxy_replacement,[],[f137,f657]) ).

fof(f137,plain,
    ( e1 != op(e1,e1)
    | ~ sP14 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f791,plain,
    ( sQ24_eqProxy(e3,op(e3,e1))
    | ~ sQ24_eqProxy(e1,op(e3,e3)) ),
    inference(equality_proxy_replacement,[],[f187,f657,f657]) ).

fof(f187,plain,
    ( e3 = op(e3,e1)
    | e1 != op(e3,e3) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f688,plain,
    ( ~ sQ24_eqProxy(op(e0,e0),e2)
    | sQ24_eqProxy(e0,op(e0,e2)) ),
    inference(equality_proxy_replacement,[],[f200,f657,f657]) ).

fof(f200,plain,
    ( op(e0,e0) != e2
    | e0 = op(e0,e2) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f871,plain,
    ( ~ sP23
    | ~ sQ24_eqProxy(e1,op(e1,e3)) ),
    inference(equality_proxy_replacement,[],[f109,f657]) ).

fof(f109,plain,
    ( ~ sP23
    | e1 != op(e1,e3) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ( ( e1 = op(e3,e3)
      & e1 != op(e1,e3)
      & e3 = op(e1,e1) )
    | ~ sP23 ),
    inference(nnf_transformation,[],[f33]) ).

fof(f838,plain,
    ( ~ sQ24_eqProxy(e2,op(e2,e1))
    | ~ sP19 ),
    inference(equality_proxy_replacement,[],[f121,f657]) ).

fof(f121,plain,
    ( e2 != op(e2,e1)
    | ~ sP19 ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ( ( e2 = op(e1,e1)
      & e2 != op(e2,e1)
      & e1 = op(e2,e2) )
    | ~ sP19 ),
    inference(nnf_transformation,[],[f29]) ).

fof(f867,plain,
    ( sQ24_eqProxy(e4,op(e4,e2))
    | ~ sQ24_eqProxy(e2,op(e4,e4)) ),
    inference(equality_proxy_replacement,[],[f189,f657,f657]) ).

fof(f189,plain,
    ( e2 != op(e4,e4)
    | e4 = op(e4,e2) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f679,plain,
    ( ~ sP22
    | sQ24_eqProxy(e3,op(e3,e3)) ),
    inference(equality_proxy_replacement,[],[f111,f657]) ).

fof(f111,plain,
    ( e3 = op(e3,e3)
    | ~ sP22 ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ( ( e3 != op(e3,e3)
      & e3 = op(e3,e3)
      & e3 = op(e3,e3) )
    | ~ sP22 ),
    inference(nnf_transformation,[],[f32]) ).

fof(f928,plain,
    ( sQ24_eqProxy(e4,op(e4,e0))
    | ~ sQ24_eqProxy(e0,op(e4,e4)) ),
    inference(equality_proxy_replacement,[],[f186,f657,f657]) ).

fof(f186,plain,
    ( e0 != op(e4,e4)
    | e4 = op(e4,e0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f930,plain,
    ( ~ sP1
    | sQ24_eqProxy(e0,op(e3,e3)) ),
    inference(equality_proxy_replacement,[],[f175,f657]) ).

fof(f175,plain,
    ( ~ sP1
    | e0 = op(e3,e3) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f776,plain,
    ( ~ sQ24_eqProxy(e4,op(e4,e2))
    | ~ sP17 ),
    inference(equality_proxy_replacement,[],[f127,f657]) ).

fof(f127,plain,
    ( ~ sP17
    | e4 != op(e4,e2) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ( ( e2 = op(e4,e4)
      & e4 != op(e4,e2)
      & e4 = op(e2,e2) )
    | ~ sP17 ),
    inference(nnf_transformation,[],[f27]) ).

fof(f741,plain,
    ( sQ24_eqProxy(e3,op(e4,e4))
    | ~ sP16 ),
    inference(equality_proxy_replacement,[],[f131,f657]) ).

fof(f131,plain,
    ( ~ sP16
    | e3 = op(e4,e4) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f707,plain,
    ( sQ24_eqProxy(e3,op(e2,e2))
    | ~ sP4 ),
    inference(equality_proxy_replacement,[],[f166,f657]) ).

fof(f166,plain,
    ( e3 = op(e2,e2)
    | ~ sP4 ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ( ( e2 = op(e3,e3)
      & e3 = op(e2,e2)
      & e2 != op(e2,e3) )
    | ~ sP4 ),
    inference(nnf_transformation,[],[f14]) ).

fof(f916,plain,
    ( ~ sQ24_eqProxy(e1,op(e1,e4))
    | ~ sP3 ),
    inference(equality_proxy_replacement,[],[f169,f657]) ).

fof(f169,plain,
    ( e1 != op(e1,e4)
    | ~ sP3 ),
    inference(cnf_transformation,[],[f55]) ).

fof(f750,plain,
    ( sQ24_eqProxy(e1,op(e1,e3))
    | ~ sQ24_eqProxy(e3,op(e1,e1)) ),
    inference(equality_proxy_replacement,[],[f202,f657,f657]) ).

fof(f202,plain,
    ( e3 != op(e1,e1)
    | e1 = op(e1,e3) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f715,plain,
    ( ~ sQ24_eqProxy(e2,op(e2,e2))
    | ~ sP18 ),
    inference(equality_proxy_replacement,[],[f124,f657]) ).

fof(f124,plain,
    ( e2 != op(e2,e2)
    | ~ sP18 ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ( ( e2 = op(e2,e2)
      & e2 != op(e2,e2)
      & e2 = op(e2,e2) )
    | ~ sP18 ),
    inference(nnf_transformation,[],[f28]) ).

fof(f915,plain,
    ( sQ24_eqProxy(e2,op(e4,e4))
    | ~ sP17 ),
    inference(equality_proxy_replacement,[],[f128,f657]) ).

fof(f128,plain,
    ( ~ sP17
    | e2 = op(e4,e4) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f785,plain,
    ( sP10
    | sP11
    | sP3
    | sP6
    | sP18
    | sP9
    | sP4
    | ~ sQ24_eqProxy(e3,op(e3,e4))
    | sP16
    | sP7
    | sP23
    | sP14
    | sP17
    | sP15
    | sP12
    | sP22
    | sP5
    | sP21
    | sP8
    | sP13
    | sP1
    | sP2
    | sP20
    | sP19
    | sP0 ),
    inference(equality_proxy_replacement,[],[f183,f657]) ).

fof(f183,plain,
    ( sP7
    | sP3
    | sP6
    | sP12
    | sP8
    | e3 != op(e3,e4)
    | sP19
    | sP11
    | sP0
    | sP10
    | sP15
    | sP2
    | sP18
    | sP23
    | sP20
    | sP4
    | sP16
    | sP22
    | sP14
    | sP1
    | sP21
    | sP17
    | sP5
    | sP13
    | sP9 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f777,plain,
    ( ~ sP6
    | sQ24_eqProxy(e4,op(e4,e4)) ),
    inference(equality_proxy_replacement,[],[f159,f657]) ).

fof(f159,plain,
    ( ~ sP6
    | e4 = op(e4,e4) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f686,plain,
    ( ~ sP19
    | sQ24_eqProxy(e1,op(e2,e2)) ),
    inference(equality_proxy_replacement,[],[f120,f657]) ).

fof(f120,plain,
    ( ~ sP19
    | e1 = op(e2,e2) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f935,plain,
    ( ~ sP4
    | ~ sQ24_eqProxy(e2,op(e2,e3)) ),
    inference(equality_proxy_replacement,[],[f165,f657]) ).

fof(f165,plain,
    ( ~ sP4
    | e2 != op(e2,e3) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f817,plain,
    ( sQ24_eqProxy(e2,op(e2,e2))
    | ~ sP18 ),
    inference(equality_proxy_replacement,[],[f123,f657]) ).

fof(f123,plain,
    ( e2 = op(e2,e2)
    | ~ sP18 ),
    inference(cnf_transformation,[],[f40]) ).

fof(f896,plain,
    ( ~ sP5
    | ~ sQ24_eqProxy(e3,op(e3,e2)) ),
    inference(equality_proxy_replacement,[],[f162,f657]) ).

fof(f162,plain,
    ( ~ sP5
    | e3 != op(e3,e2) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ( ( e2 = op(e3,e3)
      & e3 = op(e2,e2)
      & e3 != op(e3,e2) )
    | ~ sP5 ),
    inference(nnf_transformation,[],[f15]) ).

fof(f798,plain,
    ( ~ sP11
    | sQ24_eqProxy(op(e0,e0),e3) ),
    inference(equality_proxy_replacement,[],[f145,f657]) ).

fof(f145,plain,
    ( ~ sP11
    | op(e0,e0) = e3 ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ( ( e0 != op(e0,e3)
      & op(e0,e0) = e3
      & e0 = op(e3,e3) )
    | ~ sP11 ),
    inference(nnf_transformation,[],[f21]) ).

fof(f947,plain,
    ( ~ sP10
    | sQ24_eqProxy(e2,op(e1,e1)) ),
    inference(equality_proxy_replacement,[],[f147,f657]) ).

fof(f147,plain,
    ( e2 = op(e1,e1)
    | ~ sP10 ),
    inference(cnf_transformation,[],[f48]) ).

fof(f756,plain,
    ( ~ sP22
    | ~ sQ24_eqProxy(e3,op(e3,e3)) ),
    inference(equality_proxy_replacement,[],[f113,f657]) ).

fof(f113,plain,
    ( ~ sP22
    | e3 != op(e3,e3) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f847,plain,
    ( ~ sQ24_eqProxy(e4,op(e4,e1))
    | ~ sP15 ),
    inference(equality_proxy_replacement,[],[f133,f657]) ).

fof(f133,plain,
    ( ~ sP15
    | e4 != op(e4,e1) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ( ( e4 = op(e1,e1)
      & e4 != op(e4,e1)
      & e1 = op(e4,e4) )
    | ~ sP15 ),
    inference(nnf_transformation,[],[f25]) ).

fof(f713,plain,
    ( sQ24_eqProxy(op(e0,e0),e2)
    | ~ sP0 ),
    inference(equality_proxy_replacement,[],[f178,f657]) ).

fof(f178,plain,
    ( op(e0,e0) = e2
    | ~ sP0 ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ( ( e0 = op(e2,e2)
      & op(e0,e0) = e2
      & e0 != op(e0,e2) )
    | ~ sP0 ),
    inference(nnf_transformation,[],[f10]) ).

fof(f732,plain,
    ( ~ sP0
    | ~ sQ24_eqProxy(e0,op(e0,e2)) ),
    inference(equality_proxy_replacement,[],[f177,f657]) ).

fof(f177,plain,
    ( ~ sP0
    | e0 != op(e0,e2) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f853,plain,
    ( sQ24_eqProxy(e0,op(e0,e0))
    | ~ sP13 ),
    inference(equality_proxy_replacement,[],[f139,f657]) ).

fof(f139,plain,
    ( ~ sP13
    | e0 = op(e0,e0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f942,plain,
    ( sQ24_eqProxy(e0,op(e0,e4))
    | ~ sQ24_eqProxy(op(e0,e0),e4) ),
    inference(equality_proxy_replacement,[],[f181,f657,f657]) ).

fof(f181,plain,
    ( op(e0,e0) != e4
    | e0 = op(e0,e4) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f893,plain,
    ( ~ sQ24_eqProxy(e0,op(e0,e1))
    | ~ sP20 ),
    inference(equality_proxy_replacement,[],[f119,f657]) ).

fof(f119,plain,
    ( e0 != op(e0,e1)
    | ~ sP20 ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ( ( e0 != op(e0,e1)
      & e0 = op(e1,e1)
      & op(e0,e0) = e1 )
    | ~ sP20 ),
    inference(nnf_transformation,[],[f30]) ).

fof(f731,plain,
    ( sQ24_eqProxy(e0,op(e1,e1))
    | ~ sP2 ),
    inference(equality_proxy_replacement,[],[f173,f657]) ).

fof(f173,plain,
    ( ~ sP2
    | e0 = op(e1,e1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ( ( e0 = op(e1,e1)
      & op(e0,e0) = e1
      & e1 != op(e1,e0) )
    | ~ sP2 ),
    inference(nnf_transformation,[],[f12]) ).

fof(f729,plain,
    ( ~ sP12
    | sQ24_eqProxy(e0,op(e4,e4)) ),
    inference(equality_proxy_replacement,[],[f142,f657]) ).

fof(f142,plain,
    ( e0 = op(e4,e4)
    | ~ sP12 ),
    inference(cnf_transformation,[],[f46]) ).

fof(f724,plain,
    ( ~ sQ24_eqProxy(e0,op(e0,e3))
    | ~ sP11 ),
    inference(equality_proxy_replacement,[],[f146,f657]) ).

fof(f146,plain,
    ( e0 != op(e0,e3)
    | ~ sP11 ),
    inference(cnf_transformation,[],[f47]) ).

fof(f761,plain,
    ( ~ sP2
    | ~ sQ24_eqProxy(e1,op(e1,e0)) ),
    inference(equality_proxy_replacement,[],[f171,f657]) ).

fof(f171,plain,
    ( e1 != op(e1,e0)
    | ~ sP2 ),
    inference(cnf_transformation,[],[f56]) ).

fof(f674,plain,
    ( sQ24_eqProxy(e1,op(e1,e2))
    | ~ sQ24_eqProxy(e2,op(e1,e1)) ),
    inference(equality_proxy_replacement,[],[f195,f657,f657]) ).

fof(f195,plain,
    ( e1 = op(e1,e2)
    | e2 != op(e1,e1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f717,plain,
    ( ~ sQ24_eqProxy(e2,op(e2,e4))
    | ~ sP8 ),
    inference(equality_proxy_replacement,[],[f153,f657]) ).

fof(f153,plain,
    ( e2 != op(e2,e4)
    | ~ sP8 ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ( ( e2 = op(e4,e4)
      & e4 = op(e2,e2)
      & e2 != op(e2,e4) )
    | ~ sP8 ),
    inference(nnf_transformation,[],[f18]) ).

fof(f808,plain,
    ( sQ24_eqProxy(e2,op(e3,e3))
    | ~ sP5 ),
    inference(equality_proxy_replacement,[],[f164,f657]) ).

fof(f164,plain,
    ( e2 = op(e3,e3)
    | ~ sP5 ),
    inference(cnf_transformation,[],[f53]) ).

fof(f804,plain,
    ( ~ sQ24_eqProxy(e3,op(e2,e2))
    | sQ24_eqProxy(e2,op(e2,e3)) ),
    inference(equality_proxy_replacement,[],[f205,f657,f657]) ).

fof(f205,plain,
    ( e3 != op(e2,e2)
    | e2 = op(e2,e3) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f712,plain,
    ( ~ sQ24_eqProxy(e0,op(e0,e4))
    | ~ sP7 ),
    inference(equality_proxy_replacement,[],[f157,f657]) ).

fof(f157,plain,
    ( e0 != op(e0,e4)
    | ~ sP7 ),
    inference(cnf_transformation,[],[f51]) ).

fof(f693,plain,
    ( sQ24_eqProxy(e3,op(e3,e2))
    | ~ sQ24_eqProxy(e2,op(e3,e3)) ),
    inference(equality_proxy_replacement,[],[f180,f657,f657]) ).

fof(f180,plain,
    ( e3 = op(e3,e2)
    | e2 != op(e3,e3) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f841,plain,
    ( sQ24_eqProxy(e2,op(e2,e0))
    | ~ sQ24_eqProxy(e0,op(e2,e2)) ),
    inference(equality_proxy_replacement,[],[f198,f657,f657]) ).

fof(f198,plain,
    ( e0 != op(e2,e2)
    | e2 = op(e2,e0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f683,plain,
    ( sQ24_eqProxy(e1,op(e1,e4))
    | ~ sQ24_eqProxy(e4,op(e1,e1)) ),
    inference(equality_proxy_replacement,[],[f203,f657,f657]) ).

fof(f203,plain,
    ( e1 = op(e1,e4)
    | e4 != op(e1,e1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f784,plain,
    ( sQ24_eqProxy(op(e0,e0),e1)
    | ~ sP20 ),
    inference(equality_proxy_replacement,[],[f117,f657]) ).

fof(f117,plain,
    ( ~ sP20
    | op(e0,e0) = e1 ),
    inference(cnf_transformation,[],[f38]) ).

fof(f852,plain,
    ( ~ sP23
    | sQ24_eqProxy(e3,op(e1,e1)) ),
    inference(equality_proxy_replacement,[],[f108,f657]) ).

fof(f108,plain,
    ( ~ sP23
    | e3 = op(e1,e1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f882,plain,
    ( ~ sP21
    | ~ sQ24_eqProxy(e3,op(e3,e1)) ),
    inference(equality_proxy_replacement,[],[f116,f657]) ).

fof(f116,plain,
    ( ~ sP21
    | e3 != op(e3,e1) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f846,plain,
    ( sQ24_eqProxy(e3,op(e3,e4))
    | ~ sQ24_eqProxy(e4,op(e3,e3)) ),
    inference(equality_proxy_replacement,[],[f192,f657,f657]) ).

fof(f192,plain,
    ( e4 != op(e3,e3)
    | e3 = op(e3,e4) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f943,plain,
    ( ~ sQ24_eqProxy(op(e0,e0),e1)
    | sQ24_eqProxy(e0,op(e0,e1)) ),
    inference(equality_proxy_replacement,[],[f182,f657,f657]) ).

fof(f182,plain,
    ( e0 = op(e0,e1)
    | op(e0,e0) != e1 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f879,plain,
    ( ~ sP8
    | sQ24_eqProxy(e4,op(e2,e2)) ),
    inference(equality_proxy_replacement,[],[f154,f657]) ).

fof(f154,plain,
    ( ~ sP8
    | e4 = op(e2,e2) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f664,plain,
    ( ~ sQ24_eqProxy(e2,op(e2,e0))
    | ~ sP9 ),
    inference(equality_proxy_replacement,[],[f150,f657]) ).

fof(f150,plain,
    ( e2 != op(e2,e0)
    | ~ sP9 ),
    inference(cnf_transformation,[],[f49]) ).

fof(f865,plain,
    ( ~ sP15
    | sQ24_eqProxy(e1,op(e4,e4)) ),
    inference(equality_proxy_replacement,[],[f132,f657]) ).

fof(f132,plain,
    ( e1 = op(e4,e4)
    | ~ sP15 ),
    inference(cnf_transformation,[],[f43]) ).

fof(f762,plain,
    ( sQ24_eqProxy(e0,op(e0,e3))
    | ~ sQ24_eqProxy(op(e0,e0),e3) ),
    inference(equality_proxy_replacement,[],[f199,f657,f657]) ).

fof(f199,plain,
    ( e0 = op(e0,e3)
    | op(e0,e0) != e3 ),
    inference(cnf_transformation,[],[f34]) ).

fof(f711,plain,
    ( sP21
    | sP23
    | sP4
    | sP7
    | sP16
    | sQ24_eqProxy(e4,op(e3,e3))
    | sP13
    | sP17
    | sP19
    | sP0
    | sP10
    | sP2
    | sP15
    | sP5
    | sP6
    | sP14
    | sP1
    | sP20
    | sP11
    | sP18
    | sP8
    | sP9
    | sP22
    | sP12
    | sP3 ),
    inference(equality_proxy_replacement,[],[f185,f657]) ).

fof(f185,plain,
    ( sP11
    | sP17
    | sP16
    | sP20
    | sP14
    | sP9
    | sP0
    | sP13
    | sP1
    | sP22
    | sP4
    | sP19
    | sP18
    | sP23
    | e4 = op(e3,e3)
    | sP10
    | sP8
    | sP5
    | sP2
    | sP6
    | sP15
    | sP12
    | sP7
    | sP3
    | sP21 ),
    inference(cnf_transformation,[],[f34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : ALG067+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 29 14:49:25 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.18/0.50  % (17922)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.18/0.50  % (17914)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.18/0.50  % (17910)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.51  % (17906)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.52  % (17914)First to succeed.
% 0.18/0.52  % (17924)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.35/0.53  % (17914)Refutation found. Thanks to Tanya!
% 1.35/0.53  % SZS status Theorem for theBenchmark
% 1.35/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.35/0.53  % (17914)------------------------------
% 1.35/0.53  % (17914)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.35/0.53  % (17914)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.35/0.53  % (17914)Termination reason: Refutation
% 1.35/0.53  
% 1.35/0.53  % (17914)Memory used [KB]: 6140
% 1.35/0.53  % (17914)Time elapsed: 0.019 s
% 1.35/0.53  % (17914)Instructions burned: 13 (million)
% 1.35/0.53  % (17914)------------------------------
% 1.35/0.53  % (17914)------------------------------
% 1.35/0.53  % (17899)Success in time 0.184 s
%------------------------------------------------------------------------------