TSTP Solution File: SWW245+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWW245+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 06:58:22 EDT 2024

% Result   : Theorem 0.75s 0.89s
% Output   : Refutation 0.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   89 (   4 unt;   1 typ;   0 def)
%            Number of atoms       : 2478 ( 109 equ)
%            Maximal formula atoms :    8 (  28 avg)
%            Number of connectives :  398 ( 162   ~; 165   |;  35   &)
%                                         (  14 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       : 2154 (2154 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   40 (  38 usr;  24 prp; 0-4 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   84 (  49   !;  34   ?;  28   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_69,type,
    sQ31_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f5638,plain,
    $false,
    inference(avatar_sat_refutation,[],[f5548,f5552,f5559,f5564,f5569,f5573,f5577,f5581,f5615,f5619,f5621,f5625,f5629,f5635,f5637]) ).

tff(f5637,plain,
    ( spl32_6
    | ~ spl32_8
    | ~ spl32_9
    | ~ spl32_25 ),
    inference(avatar_contradiction_clause,[],[f5636]) ).

tff(f5636,plain,
    ( $false
    | spl32_6
    | ~ spl32_8
    | ~ spl32_9
    | ~ spl32_25 ),
    inference(subsumption_resolution,[],[f5632,f5555]) ).

tff(f5555,plain,
    ( sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3)))
    | ~ spl32_9 ),
    inference(avatar_component_clause,[],[f5554]) ).

tff(f5554,plain,
    ( spl32_9
  <=> sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_9])]) ).

tff(f5632,plain,
    ( ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3)))
    | spl32_6
    | ~ spl32_8
    | ~ spl32_25 ),
    inference(subsumption_resolution,[],[f5630,f5544]) ).

tff(f5544,plain,
    ( ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),sK4)
    | spl32_6 ),
    inference(avatar_component_clause,[],[f5543]) ).

tff(f5543,plain,
    ( spl32_6
  <=> sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_6])]) ).

tff(f5630,plain,
    ( sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),sK4)
    | ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3)))
    | ~ spl32_8
    | ~ spl32_25 ),
    inference(resolution,[],[f5618,f5551]) ).

tff(f5551,plain,
    ( ! [X3: $i] : sQ31_eqProxy($i,hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK4,sK5)),X3)))
    | ~ spl32_8 ),
    inference(avatar_component_clause,[],[f5550]) ).

tff(f5550,plain,
    ( spl32_8
  <=> ! [X3] : sQ31_eqProxy($i,hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK4,sK5)),X3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_8])]) ).

tff(f5618,plain,
    ( ! [X2: $i,X0: $i,X1: $i] :
        ( ~ sQ31_eqProxy($i,hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK30(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK30(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK30(X0,X1,X2))))
        | sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),X1)
        | ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))) )
    | ~ spl32_25 ),
    inference(avatar_component_clause,[],[f5617]) ).

tff(f5617,plain,
    ( spl32_25
  <=> ! [X2,X0,X1] :
        ( sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),X1)
        | ~ sQ31_eqProxy($i,hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK30(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK30(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK30(X0,X1,X2))))
        | ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_25])]) ).

tff(f5635,plain,
    ( spl32_12
    | ~ spl32_13
    | ~ spl32_14
    | ~ spl32_25 ),
    inference(avatar_contradiction_clause,[],[f5634]) ).

tff(f5634,plain,
    ( $false
    | spl32_12
    | ~ spl32_13
    | ~ spl32_14
    | ~ spl32_25 ),
    inference(subsumption_resolution,[],[f5633,f5576]) ).

tff(f5576,plain,
    ( sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6)))
    | ~ spl32_14 ),
    inference(avatar_component_clause,[],[f5575]) ).

tff(f5575,plain,
    ( spl32_14
  <=> sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_14])]) ).

tff(f5633,plain,
    ( ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6)))
    | spl32_12
    | ~ spl32_13
    | ~ spl32_25 ),
    inference(subsumption_resolution,[],[f5631,f5567]) ).

tff(f5567,plain,
    ( ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),sK7)
    | spl32_12 ),
    inference(avatar_component_clause,[],[f5566]) ).

tff(f5566,plain,
    ( spl32_12
  <=> sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_12])]) ).

tff(f5631,plain,
    ( sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),sK7)
    | ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6)))
    | ~ spl32_13
    | ~ spl32_25 ),
    inference(resolution,[],[f5618,f5572]) ).

tff(f5572,plain,
    ( ! [X3: $i] : sQ31_eqProxy($i,hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK6)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK7,sK8)),X3)))
    | ~ spl32_13 ),
    inference(avatar_component_clause,[],[f5571]) ).

tff(f5571,plain,
    ( spl32_13
  <=> ! [X3] : sQ31_eqProxy($i,hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK6)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK7,sK8)),X3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_13])]) ).

tff(f5629,plain,
    ( spl32_12
    | ~ spl32_13
    | ~ spl32_15
    | ~ spl32_24 ),
    inference(avatar_contradiction_clause,[],[f5628]) ).

tff(f5628,plain,
    ( $false
    | spl32_12
    | ~ spl32_13
    | ~ spl32_15
    | ~ spl32_24 ),
    inference(subsumption_resolution,[],[f5627,f5580]) ).

tff(f5580,plain,
    ( sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6)))
    | ~ spl32_15 ),
    inference(avatar_component_clause,[],[f5579]) ).

tff(f5579,plain,
    ( spl32_15
  <=> sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_15])]) ).

tff(f5627,plain,
    ( ~ sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6)))
    | spl32_12
    | ~ spl32_13
    | ~ spl32_24 ),
    inference(subsumption_resolution,[],[f5626,f5567]) ).

tff(f5626,plain,
    ( sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),sK7)
    | ~ sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6)))
    | ~ spl32_13
    | ~ spl32_24 ),
    inference(resolution,[],[f5572,f5614]) ).

tff(f5614,plain,
    ( ! [X2: $i,X0: $i,X1: $i] :
        ( ~ sQ31_eqProxy($i,hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK30(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK30(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK30(X0,X1,X2))))
        | sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),X1)
        | ~ sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))) )
    | ~ spl32_24 ),
    inference(avatar_component_clause,[],[f5613]) ).

tff(f5613,plain,
    ( spl32_24
  <=> ! [X2,X0,X1] :
        ( sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),X1)
        | ~ sQ31_eqProxy($i,hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK30(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK30(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK30(X0,X1,X2))))
        | ~ sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_24])]) ).

tff(f5625,plain,
    ( spl32_6
    | ~ spl32_8
    | ~ spl32_11
    | ~ spl32_24 ),
    inference(avatar_contradiction_clause,[],[f5624]) ).

tff(f5624,plain,
    ( $false
    | spl32_6
    | ~ spl32_8
    | ~ spl32_11
    | ~ spl32_24 ),
    inference(subsumption_resolution,[],[f5623,f5562]) ).

tff(f5562,plain,
    ( sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3)))
    | ~ spl32_11 ),
    inference(avatar_component_clause,[],[f5561]) ).

tff(f5561,plain,
    ( spl32_11
  <=> sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_11])]) ).

tff(f5623,plain,
    ( ~ sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3)))
    | spl32_6
    | ~ spl32_8
    | ~ spl32_24 ),
    inference(subsumption_resolution,[],[f5622,f5544]) ).

tff(f5622,plain,
    ( sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),sK4)
    | ~ sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3)))
    | ~ spl32_8
    | ~ spl32_24 ),
    inference(resolution,[],[f5551,f5614]) ).

tff(f5621,plain,
    spl32_2,
    inference(avatar_contradiction_clause,[],[f5620]) ).

tff(f5620,plain,
    ( $false
    | spl32_2 ),
    inference(subsumption_resolution,[],[f4607,f5528]) ).

tff(f5528,plain,
    ( ~ class_Rings_Oidom(t_a)
    | spl32_2 ),
    inference(avatar_component_clause,[],[f5527]) ).

tff(f5527,plain,
    ( spl32_2
  <=> class_Rings_Oidom(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_2])]) ).

tff(f4607,plain,
    class_Rings_Oidom(t_a),
    inference(cnf_transformation,[],[f1162]) ).

tff(f1162,axiom,
    class_Rings_Oidom(t_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).

tff(f5619,plain,
    ( ~ spl32_10
    | spl32_25 ),
    inference(avatar_split_clause,[],[f5520,f5617,f5557]) ).

tff(f5557,plain,
    ( spl32_10
  <=> sQ31_eqProxy($i,c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_10])]) ).

tff(f5520,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),X1)
      | ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)))
      | ~ sQ31_eqProxy($i,c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
      | ~ sQ31_eqProxy($i,hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK30(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK30(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK30(X0,X1,X2)))) ),
    inference(equality_proxy_replacement,[],[f4604,f4776]) ).

tff(f4776,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ31_eqProxy(X0,X1,X2)
    <=> ( X1 = X2 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ31_eqProxy])]) ).

tff(f4604,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ( c_Groups_Ozero__class_Ozero(t_a) = X1 )
      | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
      | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
      | ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK30(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK30(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK30(X0,X1,X2))) ) ),
    inference(cnf_transformation,[],[f3331]) ).

tff(f3331,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ? [X3] : ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) )
          | ( ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
            & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
          | ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
            & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) )
      | ( c_Groups_Ozero__class_Ozero(t_a) = X1 ) ),
    inference(ennf_transformation,[],[f2231]) ).

tff(f2231,plain,
    ~ ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) )
            & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
             => ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) ) )
            & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
             => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) ) ) )
        & ( c_Groups_Ozero__class_Ozero(t_a) != X1 ) ),
    inference(rectify,[],[f1161]) ).

tff(f1161,negated_conjecture,
    ~ ? [X4,X5] :
        ( ? [X6] :
            ( ! [X3] : ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X5,X6)),X3)) )
            & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
             => ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) ) )
            & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
             => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) ) ) )
        & ( c_Groups_Ozero__class_Ozero(t_a) != X5 ) ),
    inference(negated_conjecture,[],[f1160]) ).

tff(f1160,conjecture,
    ? [X4,X5] :
      ( ? [X6] :
          ( ! [X3] : ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X5,X6)),X3)) )
          & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
           => ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) ) )
          & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
           => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) ) ) )
      & ( c_Groups_Ozero__class_Ozero(t_a) != X5 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f5615,plain,
    ( spl32_10
    | spl32_24 ),
    inference(avatar_split_clause,[],[f5518,f5613,f5557]) ).

tff(f5518,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),X1)
      | sQ31_eqProxy($i,c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
      | ~ sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)))
      | ~ sQ31_eqProxy($i,hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK30(X0,X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK30(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK30(X0,X1,X2)))) ),
    inference(equality_proxy_replacement,[],[f4606,f4776]) ).

tff(f4606,plain,
    ! [X2: $i,X0: $i,X1: $i] :
      ( ( c_Groups_Ozero__class_Ozero(t_a) = X1 )
      | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
      | ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
      | ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK30(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK30(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK30(X0,X1,X2))) ) ),
    inference(cnf_transformation,[],[f3331]) ).

tff(f5581,plain,
    ( spl32_15
    | spl32_10
    | ~ spl32_7
    | ~ spl32_2 ),
    inference(avatar_split_clause,[],[f4789,f5527,f5546,f5557,f5579]) ).

tff(f5546,plain,
    ( spl32_7
  <=> sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),v_c____) ),
    introduced(avatar_definition,[new_symbols(naming,[spl32_7])]) ).

tff(f4789,plain,
    ( ~ class_Rings_Oidom(t_a)
    | ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),v_c____)
    | sQ31_eqProxy($i,c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6))) ),
    inference(equality_proxy_replacement,[],[f3341,f4776]) ).

tff(f3341,plain,
    ( ~ class_Rings_Oidom(t_a)
    | ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
    | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
    | ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6)) ) ),
    inference(cnf_transformation,[],[f2423]) ).

tff(f2423,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) )
            & ( ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
              | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
            & ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
              | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) )
        & ( c_Groups_Ozero__class_Ozero(t_a) != X1 ) )
    | ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
    | ~ class_Rings_Oidom(t_a) ),
    inference(flattening,[],[f2422]) ).

tff(f2422,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) )
            & ( ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
              | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
            & ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
              | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) )
        & ( c_Groups_Ozero__class_Ozero(t_a) != X1 ) )
    | ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
    | ~ class_Rings_Oidom(t_a) ),
    inference(ennf_transformation,[],[f1166]) ).

tff(f1166,plain,
    ( class_Rings_Oidom(t_a)
   => ( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
     => ? [X0,X1] :
          ( ? [X2] :
              ( ! [X3] : ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) )
              & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
               => ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) ) )
              & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
               => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) ) ) )
          & ( c_Groups_Ozero__class_Ozero(t_a) != X1 ) ) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ( class_Rings_Oidom(t_a)
   => ( ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
     => ? [X4,X5] :
          ( ? [X6] :
              ( ! [X3] : ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X5,X6)),X3)) )
              & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
               => ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) ) )
              & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
               => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) ) ) )
          & ( c_Groups_Ozero__class_Ozero(t_a) != X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096c_A_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096) ).

tff(f5577,plain,
    ( spl32_14
    | ~ spl32_10
    | ~ spl32_7
    | ~ spl32_2 ),
    inference(avatar_split_clause,[],[f4788,f5527,f5546,f5557,f5575]) ).

tff(f4788,plain,
    ( ~ class_Rings_Oidom(t_a)
    | ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),v_c____)
    | ~ sQ31_eqProxy($i,c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6))) ),
    inference(equality_proxy_replacement,[],[f3342,f4776]) ).

tff(f3342,plain,
    ( ~ class_Rings_Oidom(t_a)
    | ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
    | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
    | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK8,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK8))),sK6)) ) ),
    inference(cnf_transformation,[],[f2423]) ).

tff(f5573,plain,
    ( spl32_13
    | ~ spl32_7
    | ~ spl32_2 ),
    inference(avatar_split_clause,[],[f4787,f5527,f5546,f5571]) ).

tff(f4787,plain,
    ! [X3: $i] :
      ( ~ class_Rings_Oidom(t_a)
      | ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),v_c____)
      | sQ31_eqProxy($i,hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK6)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK7,sK8)),X3))) ),
    inference(equality_proxy_replacement,[],[f3343,f4776]) ).

tff(f3343,plain,
    ! [X3: $i] :
      ( ~ class_Rings_Oidom(t_a)
      | ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
      | ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK6)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK7,sK8)),X3)) ) ),
    inference(cnf_transformation,[],[f2423]) ).

tff(f5569,plain,
    ( ~ spl32_12
    | ~ spl32_7
    | ~ spl32_2 ),
    inference(avatar_split_clause,[],[f4786,f5527,f5546,f5566]) ).

tff(f4786,plain,
    ( ~ class_Rings_Oidom(t_a)
    | ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),v_c____)
    | ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),sK7) ),
    inference(equality_proxy_replacement,[],[f3344,f4776]) ).

tff(f3344,plain,
    ( ~ class_Rings_Oidom(t_a)
    | ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
    | ( c_Groups_Ozero__class_Ozero(t_a) != sK7 ) ),
    inference(cnf_transformation,[],[f2423]) ).

tff(f5564,plain,
    ( spl32_11
    | spl32_10
    | spl32_7
    | ~ spl32_2 ),
    inference(avatar_split_clause,[],[f4785,f5527,f5546,f5557,f5561]) ).

tff(f4785,plain,
    ( ~ class_Rings_Oidom(t_a)
    | sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),v_c____)
    | sQ31_eqProxy($i,c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | sQ31_eqProxy($i,c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3))) ),
    inference(equality_proxy_replacement,[],[f3337,f4776]) ).

tff(f3337,plain,
    ( ~ class_Rings_Oidom(t_a)
    | ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
    | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
    | ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3)) ) ),
    inference(cnf_transformation,[],[f2421]) ).

tff(f2421,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) )
            & ( ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
              | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
            & ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
              | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) )
        & ( c_Groups_Ozero__class_Ozero(t_a) != X1 ) )
    | ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
    | ~ class_Rings_Oidom(t_a) ),
    inference(flattening,[],[f2420]) ).

tff(f2420,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) )
            & ( ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
              | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
            & ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) )
              | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) )
        & ( c_Groups_Ozero__class_Ozero(t_a) != X1 ) )
    | ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
    | ~ class_Rings_Oidom(t_a) ),
    inference(ennf_transformation,[],[f1165]) ).

tff(f1165,plain,
    ( class_Rings_Oidom(t_a)
   => ( ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
     => ? [X0,X1] :
          ( ? [X2] :
              ( ! [X3] : ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3)) )
              & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
               => ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) ) )
              & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
               => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X2))),X0)) ) ) )
          & ( c_Groups_Ozero__class_Ozero(t_a) != X1 ) ) ) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ( class_Rings_Oidom(t_a)
   => ( ( c_Groups_Ozero__class_Ozero(t_a) != v_c____ )
     => ? [X4,X5] :
          ( ? [X6] :
              ( ! [X3] : ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X5,X6)),X3)) )
              & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
               => ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) ) )
              & ( ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
               => ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,X6))),X4)) ) ) )
          & ( c_Groups_Ozero__class_Ozero(t_a) != X5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096c_A_126_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096) ).

tff(f5559,plain,
    ( spl32_9
    | ~ spl32_10
    | spl32_7
    | ~ spl32_2 ),
    inference(avatar_split_clause,[],[f4784,f5527,f5546,f5557,f5554]) ).

tff(f4784,plain,
    ( ~ class_Rings_Oidom(t_a)
    | sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),v_c____)
    | ~ sQ31_eqProxy($i,c_Polynomial_OpCons(t_a,v_c____,v_cs____),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))
    | sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3))) ),
    inference(equality_proxy_replacement,[],[f3338,f4776]) ).

tff(f3338,plain,
    ( ~ class_Rings_Oidom(t_a)
    | ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
    | ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
    | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(c_Polynomial_Odegree(t_a,sK5))),sK3)) ) ),
    inference(cnf_transformation,[],[f2421]) ).

tff(f5552,plain,
    ( spl32_8
    | spl32_7
    | ~ spl32_2 ),
    inference(avatar_split_clause,[],[f4783,f5527,f5546,f5550]) ).

tff(f4783,plain,
    ! [X3: $i] :
      ( ~ class_Rings_Oidom(t_a)
      | sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),v_c____)
      | sQ31_eqProxy($i,hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK4,sK5)),X3))) ),
    inference(equality_proxy_replacement,[],[f3339,f4776]) ).

tff(f3339,plain,
    ! [X3: $i] :
      ( ~ class_Rings_Oidom(t_a)
      | ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
      | ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK3)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK4,sK5)),X3)) ) ),
    inference(cnf_transformation,[],[f2421]) ).

tff(f5548,plain,
    ( ~ spl32_6
    | spl32_7
    | ~ spl32_2 ),
    inference(avatar_split_clause,[],[f4782,f5527,f5546,f5543]) ).

tff(f4782,plain,
    ( ~ class_Rings_Oidom(t_a)
    | sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),v_c____)
    | ~ sQ31_eqProxy($i,c_Groups_Ozero__class_Ozero(t_a),sK4) ),
    inference(equality_proxy_replacement,[],[f3340,f4776]) ).

tff(f3340,plain,
    ( ~ class_Rings_Oidom(t_a)
    | ( c_Groups_Ozero__class_Ozero(t_a) = v_c____ )
    | ( c_Groups_Ozero__class_Ozero(t_a) != sK4 ) ),
    inference(cnf_transformation,[],[f2421]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : SWW245+1 : TPTP v8.2.0. Released v5.2.0.
% 0.09/0.11  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.31  % Computer : n017.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.31  % CPULimit   : 300
% 0.16/0.31  % WCLimit    : 300
% 0.16/0.31  % DateTime   : Sat May 18 20:59:07 EDT 2024
% 0.16/0.31  % CPUTime    : 
% 0.16/0.31  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.31  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.63/0.80  % (27682)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2995ds/33Mi)
% 0.63/0.80  % (27681)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2995ds/78Mi)
% 0.63/0.80  % (27680)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on theBenchmark for (2995ds/51Mi)
% 0.63/0.80  % (27679)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2995ds/34Mi)
% 0.63/0.80  % (27685)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2995ds/83Mi)
% 0.63/0.80  % (27683)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2995ds/34Mi)
% 0.63/0.80  % (27684)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2995ds/45Mi)
% 0.63/0.80  % (27686)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2995ds/56Mi)
% 0.63/0.82  % (27679)Instruction limit reached!
% 0.63/0.82  % (27679)------------------------------
% 0.63/0.82  % (27679)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.82  % (27679)Termination reason: Unknown
% 0.63/0.82  % (27679)Termination phase: Property scanning
% 0.63/0.82  
% 0.63/0.82  % (27679)Memory used [KB]: 2359
% 0.63/0.82  % (27679)Time elapsed: 0.016 s
% 0.63/0.82  % (27679)Instructions burned: 34 (million)
% 0.63/0.82  % (27679)------------------------------
% 0.63/0.82  % (27679)------------------------------
% 0.63/0.82  % (27682)Instruction limit reached!
% 0.63/0.82  % (27682)------------------------------
% 0.63/0.82  % (27682)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.82  % (27682)Termination reason: Unknown
% 0.63/0.82  % (27682)Termination phase: Saturation
% 0.63/0.82  
% 0.63/0.82  % (27682)Memory used [KB]: 2380
% 0.63/0.82  % (27682)Time elapsed: 0.016 s
% 0.63/0.82  % (27682)Instructions burned: 34 (million)
% 0.63/0.82  % (27682)------------------------------
% 0.63/0.82  % (27682)------------------------------
% 0.63/0.82  % (27683)Instruction limit reached!
% 0.63/0.82  % (27683)------------------------------
% 0.63/0.82  % (27683)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.82  % (27683)Termination reason: Unknown
% 0.63/0.82  % (27683)Termination phase: Preprocessing 3
% 0.63/0.82  
% 0.63/0.82  % (27683)Memory used [KB]: 3107
% 0.63/0.82  % (27683)Time elapsed: 0.017 s
% 0.63/0.82  % (27683)Instructions burned: 34 (million)
% 0.63/0.82  % (27683)------------------------------
% 0.63/0.82  % (27683)------------------------------
% 0.63/0.82  % (27687)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on theBenchmark for (2994ds/55Mi)
% 0.63/0.82  % (27689)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on theBenchmark for (2994ds/208Mi)
% 0.63/0.82  % (27684)Instruction limit reached!
% 0.63/0.82  % (27684)------------------------------
% 0.63/0.82  % (27684)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.82  % (27684)Termination reason: Unknown
% 0.63/0.82  % (27684)Termination phase: Saturation
% 0.63/0.82  
% 0.63/0.82  % (27684)Memory used [KB]: 2645
% 0.63/0.82  % (27684)Time elapsed: 0.021 s
% 0.63/0.82  % (27684)Instructions burned: 46 (million)
% 0.63/0.82  % (27684)------------------------------
% 0.63/0.82  % (27684)------------------------------
% 0.63/0.82  % (27688)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on theBenchmark for (2994ds/50Mi)
% 0.63/0.83  % (27680)Instruction limit reached!
% 0.63/0.83  % (27680)------------------------------
% 0.63/0.83  % (27680)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.83  % (27680)Termination reason: Unknown
% 0.63/0.83  % (27680)Termination phase: Property scanning
% 0.63/0.83  
% 0.63/0.83  % (27680)Memory used [KB]: 3298
% 0.63/0.83  % (27680)Time elapsed: 0.024 s
% 0.63/0.83  % (27680)Instructions burned: 52 (million)
% 0.63/0.83  % (27680)------------------------------
% 0.63/0.83  % (27680)------------------------------
% 0.63/0.83  % (27690)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on theBenchmark for (2994ds/52Mi)
% 0.63/0.83  % (27686)Instruction limit reached!
% 0.63/0.83  % (27686)------------------------------
% 0.63/0.83  % (27686)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.63/0.83  % (27686)Termination reason: Unknown
% 0.63/0.83  % (27686)Termination phase: Saturation
% 0.63/0.83  
% 0.63/0.83  % (27686)Memory used [KB]: 2849
% 0.63/0.83  % (27686)Time elapsed: 0.025 s
% 0.63/0.83  % (27686)Instructions burned: 56 (million)
% 0.63/0.83  % (27686)------------------------------
% 0.63/0.83  % (27686)------------------------------
% 0.75/0.83  % (27691)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on theBenchmark for (2994ds/518Mi)
% 0.75/0.83  % (27692)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on theBenchmark for (2994ds/42Mi)
% 0.75/0.83  % (27681)Instruction limit reached!
% 0.75/0.83  % (27681)------------------------------
% 0.75/0.83  % (27681)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.75/0.83  % (27681)Termination reason: Unknown
% 0.75/0.83  % (27681)Termination phase: Saturation
% 0.75/0.83  
% 0.75/0.83  % (27681)Memory used [KB]: 3008
% 0.75/0.83  % (27681)Time elapsed: 0.032 s
% 0.75/0.83  % (27681)Instructions burned: 79 (million)
% 0.75/0.83  % (27681)------------------------------
% 0.75/0.83  % (27681)------------------------------
% 0.75/0.84  % (27685)Instruction limit reached!
% 0.75/0.84  % (27685)------------------------------
% 0.75/0.84  % (27685)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.75/0.84  % (27685)Termination reason: Unknown
% 0.75/0.84  % (27685)Termination phase: Saturation
% 0.75/0.84  
% 0.75/0.84  % (27685)Memory used [KB]: 3630
% 0.75/0.84  % (27685)Time elapsed: 0.034 s
% 0.75/0.84  % (27685)Instructions burned: 84 (million)
% 0.75/0.84  % (27685)------------------------------
% 0.75/0.84  % (27685)------------------------------
% 0.75/0.84  % (27693)dis+1011_1258907:1048576_bsr=unit_only:to=lpo:drc=off:sil=2000:tgt=full:fde=none:sp=frequency:spb=goal:rnwc=on:nwc=6.70083:sac=on:newcnf=on:st=2:i=243:bs=unit_only:sd=3:afp=300:awrs=decay:awrsf=218:nm=16:ins=3:afq=3.76821:afr=on:ss=axioms:sgt=5:rawr=on:add=off:bsd=on_0 on theBenchmark for (2994ds/243Mi)
% 0.75/0.84  % (27694)lrs+1011_2:9_sil=2000:lsd=10:newcnf=on:i=117:sd=2:awrs=decay:ss=included:amm=off:ep=R_0 on theBenchmark for (2994ds/117Mi)
% 0.75/0.84  % (27687)Instruction limit reached!
% 0.75/0.84  % (27687)------------------------------
% 0.75/0.84  % (27687)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.75/0.84  % (27687)Termination reason: Unknown
% 0.75/0.84  % (27687)Termination phase: Property scanning
% 0.75/0.84  
% 0.75/0.84  % (27687)Memory used [KB]: 3412
% 0.75/0.84  % (27687)Time elapsed: 0.025 s
% 0.75/0.84  % (27687)Instructions burned: 57 (million)
% 0.75/0.84  % (27687)------------------------------
% 0.75/0.84  % (27687)------------------------------
% 0.75/0.85  % (27688)Instruction limit reached!
% 0.75/0.85  % (27688)------------------------------
% 0.75/0.85  % (27688)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.75/0.85  % (27688)Termination reason: Unknown
% 0.75/0.85  % (27688)Termination phase: Property scanning
% 0.75/0.85  
% 0.75/0.85  % (27688)Memory used [KB]: 3298
% 0.75/0.85  % (27688)Time elapsed: 0.023 s
% 0.75/0.85  % (27688)Instructions burned: 51 (million)
% 0.75/0.85  % (27688)------------------------------
% 0.75/0.85  % (27688)------------------------------
% 0.75/0.85  % (27692)Instruction limit reached!
% 0.75/0.85  % (27692)------------------------------
% 0.75/0.85  % (27692)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.75/0.85  % (27692)Termination reason: Unknown
% 0.75/0.85  % (27692)Termination phase: Property scanning
% 0.75/0.85  
% 0.75/0.85  % (27692)Memory used [KB]: 3297
% 0.75/0.85  % (27692)Time elapsed: 0.019 s
% 0.75/0.85  % (27692)Instructions burned: 43 (million)
% 0.75/0.85  % (27692)------------------------------
% 0.75/0.85  % (27692)------------------------------
% 0.75/0.85  % (27695)dis+1011_11:1_sil=2000:avsq=on:i=143:avsqr=1,16:ep=RS:rawr=on:aac=none:lsd=100:mep=off:fde=none:newcnf=on:bsr=unit_only_0 on theBenchmark for (2994ds/143Mi)
% 0.75/0.85  % (27690)Instruction limit reached!
% 0.75/0.85  % (27690)------------------------------
% 0.75/0.85  % (27690)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.75/0.85  % (27690)Termination reason: Unknown
% 0.75/0.85  % (27690)Termination phase: Saturation
% 0.75/0.85  
% 0.75/0.85  % (27690)Memory used [KB]: 2992
% 0.75/0.85  % (27690)Time elapsed: 0.024 s
% 0.75/0.85  % (27690)Instructions burned: 53 (million)
% 0.75/0.85  % (27690)------------------------------
% 0.75/0.85  % (27690)------------------------------
% 0.75/0.85  % (27696)lrs+1011_1:2_to=lpo:sil=8000:plsqc=1:plsq=on:plsqr=326,59:sp=weighted_frequency:plsql=on:nwc=10.0:newcnf=on:i=93:awrs=converge:awrsf=200:bd=off:ins=1:rawr=on:alpa=false:avsq=on:avsqr=1,16_0 on theBenchmark for (2994ds/93Mi)
% 0.75/0.85  % (27697)lrs+1666_1:1_sil=4000:sp=occurrence:sos=on:urr=on:newcnf=on:i=62:amm=off:ep=R:erd=off:nm=0:plsq=on:plsqr=14,1_0 on theBenchmark for (2994ds/62Mi)
% 0.75/0.85  % (27698)lrs+21_2461:262144_anc=none:drc=off:sil=2000:sp=occurrence:nwc=6.0:updr=off:st=3.0:i=32:sd=2:afp=4000:erml=3:nm=14:afq=2.0:uhcvi=on:ss=included:er=filter:abs=on:nicw=on:ile=on:sims=off:s2a=on:s2agt=50:s2at=-1.0:plsq=on:plsql=on:plsqc=2:plsqr=1,32:newcnf=on:bd=off:to=lpo_0 on theBenchmark for (2994ds/32Mi)
% 0.75/0.87  % (27698)Instruction limit reached!
% 0.75/0.87  % (27698)------------------------------
% 0.75/0.87  % (27698)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.75/0.87  % (27698)Termination reason: Unknown
% 0.75/0.87  % (27698)Termination phase: NewCNF
% 0.75/0.87  
% 0.75/0.87  % (27698)Memory used [KB]: 2886
% 0.75/0.87  % (27698)Time elapsed: 0.017 s
% 0.75/0.87  % (27698)Instructions burned: 32 (million)
% 0.75/0.87  % (27698)------------------------------
% 0.75/0.87  % (27698)------------------------------
% 0.75/0.87  % (27699)dis+1011_1:1_sil=16000:nwc=7.0:s2agt=64:s2a=on:i=1919:ss=axioms:sgt=8:lsd=50:sd=7_0 on theBenchmark for (2994ds/1919Mi)
% 0.75/0.87  % (27697)Instruction limit reached!
% 0.75/0.87  % (27697)------------------------------
% 0.75/0.87  % (27697)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.75/0.88  % (27697)Termination reason: Unknown
% 0.75/0.88  % (27697)Termination phase: Equality proxy
% 0.75/0.88  
% 0.75/0.88  % (27697)Memory used [KB]: 3374
% 0.75/0.88  % (27697)Time elapsed: 0.026 s
% 0.75/0.88  % (27697)Instructions burned: 62 (million)
% 0.75/0.88  % (27697)------------------------------
% 0.75/0.88  % (27697)------------------------------
% 0.75/0.88  % (27700)ott-32_5:1_sil=4000:sp=occurrence:urr=full:rp=on:nwc=5.0:newcnf=on:st=5.0:s2pl=on:i=55:sd=2:ins=2:ss=included:rawr=on:anc=none:sos=on:s2agt=8:spb=intro:ep=RS:avsq=on:avsqr=27,155:lma=on_0 on theBenchmark for (2994ds/55Mi)
% 0.75/0.88  % (27694)Instruction limit reached!
% 0.75/0.88  % (27694)------------------------------
% 0.75/0.88  % (27694)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.75/0.88  % (27694)Termination reason: Unknown
% 0.75/0.88  % (27694)Termination phase: Saturation
% 0.75/0.88  
% 0.75/0.88  % (27694)Memory used [KB]: 4180
% 0.75/0.88  % (27694)Time elapsed: 0.046 s
% 0.75/0.88  % (27694)Instructions burned: 117 (million)
% 0.75/0.88  % (27694)------------------------------
% 0.75/0.88  % (27694)------------------------------
% 0.75/0.88  % (27695)First to succeed.
% 0.75/0.89  % (27695)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-27678"
% 0.75/0.89  % (27701)lrs-1011_1:1_sil=2000:sos=on:urr=on:i=53:sd=1:bd=off:ins=3:av=off:ss=axioms:sgt=16:gsp=on:lsd=10_0 on theBenchmark for (2994ds/53Mi)
% 0.75/0.89  % (27695)Refutation found. Thanks to Tanya!
% 0.75/0.89  % SZS status Theorem for theBenchmark
% 0.75/0.89  % SZS output start Proof for theBenchmark
% See solution above
% 0.75/0.89  % (27695)------------------------------
% 0.75/0.89  % (27695)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.75/0.89  % (27695)Termination reason: Refutation
% 0.75/0.89  
% 0.75/0.89  % (27695)Memory used [KB]: 3759
% 0.75/0.89  % (27695)Time elapsed: 0.040 s
% 0.75/0.89  % (27695)Instructions burned: 100 (million)
% 0.75/0.89  % (27678)Success in time 0.573 s
% 0.75/0.89  % Vampire---4.8 exiting
%------------------------------------------------------------------------------