TSTP Solution File: ITP006_2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : ITP006_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 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 : n004.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 : Sun May  5 06:46:52 EDT 2024

% Result   : Theorem 0.61s 0.83s
% Output   : Refutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :  108
% Syntax   : Number of formulae    :  157 (  18 unt;  98 typ;   0 def)
%            Number of atoms       :  549 (   8 equ)
%            Maximal formula atoms :   36 (   9 avg)
%            Number of connectives :  416 ( 151   ~; 125   |;  46   &)
%                                         (  31 <=>;  63  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :  225 ( 225 fml;   0 var)
%            Number of types       :    4 (   2 usr)
%            Number of type conns  :  187 (  90   >;  97   *;   0   +;   0  <<)
%            Number of predicates  :   68 (  66 usr;   4 prp; 0-4 aty)
%            Number of functors    :   35 (  35 usr;   6 con; 0-4 aty)
%            Number of variables   :  221 ( 195   !;  26   ?;  98   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    del: $tType ).

tff(type_def_6,type,
    tp__o: $tType ).

tff(func_def_0,type,
    bool: del ).

tff(func_def_1,type,
    ind: del ).

tff(func_def_2,type,
    arr: ( del * del ) > del ).

tff(func_def_4,type,
    k: ( del * $i ) > $i ).

tff(func_def_5,type,
    i: del > $i ).

tff(func_def_6,type,
    inj__o: tp__o > $i ).

tff(func_def_7,type,
    surj__o: $i > tp__o ).

tff(func_def_9,type,
    fo__c_2Ebool_2ET: tp__o ).

tff(func_def_10,type,
    c_2EquantHeuristics_2EGUESS__FORALL__GAP: ( del * del ) > $i ).

tff(func_def_11,type,
    c_2EquantHeuristics_2EGUESS__EXISTS__GAP: ( del * del ) > $i ).

tff(func_def_12,type,
    c_2EquantHeuristics_2EGUESS__FORALL__POINT: ( del * del ) > $i ).

tff(func_def_13,type,
    c_2EquantHeuristics_2EGUESS__EXISTS__POINT: ( del * del ) > $i ).

tff(func_def_14,type,
    c_2EquantHeuristics_2EGUESS__FORALL: ( del * del ) > $i ).

tff(func_def_15,type,
    c_2Ebool_2E_3F: del > $i ).

tff(func_def_16,type,
    c_2EquantHeuristics_2EGUESS__EXISTS: ( del * del ) > $i ).

tff(func_def_18,type,
    fo__c_2Ebool_2EF: tp__o ).

tff(func_def_20,type,
    fo__c_2Ebool_2E_5C_2F: ( tp__o * tp__o ) > tp__o ).

tff(func_def_22,type,
    fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).

tff(func_def_23,type,
    c_2Emin_2E_3D: del > $i ).

tff(func_def_25,type,
    fo__c_2Ebool_2E_7E: tp__o > tp__o ).

tff(func_def_27,type,
    fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).

tff(func_def_28,type,
    c_2Ebool_2E_21: del > $i ).

tff(func_def_29,type,
    sK0: del ).

tff(func_def_30,type,
    sK1: del ).

tff(func_def_34,type,
    sK30: ( del * $i * $i ) > $i ).

tff(func_def_35,type,
    sK31: ( del * del * $i * $i ) > $i ).

tff(func_def_36,type,
    sK32: ( del * del * $i * $i ) > $i ).

tff(func_def_37,type,
    sK33: ( del * $i * $i ) > $i ).

tff(func_def_38,type,
    sK34: ( del * $i * $i ) > $i ).

tff(func_def_39,type,
    sK35: ( del * $i * $i ) > $i ).

tff(func_def_40,type,
    sK36: ( del * $i * $i ) > $i ).

tff(func_def_41,type,
    sK37: ( del * del * $i * $i ) > $i ).

tff(func_def_42,type,
    sK38: ( del * del * $i * $i ) > $i ).

tff(func_def_43,type,
    sK39: ( del * $i * $i ) > $i ).

tff(func_def_44,type,
    sK40: ( del * $i * $i ) > $i ).

tff(pred_def_1,type,
    mem: ( $i * del ) > $o ).

tff(pred_def_3,type,
    sP5: ( tp__o * tp__o ) > $o ).

tff(pred_def_4,type,
    sP6: ( tp__o * tp__o ) > $o ).

tff(pred_def_5,type,
    sP7: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_6,type,
    sP8: ( tp__o * tp__o ) > $o ).

tff(pred_def_7,type,
    sP9: ( tp__o * tp__o ) > $o ).

tff(pred_def_8,type,
    sP10: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_9,type,
    sP11: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_10,type,
    sP12: ( tp__o * tp__o ) > $o ).

tff(pred_def_11,type,
    sP13: ( tp__o * tp__o ) > $o ).

tff(pred_def_12,type,
    sP14: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_13,type,
    sP15: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_14,type,
    sP16: ( tp__o * tp__o ) > $o ).

tff(pred_def_15,type,
    sP17: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_16,type,
    sP18: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_17,type,
    sP19: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_20,type,
    sP22: ( tp__o * tp__o ) > $o ).

tff(pred_def_21,type,
    sP23: ( tp__o * tp__o ) > $o ).

tff(pred_def_23,type,
    sP25: ( tp__o * tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_24,type,
    sP26: ( tp__o * tp__o ) > $o ).

tff(pred_def_25,type,
    sP27: ( tp__o * tp__o * tp__o ) > $o ).

tff(pred_def_28,type,
    sP41: ( $i * del ) > $o ).

tff(pred_def_29,type,
    sP42: ( $i * del ) > $o ).

tff(pred_def_30,type,
    sP43: ( del * $i * $i ) > $o ).

tff(pred_def_31,type,
    sP44: ( $i * del ) > $o ).

tff(pred_def_32,type,
    sP45: ( $i * del ) > $o ).

tff(pred_def_33,type,
    sP46: ( del * $i * $i ) > $o ).

tff(pred_def_34,type,
    sP47: del > $o ).

tff(pred_def_35,type,
    sP48: ( del * del ) > $o ).

tff(pred_def_36,type,
    sP49: del > $o ).

tff(pred_def_37,type,
    sP50: ( del * del ) > $o ).

tff(pred_def_38,type,
    sP51: del > $o ).

tff(pred_def_39,type,
    sP52: ( del * del ) > $o ).

tff(pred_def_40,type,
    sP53: ( $i * del * $i ) > $o ).

tff(pred_def_41,type,
    sP54: del > $o ).

tff(pred_def_42,type,
    sP55: ( del * del ) > $o ).

tff(pred_def_43,type,
    sP56: del > $o ).

tff(pred_def_44,type,
    sP57: ( del * del ) > $o ).

tff(pred_def_45,type,
    sP58: del > $o ).

tff(pred_def_46,type,
    sP59: ( del * del ) > $o ).

tff(pred_def_47,type,
    sP60: ( $i * del * $i ) > $o ).

tff(pred_def_48,type,
    sP61: del > $o ).

tff(pred_def_49,type,
    sP62: ( del * del ) > $o ).

tff(pred_def_50,type,
    sP63: del > $o ).

tff(pred_def_51,type,
    sP64: ( del * del ) > $o ).

tff(pred_def_52,type,
    sP65: del > $o ).

tff(pred_def_53,type,
    sP66: ( del * del ) > $o ).

tff(pred_def_54,type,
    sP67: del > $o ).

tff(pred_def_55,type,
    sP68: ( del * del ) > $o ).

tff(pred_def_56,type,
    sP69: del > $o ).

tff(pred_def_57,type,
    sP70: ( del * del ) > $o ).

tff(pred_def_58,type,
    sP71: del > $o ).

tff(pred_def_59,type,
    sP72: ( del * del ) > $o ).

tff(pred_def_60,type,
    sP73: del > $o ).

tff(pred_def_61,type,
    sP74: ( del * del ) > $o ).

tff(pred_def_62,type,
    sP75: del > $o ).

tff(pred_def_63,type,
    sP76: ( del * del ) > $o ).

tff(pred_def_64,type,
    sP77: del > $o ).

tff(pred_def_65,type,
    sP78: ( del * del ) > $o ).

tff(pred_def_66,type,
    sP79: del > $o ).

tff(pred_def_67,type,
    sP80: ( del * del ) > $o ).

tff(f639,plain,
    $false,
    inference(subsumption_resolution,[],[f629,f607]) ).

tff(f607,plain,
    ~ p(ap(sK3,ap(sK2,sK36(sK1,sK2,sK4)))),
    inference(unit_resulting_resolution,[],[f600,f604,f319]) ).

tff(f319,plain,
    ! [X0: del,X14: $i,X12: $i,X13: $i] :
      ( ~ p(ap(X13,ap(X12,X14)))
      | ~ mem(X14,X0)
      | ~ sP60(X13,X0,X12) ),
    inference(general_splitting,[],[f317,f318_D]) ).

tff(f318,plain,
    ! [X0: del,X1: del,X12: $i,X13: $i] :
      ( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
      | ~ mem(X13,arr(X1,bool))
      | ~ mem(X12,arr(X0,X1))
      | ~ sP58(X1)
      | ~ sP59(X0,X1)
      | sP60(X13,X0,X12) ),
    inference(cnf_transformation,[],[f318_D]) ).

tff(f318_D,plain,
    ! [X12,X0,X13] :
      ( ! [X1] :
          ( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
          | ~ mem(X13,arr(X1,bool))
          | ~ mem(X12,arr(X0,X1))
          | ~ sP58(X1)
          | ~ sP59(X0,X1) )
    <=> ~ sP60(X13,X0,X12) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP60])]) ).

tff(f317,plain,
    ! [X0: del,X1: del,X14: $i,X12: $i,X13: $i] :
      ( ~ mem(X12,arr(X0,X1))
      | ~ mem(X13,arr(X1,bool))
      | ~ mem(X14,X0)
      | ~ p(ap(X13,ap(X12,X14)))
      | ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
      | ~ sP58(X1)
      | ~ sP59(X0,X1) ),
    inference(general_splitting,[],[f315,f316_D]) ).

tff(f316,plain,
    ! [X2: $i,X0: del,X1: del] :
      ( ~ mem(X2,arr(X0,X1))
      | sP59(X0,X1) ),
    inference(cnf_transformation,[],[f316_D]) ).

tff(f316_D,plain,
    ! [X1,X0] :
      ( ! [X2] : ~ mem(X2,arr(X0,X1))
    <=> ~ sP59(X0,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP59])]) ).

tff(f315,plain,
    ! [X2: $i,X0: del,X1: del,X14: $i,X12: $i,X13: $i] :
      ( ~ mem(X2,arr(X0,X1))
      | ~ mem(X12,arr(X0,X1))
      | ~ mem(X13,arr(X1,bool))
      | ~ mem(X14,X0)
      | ~ p(ap(X13,ap(X12,X14)))
      | ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
      | ~ sP58(X1) ),
    inference(general_splitting,[],[f256,f314_D]) ).

tff(f314,plain,
    ! [X3: $i,X1: del] :
      ( ~ mem(X3,arr(X1,bool))
      | sP58(X1) ),
    inference(cnf_transformation,[],[f314_D]) ).

tff(f314_D,plain,
    ! [X1] :
      ( ! [X3] : ~ mem(X3,arr(X1,bool))
    <=> ~ sP58(X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP58])]) ).

tff(f256,plain,
    ! [X2: $i,X3: $i,X0: del,X1: del,X14: $i,X12: $i,X13: $i] :
      ( ~ mem(X2,arr(X0,X1))
      | ~ mem(X3,arr(X1,bool))
      | ~ mem(X12,arr(X0,X1))
      | ~ mem(X13,arr(X1,bool))
      | ~ mem(X14,X0)
      | ~ p(ap(X13,ap(X12,X14)))
      | ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13)) ),
    inference(cnf_transformation,[],[f113]) ).

tff(f113,plain,
    ! [X0: del,X1: del,X2] :
      ( ! [X3] :
          ( ( ! [X4] :
                ( ! [X5] :
                    ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X0,X1),X4),X5))
                    <=> ! [X6] :
                          ( ? [X7] :
                              ( ( ap(X4,X7) = X6 )
                              & mem(X7,X0) )
                          | p(ap(X5,X6))
                          | ~ mem(X6,X1) ) )
                    | ~ mem(X5,arr(X1,bool)) )
                | ~ mem(X4,arr(X0,X1)) )
            & ! [X8] :
                ( ! [X9] :
                    ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X0,X1),X8),X9))
                    <=> ! [X10] :
                          ( ? [X11] :
                              ( ( ap(X8,X11) = X10 )
                              & mem(X11,X0) )
                          | ~ p(ap(X9,X10))
                          | ~ mem(X10,X1) ) )
                    | ~ mem(X9,arr(X1,bool)) )
                | ~ mem(X8,arr(X0,X1)) )
            & ! [X12] :
                ( ! [X13] :
                    ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
                    <=> ! [X14] :
                          ( ~ p(ap(X13,ap(X12,X14)))
                          | ~ mem(X14,X0) ) )
                    | ~ mem(X13,arr(X1,bool)) )
                | ~ mem(X12,arr(X0,X1)) )
            & ! [X15] :
                ( ! [X16] :
                    ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X15),X16))
                    <=> ! [X17] :
                          ( p(ap(X16,ap(X15,X17)))
                          | ~ mem(X17,X0) ) )
                    | ~ mem(X16,arr(X1,bool)) )
                | ~ mem(X15,arr(X0,X1)) )
            & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X0,X1),X2),X3))
            <=> ! [X18] :
                  ( ? [X19] :
                      ( ~ p(ap(X3,ap(X2,X19)))
                      & mem(X19,X0) )
                  | p(ap(X3,X18))
                  | ~ mem(X18,X1) ) )
            & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X0,X1),X2),X3))
            <=> ! [X20] :
                  ( ? [X21] :
                      ( p(ap(X3,ap(X2,X21)))
                      & mem(X21,X0) )
                  | ~ p(ap(X3,X20))
                  | ~ mem(X20,X1) ) ) )
          | ~ mem(X3,arr(X1,bool)) )
      | ~ mem(X2,arr(X0,X1)) ),
    inference(flattening,[],[f112]) ).

tff(f112,plain,
    ! [X0: del,X1: del,X2] :
      ( ! [X3] :
          ( ( ! [X4] :
                ( ! [X5] :
                    ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X0,X1),X4),X5))
                    <=> ! [X6] :
                          ( ? [X7] :
                              ( ( ap(X4,X7) = X6 )
                              & mem(X7,X0) )
                          | p(ap(X5,X6))
                          | ~ mem(X6,X1) ) )
                    | ~ mem(X5,arr(X1,bool)) )
                | ~ mem(X4,arr(X0,X1)) )
            & ! [X8] :
                ( ! [X9] :
                    ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X0,X1),X8),X9))
                    <=> ! [X10] :
                          ( ? [X11] :
                              ( ( ap(X8,X11) = X10 )
                              & mem(X11,X0) )
                          | ~ p(ap(X9,X10))
                          | ~ mem(X10,X1) ) )
                    | ~ mem(X9,arr(X1,bool)) )
                | ~ mem(X8,arr(X0,X1)) )
            & ! [X12] :
                ( ! [X13] :
                    ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
                    <=> ! [X14] :
                          ( ~ p(ap(X13,ap(X12,X14)))
                          | ~ mem(X14,X0) ) )
                    | ~ mem(X13,arr(X1,bool)) )
                | ~ mem(X12,arr(X0,X1)) )
            & ! [X15] :
                ( ! [X16] :
                    ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X15),X16))
                    <=> ! [X17] :
                          ( p(ap(X16,ap(X15,X17)))
                          | ~ mem(X17,X0) ) )
                    | ~ mem(X16,arr(X1,bool)) )
                | ~ mem(X15,arr(X0,X1)) )
            & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X0,X1),X2),X3))
            <=> ! [X18] :
                  ( ? [X19] :
                      ( ~ p(ap(X3,ap(X2,X19)))
                      & mem(X19,X0) )
                  | p(ap(X3,X18))
                  | ~ mem(X18,X1) ) )
            & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X0,X1),X2),X3))
            <=> ! [X20] :
                  ( ? [X21] :
                      ( p(ap(X3,ap(X2,X21)))
                      & mem(X21,X0) )
                  | ~ p(ap(X3,X20))
                  | ~ mem(X20,X1) ) ) )
          | ~ mem(X3,arr(X1,bool)) )
      | ~ mem(X2,arr(X0,X1)) ),
    inference(ennf_transformation,[],[f79]) ).

tff(f79,plain,
    ! [X0: del,X1: del,X2] :
      ( mem(X2,arr(X0,X1))
     => ! [X3] :
          ( mem(X3,arr(X1,bool))
         => ( ! [X4] :
                ( mem(X4,arr(X0,X1))
               => ! [X5] :
                    ( mem(X5,arr(X1,bool))
                   => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X0,X1),X4),X5))
                    <=> ! [X6] :
                          ( mem(X6,X1)
                         => ( ~ p(ap(X5,X6))
                           => ? [X7] :
                                ( ( ap(X4,X7) = X6 )
                                & mem(X7,X0) ) ) ) ) ) )
            & ! [X8] :
                ( mem(X8,arr(X0,X1))
               => ! [X9] :
                    ( mem(X9,arr(X1,bool))
                   => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X0,X1),X8),X9))
                    <=> ! [X10] :
                          ( mem(X10,X1)
                         => ( p(ap(X9,X10))
                           => ? [X11] :
                                ( ( ap(X8,X11) = X10 )
                                & mem(X11,X0) ) ) ) ) ) )
            & ! [X12] :
                ( mem(X12,arr(X0,X1))
               => ! [X13] :
                    ( mem(X13,arr(X1,bool))
                   => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
                    <=> ! [X14] :
                          ( mem(X14,X0)
                         => ~ p(ap(X13,ap(X12,X14))) ) ) ) )
            & ! [X15] :
                ( mem(X15,arr(X0,X1))
               => ! [X16] :
                    ( mem(X16,arr(X1,bool))
                   => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X15),X16))
                    <=> ! [X17] :
                          ( mem(X17,X0)
                         => p(ap(X16,ap(X15,X17))) ) ) ) )
            & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X0,X1),X2),X3))
            <=> ! [X18] :
                  ( mem(X18,X1)
                 => ( ~ p(ap(X3,X18))
                   => ? [X19] :
                        ( ~ p(ap(X3,ap(X2,X19)))
                        & mem(X19,X0) ) ) ) )
            & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X0,X1),X2),X3))
            <=> ! [X20] :
                  ( mem(X20,X1)
                 => ( p(ap(X3,X20))
                   => ? [X21] :
                        ( p(ap(X3,ap(X2,X21)))
                        & mem(X21,X0) ) ) ) ) ) ) ),
    inference(rectify,[],[f46]) ).

tff(f46,axiom,
    ! [X8: del,X9: del,X21] :
      ( mem(X21,arr(X8,X9))
     => ! [X22] :
          ( mem(X22,arr(X9,bool))
         => ( ! [X37] :
                ( mem(X37,arr(X8,X9))
               => ! [X38] :
                    ( mem(X38,arr(X9,bool))
                   => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X8,X9),X37),X38))
                    <=> ! [X39] :
                          ( mem(X39,X9)
                         => ( ~ p(ap(X38,X39))
                           => ? [X40] :
                                ( ( ap(X37,X40) = X39 )
                                & mem(X40,X8) ) ) ) ) ) )
            & ! [X33] :
                ( mem(X33,arr(X8,X9))
               => ! [X34] :
                    ( mem(X34,arr(X9,bool))
                   => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X8,X9),X33),X34))
                    <=> ! [X35] :
                          ( mem(X35,X9)
                         => ( p(ap(X34,X35))
                           => ? [X36] :
                                ( ( ap(X33,X36) = X35 )
                                & mem(X36,X8) ) ) ) ) ) )
            & ! [X30] :
                ( mem(X30,arr(X8,X9))
               => ! [X31] :
                    ( mem(X31,arr(X9,bool))
                   => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X8,X9),X30),X31))
                    <=> ! [X32] :
                          ( mem(X32,X8)
                         => ~ p(ap(X31,ap(X30,X32))) ) ) ) )
            & ! [X27] :
                ( mem(X27,arr(X8,X9))
               => ! [X28] :
                    ( mem(X28,arr(X9,bool))
                   => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X8,X9),X27),X28))
                    <=> ! [X29] :
                          ( mem(X29,X8)
                         => p(ap(X28,ap(X27,X29))) ) ) ) )
            & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X8,X9),X21),X22))
            <=> ! [X25] :
                  ( mem(X25,X9)
                 => ( ~ p(ap(X22,X25))
                   => ? [X26] :
                        ( ~ p(ap(X22,ap(X21,X26)))
                        & mem(X26,X8) ) ) ) )
            & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X8,X9),X21),X22))
            <=> ! [X23] :
                  ( mem(X23,X9)
                 => ( p(ap(X22,X23))
                   => ? [X24] :
                        ( p(ap(X22,ap(X21,X24)))
                        & mem(X24,X8) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.9tnApr3Tqf/Vampire---4.8_24836',conj_thm_2EquantHeuristics_2EGUESS__REWRITES) ).

tff(f604,plain,
    mem(sK36(sK1,sK2,sK4),sK1),
    inference(unit_resulting_resolution,[],[f364,f118,f122,f120,f554,f313]) ).

tff(f313,plain,
    ! [X0: del,X1: del,X12: $i,X13: $i] :
      ( ~ mem(X13,arr(X1,bool))
      | ~ mem(X12,arr(X0,X1))
      | mem(sK36(X0,X12,X13),X0)
      | p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
      | ~ sP56(X1)
      | ~ sP57(X0,X1) ),
    inference(general_splitting,[],[f311,f312_D]) ).

tff(f312,plain,
    ! [X2: $i,X0: del,X1: del] :
      ( ~ mem(X2,arr(X0,X1))
      | sP57(X0,X1) ),
    inference(cnf_transformation,[],[f312_D]) ).

tff(f312_D,plain,
    ! [X1,X0] :
      ( ! [X2] : ~ mem(X2,arr(X0,X1))
    <=> ~ sP57(X0,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP57])]) ).

tff(f311,plain,
    ! [X2: $i,X0: del,X1: del,X12: $i,X13: $i] :
      ( ~ mem(X2,arr(X0,X1))
      | ~ mem(X12,arr(X0,X1))
      | ~ mem(X13,arr(X1,bool))
      | mem(sK36(X0,X12,X13),X0)
      | p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
      | ~ sP56(X1) ),
    inference(general_splitting,[],[f257,f310_D]) ).

tff(f310,plain,
    ! [X3: $i,X1: del] :
      ( ~ mem(X3,arr(X1,bool))
      | sP56(X1) ),
    inference(cnf_transformation,[],[f310_D]) ).

tff(f310_D,plain,
    ! [X1] :
      ( ! [X3] : ~ mem(X3,arr(X1,bool))
    <=> ~ sP56(X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP56])]) ).

tff(f257,plain,
    ! [X2: $i,X3: $i,X0: del,X1: del,X12: $i,X13: $i] :
      ( ~ mem(X2,arr(X0,X1))
      | ~ mem(X3,arr(X1,bool))
      | ~ mem(X12,arr(X0,X1))
      | ~ mem(X13,arr(X1,bool))
      | mem(sK36(X0,X12,X13),X0)
      | p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13)) ),
    inference(cnf_transformation,[],[f113]) ).

tff(f554,plain,
    sP57(sK1,sK0),
    inference(unit_resulting_resolution,[],[f122,f312]) ).

tff(f120,plain,
    ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK1,sK0),sK2),sK4)),
    inference(cnf_transformation,[],[f89]) ).

tff(f89,plain,
    ? [X0: del,X1: del,X2] :
      ( ? [X3] :
          ( ? [X4] :
              ( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X4))
              & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X3))
              & ! [X5] :
                  ( p(ap(X3,X5))
                  | ~ p(ap(X4,X5))
                  | ~ mem(X5,X0) )
              & mem(X4,arr(X0,bool)) )
          & mem(X3,arr(X0,bool)) )
      & mem(X2,arr(X1,X0)) ),
    inference(flattening,[],[f88]) ).

tff(f88,plain,
    ? [X0: del,X1: del,X2] :
      ( ? [X3] :
          ( ? [X4] :
              ( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X4))
              & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X3))
              & ! [X5] :
                  ( p(ap(X3,X5))
                  | ~ p(ap(X4,X5))
                  | ~ mem(X5,X0) )
              & mem(X4,arr(X0,bool)) )
          & mem(X3,arr(X0,bool)) )
      & mem(X2,arr(X1,X0)) ),
    inference(ennf_transformation,[],[f60]) ).

tff(f60,plain,
    ~ ! [X0: del,X1: del,X2] :
        ( mem(X2,arr(X1,X0))
       => ! [X3] :
            ( mem(X3,arr(X0,bool))
           => ! [X4] :
                ( mem(X4,arr(X0,bool))
               => ( ! [X5] :
                      ( mem(X5,X0)
                     => ( p(ap(X4,X5))
                       => p(ap(X3,X5)) ) )
                 => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X3))
                   => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X4)) ) ) ) ) ),
    inference(rectify,[],[f59]) ).

tff(f59,negated_conjecture,
    ~ ! [X8: del,X9: del,X21] :
        ( mem(X21,arr(X9,X8))
       => ! [X22] :
            ( mem(X22,arr(X8,bool))
           => ! [X46] :
                ( mem(X46,arr(X8,bool))
               => ( ! [X47] :
                      ( mem(X47,X8)
                     => ( p(ap(X46,X47))
                       => p(ap(X22,X47)) ) )
                 => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X9,X8),X21),X22))
                   => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X9,X8),X21),X46)) ) ) ) ) ),
    inference(negated_conjecture,[],[f58]) ).

tff(f58,conjecture,
    ! [X8: del,X9: del,X21] :
      ( mem(X21,arr(X9,X8))
     => ! [X22] :
          ( mem(X22,arr(X8,bool))
         => ! [X46] :
              ( mem(X46,arr(X8,bool))
             => ( ! [X47] :
                    ( mem(X47,X8)
                   => ( p(ap(X46,X47))
                     => p(ap(X22,X47)) ) )
               => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X9,X8),X21),X22))
                 => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X9,X8),X21),X46)) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.9tnApr3Tqf/Vampire---4.8_24836',conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).

tff(f122,plain,
    mem(sK2,arr(sK1,sK0)),
    inference(cnf_transformation,[],[f89]) ).

tff(f118,plain,
    mem(sK4,arr(sK0,bool)),
    inference(cnf_transformation,[],[f89]) ).

tff(f364,plain,
    sP56(sK0),
    inference(unit_resulting_resolution,[],[f118,f310]) ).

tff(f600,plain,
    sP60(sK3,sK1,sK2),
    inference(subsumption_resolution,[],[f599,f555]) ).

tff(f555,plain,
    sP59(sK1,sK0),
    inference(unit_resulting_resolution,[],[f122,f316]) ).

tff(f599,plain,
    ( ~ sP59(sK1,sK0)
    | sP60(sK3,sK1,sK2) ),
    inference(subsumption_resolution,[],[f598,f365]) ).

tff(f365,plain,
    sP58(sK0),
    inference(unit_resulting_resolution,[],[f118,f314]) ).

tff(f598,plain,
    ( ~ sP58(sK0)
    | ~ sP59(sK1,sK0)
    | sP60(sK3,sK1,sK2) ),
    inference(subsumption_resolution,[],[f597,f122]) ).

tff(f597,plain,
    ( ~ mem(sK2,arr(sK1,sK0))
    | ~ sP58(sK0)
    | ~ sP59(sK1,sK0)
    | sP60(sK3,sK1,sK2) ),
    inference(subsumption_resolution,[],[f594,f121]) ).

tff(f121,plain,
    mem(sK3,arr(sK0,bool)),
    inference(cnf_transformation,[],[f89]) ).

tff(f594,plain,
    ( ~ mem(sK3,arr(sK0,bool))
    | ~ mem(sK2,arr(sK1,sK0))
    | ~ sP58(sK0)
    | ~ sP59(sK1,sK0)
    | sP60(sK3,sK1,sK2) ),
    inference(resolution,[],[f119,f318]) ).

tff(f119,plain,
    p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK1,sK0),sK2),sK3)),
    inference(cnf_transformation,[],[f89]) ).

tff(f629,plain,
    p(ap(sK3,ap(sK2,sK36(sK1,sK2,sK4)))),
    inference(unit_resulting_resolution,[],[f606,f603,f117]) ).

tff(f117,plain,
    ! [X5: $i] :
      ( ~ p(ap(sK4,X5))
      | ~ mem(X5,sK0)
      | p(ap(sK3,X5)) ),
    inference(cnf_transformation,[],[f89]) ).

tff(f603,plain,
    p(ap(sK4,ap(sK2,sK36(sK1,sK2,sK4)))),
    inference(unit_resulting_resolution,[],[f363,f118,f122,f120,f553,f309]) ).

tff(f309,plain,
    ! [X0: del,X1: del,X12: $i,X13: $i] :
      ( ~ mem(X13,arr(X1,bool))
      | ~ mem(X12,arr(X0,X1))
      | p(ap(X13,ap(X12,sK36(X0,X12,X13))))
      | p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
      | ~ sP54(X1)
      | ~ sP55(X0,X1) ),
    inference(general_splitting,[],[f307,f308_D]) ).

tff(f308,plain,
    ! [X2: $i,X0: del,X1: del] :
      ( ~ mem(X2,arr(X0,X1))
      | sP55(X0,X1) ),
    inference(cnf_transformation,[],[f308_D]) ).

tff(f308_D,plain,
    ! [X1,X0] :
      ( ! [X2] : ~ mem(X2,arr(X0,X1))
    <=> ~ sP55(X0,X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP55])]) ).

tff(f307,plain,
    ! [X2: $i,X0: del,X1: del,X12: $i,X13: $i] :
      ( ~ mem(X2,arr(X0,X1))
      | ~ mem(X12,arr(X0,X1))
      | ~ mem(X13,arr(X1,bool))
      | p(ap(X13,ap(X12,sK36(X0,X12,X13))))
      | p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
      | ~ sP54(X1) ),
    inference(general_splitting,[],[f258,f306_D]) ).

tff(f306,plain,
    ! [X3: $i,X1: del] :
      ( ~ mem(X3,arr(X1,bool))
      | sP54(X1) ),
    inference(cnf_transformation,[],[f306_D]) ).

tff(f306_D,plain,
    ! [X1] :
      ( ! [X3] : ~ mem(X3,arr(X1,bool))
    <=> ~ sP54(X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP54])]) ).

tff(f258,plain,
    ! [X2: $i,X3: $i,X0: del,X1: del,X12: $i,X13: $i] :
      ( ~ mem(X2,arr(X0,X1))
      | ~ mem(X3,arr(X1,bool))
      | ~ mem(X12,arr(X0,X1))
      | ~ mem(X13,arr(X1,bool))
      | p(ap(X13,ap(X12,sK36(X0,X12,X13))))
      | p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13)) ),
    inference(cnf_transformation,[],[f113]) ).

tff(f553,plain,
    sP55(sK1,sK0),
    inference(unit_resulting_resolution,[],[f122,f308]) ).

tff(f363,plain,
    sP54(sK0),
    inference(unit_resulting_resolution,[],[f118,f306]) ).

tff(f606,plain,
    mem(ap(sK2,sK36(sK1,sK2,sK4)),sK0),
    inference(unit_resulting_resolution,[],[f122,f604,f245]) ).

tff(f245,plain,
    ! [X2: $i,X3: $i,X0: del,X1: del] :
      ( ~ mem(X2,arr(X0,X1))
      | ~ mem(X3,X0)
      | mem(ap(X2,X3),X1) ),
    inference(cnf_transformation,[],[f111]) ).

tff(f111,plain,
    ! [X0: del,X1: del,X2] :
      ( ! [X3] :
          ( mem(ap(X2,X3),X1)
          | ~ mem(X3,X0) )
      | ~ mem(X2,arr(X0,X1)) ),
    inference(ennf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: del,X1: del,X2] :
      ( mem(X2,arr(X0,X1))
     => ! [X3] :
          ( mem(X3,X0)
         => mem(ap(X2,X3),X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.9tnApr3Tqf/Vampire---4.8_24836',ap_tp) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : ITP006_2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.10/0.12  % 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
% 0.11/0.32  % Computer : n004.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri May  3 19:21:53 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  This is a TF0_THM_EQU_NAR problem
% 0.11/0.32  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/tmp/tmp.9tnApr3Tqf/Vampire---4.8_24836
% 0.61/0.81  % (24954)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.61/0.81  % (24955)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 Vampire---4 for (2995ds/34Mi)
% 0.61/0.81  % (24951)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 Vampire---4 for (2995ds/34Mi)
% 0.61/0.81  % (24956)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.61/0.81  % (24953)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.61/0.81  % (24952)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 Vampire---4 for (2995ds/51Mi)
% 0.61/0.81  % (24957)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 Vampire---4 for (2995ds/83Mi)
% 0.61/0.81  % (24958)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2995ds/56Mi)
% 0.61/0.81  % (24958)Refutation not found, incomplete strategy% (24958)------------------------------
% 0.61/0.81  % (24958)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.81  % (24958)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.81  
% 0.61/0.81  % (24958)Memory used [KB]: 1044
% 0.61/0.81  % (24958)Time elapsed: 0.002 s
% 0.61/0.81  % (24958)Instructions burned: 2 (million)
% 0.61/0.81  % (24958)------------------------------
% 0.61/0.81  % (24958)------------------------------
% 0.61/0.81  % (24956)Refutation not found, incomplete strategy% (24956)------------------------------
% 0.61/0.81  % (24956)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.81  % (24956)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.81  
% 0.61/0.81  % (24956)Memory used [KB]: 1044
% 0.61/0.81  % (24956)Time elapsed: 0.004 s
% 0.61/0.81  % (24956)Instructions burned: 2 (million)
% 0.61/0.81  % (24956)------------------------------
% 0.61/0.81  % (24956)------------------------------
% 0.61/0.81  % (24959)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 Vampire---4 for (2995ds/55Mi)
% 0.61/0.81  % (24960)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 Vampire---4 for (2995ds/50Mi)
% 0.61/0.82  % (24954)Instruction limit reached!
% 0.61/0.82  % (24954)------------------------------
% 0.61/0.82  % (24954)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.82  % (24957)First to succeed.
% 0.61/0.82  % (24954)Termination reason: Unknown
% 0.61/0.82  % (24954)Termination phase: Saturation
% 0.61/0.82  
% 0.61/0.82  % (24954)Memory used [KB]: 1347
% 0.61/0.82  % (24954)Time elapsed: 0.017 s
% 0.61/0.82  % (24954)Instructions burned: 33 (million)
% 0.61/0.82  % (24954)------------------------------
% 0.61/0.82  % (24954)------------------------------
% 0.61/0.82  % (24951)Instruction limit reached!
% 0.61/0.82  % (24951)------------------------------
% 0.61/0.82  % (24951)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.82  % (24951)Termination reason: Unknown
% 0.61/0.82  % (24951)Termination phase: Saturation
% 0.61/0.83  
% 0.61/0.83  % (24951)Memory used [KB]: 1529
% 0.61/0.83  % (24951)Time elapsed: 0.019 s
% 0.61/0.83  % (24951)Instructions burned: 34 (million)
% 0.61/0.83  % (24951)------------------------------
% 0.61/0.83  % (24951)------------------------------
% 0.61/0.83  % (24955)Instruction limit reached!
% 0.61/0.83  % (24955)------------------------------
% 0.61/0.83  % (24955)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.83  % (24955)Termination reason: Unknown
% 0.61/0.83  % (24957)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24947"
% 0.61/0.83  % (24955)Termination phase: Saturation
% 0.61/0.83  
% 0.61/0.83  % (24955)Memory used [KB]: 1667
% 0.61/0.83  % (24955)Time elapsed: 0.019 s
% 0.61/0.83  % (24955)Instructions burned: 35 (million)
% 0.61/0.83  % (24955)------------------------------
% 0.61/0.83  % (24955)------------------------------
% 0.61/0.83  % (24957)Refutation found. Thanks to Tanya!
% 0.61/0.83  % SZS status Theorem for Vampire---4
% 0.61/0.83  % SZS output start Proof for Vampire---4
% See solution above
% 0.61/0.83  % (24957)------------------------------
% 0.61/0.83  % (24957)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.83  % (24957)Termination reason: Refutation
% 0.61/0.83  
% 0.61/0.83  % (24957)Memory used [KB]: 1553
% 0.61/0.83  % (24957)Time elapsed: 0.018 s
% 0.61/0.83  % (24957)Instructions burned: 35 (million)
% 0.61/0.83  % (24947)Success in time 0.499 s
% 0.61/0.83  % Vampire---4.8 exiting
%------------------------------------------------------------------------------