TSTP Solution File: SCT241_5 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SCT241_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n002.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 Apr 30 14:57:26 EDT 2024

% Result   : Theorem 0.15s 0.52s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  123
% Syntax   : Number of formulae    :  135 (  10 unt; 119 typ;   0 def)
%            Number of atoms       :   27 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   28 (  17   ~;   7   |;   0   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  219 ( 103   >; 116   *;   0   +;   0  <<)
%            Number of predicates  :   17 (  16 usr;   1 prp; 0-5 aty)
%            Number of functors    :  100 ( 100 usr;  10 con; 0-7 aty)
%            Number of variables   :  292 (  15   !;   0   ?; 292   :)
%                                         ( 277  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    arrow_411405190le_alt: $tType ).

tff(type_def_6,type,
    arrow_159774573e_indi: $tType ).

tff(type_def_7,type,
    bool: $tType ).

tff(type_def_8,type,
    fun: ( $tType * $tType ) > $tType ).

tff(type_def_9,type,
    product_prod: ( $tType * $tType ) > $tType ).

tff(func_def_0,type,
    arrow_1985332922le_Lin: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool) ).

tff(func_def_1,type,
    arrow_610318064e_Prof: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),bool) ).

tff(func_def_2,type,
    arrow_1158827142_above: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_3,type,
    arrow_319942042_below: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_4,type,
    arrow_276188178_mkbot: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_5,type,
    arrow_424895264_mktop: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_6,type,
    product_Pair: 
      !>[X0: $tType,X1: $tType] : fun(X0,fun(X1,product_prod(X0,X1))) ).

tff(func_def_7,type,
    product_apfst: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X0,X2) ) > product_prod(X1,X2) ) ).

tff(func_def_8,type,
    product_apsnd: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X2,X0) ) > product_prod(X2,X1) ) ).

tff(func_def_9,type,
    product_curry: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X0,X1),X2) > fun(X0,fun(X1,X2)) ) ).

tff(func_def_10,type,
    produc1605651328_split: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).

tff(func_def_11,type,
    product_prod_case: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).

tff(func_def_12,type,
    product_prod_rec: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).

tff(func_def_13,type,
    product_scomp: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( fun(X0,product_prod(X1,X2)) * fun(X1,fun(X2,X3)) ) > fun(X0,X3) ) ).

tff(func_def_14,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_15,type,
    fFalse: bool ).

tff(func_def_16,type,
    fTrue: bool ).

tff(func_def_17,type,
    f: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).

tff(func_def_18,type,
    lab: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_19,type,
    a: arrow_411405190le_alt ).

tff(func_def_20,type,
    b: arrow_411405190le_alt ).

tff(func_def_21,type,
    sK10: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_22,type,
    sK11: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_23,type,
    sK12: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_24,type,
    sK13: ( arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(func_def_25,type,
    sK14: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).

tff(func_def_26,type,
    sK15: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).

tff(func_def_27,type,
    sK16: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).

tff(func_def_28,type,
    sK17: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).

tff(func_def_29,type,
    sK18: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).

tff(func_def_30,type,
    sK19: 
      !>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).

tff(func_def_31,type,
    sK20: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_32,type,
    sK21: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(func_def_33,type,
    sK22: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_34,type,
    sK23: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(func_def_35,type,
    sK24: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_36,type,
    sK25: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(func_def_37,type,
    sK26: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_38,type,
    sK27: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X0 ) ).

tff(func_def_39,type,
    sK28: 
      !>[X0: $tType,X1: $tType] : ( ( product_prod(X0,X1) * fun(X0,fun(X1,bool)) ) > X1 ) ).

tff(func_def_40,type,
    sK29: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_41,type,
    sK30: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X1 ) ).

tff(func_def_42,type,
    sK31: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * product_prod(X1,X0) ) > X0 ) ).

tff(func_def_43,type,
    sK32: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).

tff(func_def_44,type,
    sK33: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).

tff(func_def_45,type,
    sK34: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).

tff(func_def_46,type,
    sK35: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_47,type,
    sK36: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X2 ) ).

tff(func_def_48,type,
    sK37: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X1 ) ).

tff(func_def_49,type,
    sK38: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X2,product_prod(X1,X0)),bool) > X0 ) ).

tff(func_def_50,type,
    sK39: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).

tff(func_def_51,type,
    sK40: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).

tff(func_def_52,type,
    sK41: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).

tff(func_def_53,type,
    sK42: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).

tff(func_def_54,type,
    sK43: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_55,type,
    sK44: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_56,type,
    sK45: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).

tff(func_def_57,type,
    sK46: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X0 ) ).

tff(func_def_58,type,
    sK47: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,X1) * product_prod(X1,X2) ) > X2 ) ).

tff(func_def_59,type,
    sK48: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X0 ) ).

tff(func_def_60,type,
    sK49: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,X1)) * fun(X1,bool) ) > X2 ) ).

tff(func_def_61,type,
    sK50: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X0 ) ).

tff(func_def_62,type,
    sK51: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X2 ) ).

tff(func_def_63,type,
    sK52: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X1 ) ).

tff(func_def_64,type,
    sK53: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * product_prod(X1,X0) * fun(X1,fun(X0,fun(X2,bool))) ) > X0 ) ).

tff(func_def_65,type,
    sK54: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X2 ) ).

tff(func_def_66,type,
    sK55: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X1 ) ).

tff(func_def_67,type,
    sK56: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X0 ) ).

tff(func_def_68,type,
    sK57: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X2 * fun(X0,fun(X1,fun(X2,bool))) * product_prod(X0,X1) ) > X1 ) ).

tff(func_def_69,type,
    sK58: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X3 ) ).

tff(func_def_70,type,
    sK59: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X2 ) ).

tff(func_def_71,type,
    sK60: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X1 ) ).

tff(func_def_72,type,
    sK61: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( fun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),bool) > X0 ) ).

tff(func_def_73,type,
    sK62: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0 ) ).

tff(func_def_74,type,
    sK63: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X1 ) ).

tff(func_def_75,type,
    sK64: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2 ) ).

tff(func_def_76,type,
    sK65: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3 ) ).

tff(func_def_77,type,
    sK66: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4 ) ).

tff(func_def_78,type,
    sK67: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X2 ) ).

tff(func_def_79,type,
    sK68: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,X0)) * fun(X2,fun(X1,X0)) * product_prod(X2,X1) ) > X1 ) ).

tff(func_def_80,type,
    sK69: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X4 ) ).

tff(func_def_81,type,
    sK70: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X3 ) ).

tff(func_def_82,type,
    sK71: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X2 ) ).

tff(func_def_83,type,
    sK72: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X1 ) ).

tff(func_def_84,type,
    sK73: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( fun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),bool) > X0 ) ).

tff(func_def_85,type,
    sK74: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0 ) ).

tff(func_def_86,type,
    sK75: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1 ) ).

tff(func_def_87,type,
    sK76: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2 ) ).

tff(func_def_88,type,
    sK77: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3 ) ).

tff(func_def_89,type,
    sK78: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4 ) ).

tff(func_def_90,type,
    sK79: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5 ) ).

tff(func_def_91,type,
    sK80: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X5 ) ).

tff(func_def_92,type,
    sK81: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X4 ) ).

tff(func_def_93,type,
    sK82: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X3 ) ).

tff(func_def_94,type,
    sK83: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X2 ) ).

tff(func_def_95,type,
    sK84: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X1 ) ).

tff(func_def_96,type,
    sK85: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( fun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),bool) > X0 ) ).

tff(func_def_97,type,
    sK86: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).

tff(pred_def_1,type,
    arrow_1958449194le_IIA: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).

tff(pred_def_2,type,
    arrow_987702531ctator: ( fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_159774573e_indi ) > $o ).

tff(pred_def_3,type,
    arrow_2069624013nimity: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).

tff(pred_def_4,type,
    in_rel: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).

tff(pred_def_5,type,
    member: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).

tff(pred_def_6,type,
    pp: bool > $o ).

tff(pred_def_7,type,
    sP0: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_8,type,
    sP1: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_9,type,
    sP2: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_10,type,
    sP3: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_11,type,
    sP4: ( arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ) > $o ).

tff(pred_def_12,type,
    sP5: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_13,type,
    sP6: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_14,type,
    sP7: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(pred_def_15,type,
    sP8: ( arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ) > $o ).

tff(pred_def_16,type,
    sP9: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).

tff(f2181,plain,
    $false,
    inference(subsumption_resolution,[],[f2180,f350]) ).

tff(f350,plain,
    member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),lab,arrow_1985332922le_Lin),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),lab,arrow_1985332922le_Lin),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096Lab_A_058_ALin_096) ).

tff(f2180,plain,
    ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),lab,arrow_1985332922le_Lin),
    inference(subsumption_resolution,[],[f2115,f351]) ).

tff(f351,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),lab),
    inference(cnf_transformation,[],[f3]) ).

tff(f3,axiom,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),lab),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

tff(f2115,plain,
    ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),lab)
    | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),lab,arrow_1985332922le_Lin) ),
    inference(resolution,[],[f368,f344]) ).

tff(f344,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),lab),
    inference(cnf_transformation,[],[f82]) ).

tff(f82,plain,
    member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),lab),
    inference(flattening,[],[f81]) ).

tff(f81,negated_conjecture,
    ~ ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),lab),
    inference(negated_conjecture,[],[f80]) ).

tff(f80,conjecture,
    ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),lab),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f368,plain,
    ! [X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(cnf_transformation,[],[f170]) ).

tff(f170,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(flattening,[],[f169]) ).

tff(f169,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2)
      | ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
      | ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin) ),
    inference(ennf_transformation,[],[f94]) ).

tff(f94,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X2,arrow_1985332922le_Lin)
     => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X0),X2)
       => ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X0),X1),X2) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X12: arrow_411405190le_alt,X13: arrow_411405190le_alt,X16: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
      ( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X16,arrow_1985332922le_Lin)
     => ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X13),X12),X16)
       => ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X12),X13),X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_Lin__irrefl) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : SCT241_5 : TPTP v8.1.2. Released v6.0.0.
% 0.10/0.10  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n002.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Mon Apr 29 22:37:09 EDT 2024
% 0.15/0.31  % CPUTime    : 
% 0.15/0.31  % (5208)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.34  % (5211)WARNING: value z3 for option sas not known
% 0.15/0.34  % (5212)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.34  % (5214)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.34  % (5209)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.34  % (5215)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.34  % (5210)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.34  % (5211)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.34  % (5213)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.35  % (5215)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.35  % Exception at run slice level
% 0.15/0.35  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.35  % Exception at run slice level
% 0.15/0.35  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.35  % Exception at run slice level
% 0.15/0.35  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.36  % (5218)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.15/0.37  % (5216)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.15/0.37  % (5217)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.15/0.38  % (5216)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.38  % Exception at run slice level
% 0.15/0.38  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.38  % (5217)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39  % (5220)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.15/0.52  % (5218)First to succeed.
% 0.15/0.52  % (5218)Refutation found. Thanks to Tanya!
% 0.15/0.52  % SZS status Theorem for theBenchmark
% 0.15/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.52  % (5218)------------------------------
% 0.15/0.52  % (5218)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.52  % (5218)Termination reason: Refutation
% 0.15/0.52  
% 0.15/0.52  % (5218)Memory used [KB]: 2666
% 0.15/0.52  % (5218)Time elapsed: 0.160 s
% 0.15/0.52  % (5218)Instructions burned: 330 (million)
% 0.15/0.52  % (5218)------------------------------
% 0.15/0.52  % (5218)------------------------------
% 0.15/0.52  % (5208)Success in time 0.2 s
%------------------------------------------------------------------------------