TSTP Solution File: SCT196_5 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SCT196_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n027.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 08:59:56 EDT 2024

% Result   : Theorem 0.58s 0.75s
% Output   : Refutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   83
% Syntax   : Number of formulae    :  106 (  13 unt;  76 typ;   0 def)
%            Number of atoms       :   87 (   8 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   99 (  42   ~;  36   |;  11   &)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   85 (  60   >;  25   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-6 aty)
%            Number of functors    :   65 (  65 usr;   7 con; 0-7 aty)
%            Number of variables   :  209 (  51   !;   7   ?; 209   :)
%                                         ( 151  !>;   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_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_2,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_3,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_4,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_5,type,
    combk: 
      !>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).

tff(func_def_6,type,
    order_215145569der_on: 
      !>[X0: $tType] : ( fun(X0,bool) > fun(fun(product_prod(X0,X0),bool),bool) ) ).

tff(func_def_7,type,
    top_top: 
      !>[X0: $tType] : X0 ).

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

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

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

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

tff(func_def_12,type,
    produc1605651328_split: 
      !>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).

tff(func_def_13,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_14,type,
    product_prod_rec: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).

tff(func_def_15,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_16,type,
    inv_image: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X1,X0) ) > fun(product_prod(X1,X1),bool) ) ).

tff(func_def_17,type,
    collect: 
      !>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).

tff(func_def_18,type,
    lex_prod: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(product_prod(X1,X1),bool) ) > fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) ) ).

tff(func_def_19,type,
    aa: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_20,type,
    fFalse: bool ).

tff(func_def_21,type,
    fTrue: bool ).

tff(func_def_22,type,
    f: 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_23,type,
    p: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).

tff(func_def_24,type,
    a: arrow_411405190le_alt ).

tff(func_def_25,type,
    b: arrow_411405190le_alt ).

tff(func_def_26,type,
    i: arrow_159774573e_indi ).

tff(func_def_27,type,
    sK0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > arrow_159774573e_indi ).

tff(func_def_28,type,
    sK1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > arrow_159774573e_indi ).

tff(func_def_29,type,
    sK2: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_30,type,
    sK3: 
      !>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X0,bool) ) > X0 ) ).

tff(func_def_31,type,
    sK4: 
      !>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X0,bool) ) > X0 ) ).

tff(func_def_32,type,
    sK5: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_33,type,
    sK6: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_34,type,
    sK7: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_35,type,
    sK8: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_36,type,
    sK9: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_37,type,
    sK10: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).

tff(func_def_38,type,
    sK11: 
      !>[X0: $tType] : X0 ).

tff(func_def_39,type,
    sK12: 
      !>[X0: $tType] : ( fun(X0,bool) > X0 ) ).

tff(func_def_40,type,
    sK13: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).

tff(func_def_41,type,
    sK14: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).

tff(func_def_42,type,
    sK15: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).

tff(func_def_43,type,
    sK16: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).

tff(func_def_44,type,
    sK17: 
      !>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).

tff(func_def_45,type,
    sK18: 
      !>[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_46,type,
    sK19: 
      !>[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_47,type,
    sK20: 
      !>[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_48,type,
    sK21: 
      !>[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_49,type,
    sK22: 
      !>[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_50,type,
    sK23: 
      !>[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_51,type,
    sK24: 
      !>[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_52,type,
    sK25: 
      !>[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_53,type,
    sK26: 
      !>[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_54,type,
    sK27: 
      !>[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_55,type,
    sK28: 
      !>[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_56,type,
    sK29: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).

tff(func_def_57,type,
    sK30: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).

tff(func_def_58,type,
    sK31: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).

tff(func_def_59,type,
    sK32: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_60,type,
    sK33: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(func_def_61,type,
    sK34: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).

tff(func_def_62,type,
    sK35: 
      !>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).

tff(pred_def_1,type,
    top: 
      !>[X0: $tType] : $o ).

tff(pred_def_2,type,
    in_rel: 
      !>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).

tff(pred_def_3,type,
    inv_imagep: 
      !>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).

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

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

tff(pred_def_6,type,
    trans: 
      !>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).

tff(pred_def_7,type,
    member: 
      !>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).

tff(pred_def_8,type,
    pp: bool > $o ).

tff(f266,plain,
    $false,
    inference(subsumption_resolution,[],[f265,f223]) ).

tff(f223,plain,
    ! [X0: arrow_411405190le_alt,X1: arrow_159774573e_indi] : ~ 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),X0),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X1)),
    inference(unit_resulting_resolution,[],[f184,f188]) ).

tff(f188,plain,
    ! [X0: $tType,X3: X0,X1: fun(product_prod(X0,X0),bool)] :
      ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
      | ~ irrefl(X0,X1) ),
    inference(cnf_transformation,[],[f147]) ).

tff(f147,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ( irrefl(X0,X1)
        | member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK2(X0,X1)),sK2(X0,X1)),X1) )
      & ( ! [X3: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
        | ~ irrefl(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f145,f146]) ).

tff(f146,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1)
     => member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK2(X0,X1)),sK2(X0,X1)),X1) ),
    introduced(choice_axiom,[]) ).

tff(f145,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ( irrefl(X0,X1)
        | ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) )
      & ( ! [X3: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
        | ~ irrefl(X0,X1) ) ),
    inference(rectify,[],[f144]) ).

tff(f144,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( ( irrefl(X0,X1)
        | ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) )
      & ( ! [X2: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1)
        | ~ irrefl(X0,X1) ) ),
    inference(nnf_transformation,[],[f99]) ).

tff(f99,plain,
    ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
      ( irrefl(X0,X1)
    <=> ! [X2: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) ),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ! [X0: $tType,X5: fun(product_prod(X0,X0),bool)] :
      ( irrefl(X0,X5)
    <=> ! [X6: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X6),X5) ),
    file('/export/starexec/sandbox/tmp/tmp.3TpEljTeFp/Vampire---4.8_30375',fact_0_irrefl__def) ).

tff(f184,plain,
    ! [X0: arrow_159774573e_indi] : irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),
    inference(cnf_transformation,[],[f97]) ).

tff(f97,plain,
    ! [X0: arrow_159774573e_indi] :
      ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
      & irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
      & trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
    inference(rectify,[],[f91]) ).

tff(f91,axiom,
    ! [X52: arrow_159774573e_indi] :
      ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X52))
      & irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X52))
      & trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X52)) ),
    file('/export/starexec/sandbox/tmp/tmp.3TpEljTeFp/Vampire---4.8_30375',conj_2) ).

tff(f265,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),a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
    inference(backward_demodulation,[],[f186,f261]) ).

tff(f261,plain,
    a = b,
    inference(unit_resulting_resolution,[],[f183,f184,f185,f187,f186,f182]) ).

tff(f182,plain,
    ! [X2: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: arrow_411405190le_alt] :
      ( ( 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),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
      | 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),X2),f(X0))
      | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0)))
      | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0)))
      | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0))) ),
    inference(cnf_transformation,[],[f143]) ).

tff(f143,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X1: arrow_411405190le_alt,X2: 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),X1),X2),f(X0))
          | ~ 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),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
          | ( X1 = X2 ) )
      | ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0)))
      | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0)))
      | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f141,f142]) ).

tff(f142,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ? [X3: arrow_159774573e_indi] :
          ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
          | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
          | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3)) )
     => ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0)))
        | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0)))
        | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f141,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X1: arrow_411405190le_alt,X2: 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),X1),X2),f(X0))
          | ~ 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),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
          | ( X1 = X2 ) )
      | ? [X3: arrow_159774573e_indi] :
          ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
          | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
          | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3)) ) ),
    inference(rectify,[],[f121]) ).

tff(f121,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X2: arrow_411405190le_alt,X3: 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),X2),X3),f(X0))
          | ~ 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),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
          | ( X2 = X3 ) )
      | ? [X1: arrow_159774573e_indi] :
          ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
          | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
          | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) ),
    inference(flattening,[],[f120]) ).

tff(f120,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X2: arrow_411405190le_alt,X3: 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),X2),X3),f(X0))
          | ~ 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),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
          | ( X2 = X3 ) )
      | ? [X1: arrow_159774573e_indi] :
          ( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
          | ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
          | ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) ),
    inference(ennf_transformation,[],[f96]) ).

tff(f96,plain,
    ! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X1: arrow_159774573e_indi] :
          ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
          & irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
          & trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) )
     => ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
          ( ( X2 != X3 )
         => ( 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),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
           => 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),X2),X3),f(X0)) ) ) ),
    inference(rectify,[],[f90]) ).

tff(f90,axiom,
    ! [X58: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
      ( ! [X28: arrow_159774573e_indi] :
          ( total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X58,X28))
          & irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X58,X28))
          & trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X58,X28)) )
     => ! [X59: arrow_411405190le_alt,X60: arrow_411405190le_alt] :
          ( ( X59 != X60 )
         => ( 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),X59),X60),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X58,i))
           => 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),X59),X60),f(X58)) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.3TpEljTeFp/Vampire---4.8_30375',conj_1) ).

tff(f187,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),f(p)),
    inference(cnf_transformation,[],[f98]) ).

tff(f98,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),f(p)),
    inference(flattening,[],[f94]) ).

tff(f94,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),a),b),f(p)),
    inference(negated_conjecture,[],[f93]) ).

tff(f93,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),a),b),f(p)),
    file('/export/starexec/sandbox/tmp/tmp.3TpEljTeFp/Vampire---4.8_30375',conj_4) ).

tff(f185,plain,
    ! [X0: arrow_159774573e_indi] : total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),
    inference(cnf_transformation,[],[f97]) ).

tff(f183,plain,
    ! [X0: arrow_159774573e_indi] : trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),
    inference(cnf_transformation,[],[f97]) ).

tff(f186,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),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
    inference(cnf_transformation,[],[f92]) ).

tff(f92,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),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
    file('/export/starexec/sandbox/tmp/tmp.3TpEljTeFp/Vampire---4.8_30375',conj_3) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SCT196_5 : TPTP v8.1.2. Released v6.0.0.
% 0.03/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35  % Computer : n027.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 13:36:36 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a TF1_THM_EQU_NAR problem
% 0.14/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.3TpEljTeFp/Vampire---4.8_30375
% 0.58/0.74  % (30490)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 (2996ds/56Mi)
% 0.58/0.74  % (30483)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 (2996ds/34Mi)
% 0.58/0.74  % (30485)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.58/0.74  % (30487)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 (2996ds/34Mi)
% 0.58/0.74  % (30486)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.58/0.74  % (30484)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 (2996ds/51Mi)
% 0.58/0.74  % (30488)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.58/0.74  % (30489)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 (2996ds/83Mi)
% 0.58/0.74  % (30489)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
% 0.58/0.75  % (30489)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.58/0.75  % (30486)First to succeed.
% 0.58/0.75  % (30488)Also succeeded, but the first one will report.
% 0.58/0.75  % (30486)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-30482"
% 0.58/0.75  % (30490)Instruction limit reached!
% 0.58/0.75  % (30490)------------------------------
% 0.58/0.75  % (30490)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.75  % (30490)Termination reason: Unknown
% 0.58/0.75  % (30490)Termination phase: Saturation
% 0.58/0.75  
% 0.58/0.75  % (30490)Memory used [KB]: 1429
% 0.58/0.75  % (30490)Time elapsed: 0.016 s
% 0.58/0.75  % (30490)Instructions burned: 60 (million)
% 0.58/0.75  % (30490)------------------------------
% 0.58/0.75  % (30490)------------------------------
% 0.58/0.75  % (30486)Refutation found. Thanks to Tanya!
% 0.58/0.75  % SZS status Theorem for Vampire---4
% 0.58/0.75  % SZS output start Proof for Vampire---4
% See solution above
% 0.58/0.75  % (30486)------------------------------
% 0.58/0.75  % (30486)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.75  % (30486)Termination reason: Refutation
% 0.58/0.75  
% 0.58/0.75  % (30486)Memory used [KB]: 1338
% 0.58/0.75  % (30486)Time elapsed: 0.014 s
% 0.58/0.75  % (30486)Instructions burned: 22 (million)
% 0.58/0.75  % (30482)Success in time 0.392 s
% 0.58/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------