TSTP Solution File: DAT239^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT239^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n009.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 : Mon May 20 19:51:54 EDT 2024

% Result   : Theorem 2.41s 0.76s
% Output   : Refutation 2.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   84
% Syntax   : Number of formulae    :  135 (  31 unt;  75 typ;   0 def)
%            Number of atoms       :  464 (  78 equ;   0 cnn)
%            Maximal formula atoms :    3 (   7 avg)
%            Number of connectives :   70 (  34   ~;  26   |;   1   &;   0   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :  113 ( 112   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :   77 (  74 usr;   4 con; 0-6 aty)
%            Number of variables   :  100 (   0   ^  40   !;   0   ?; 100   :)
%                                         (  60  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    itself: $tType > $tType ).

thf(type_def_6,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_7,type,
    num: $tType ).

thf(type_def_8,type,
    nat: $tType ).

thf(type_def_9,type,
    int: $tType ).

thf(func_def_0,type,
    num: $tType ).

thf(func_def_1,type,
    nat: $tType ).

thf(func_def_2,type,
    int: $tType ).

thf(func_def_3,type,
    itself: $tType > $tType ).

thf(func_def_4,type,
    one: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_5,type,
    zero: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_6,type,
    numeral: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_7,type,
    field: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_8,type,
    neg_numeral: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_9,type,
    group_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_10,type,
    monoid_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_11,type,
    preorder: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_12,type,
    zero_neq_one: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_13,type,
    semiring_char_0: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_14,type,
    zero_less_one: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_15,type,
    semiring_div: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_16,type,
    division_ring: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_17,type,
    semigroup_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_18,type,
    semidom_divide: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_19,type,
    linordered_idom: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_20,type,
    linordered_field: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_21,type,
    ab_semigroup_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_22,type,
    linordered_semidom: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_23,type,
    semiring_div_parity: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_24,type,
    cancel_semigroup_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_25,type,
    semiring_numeral_div: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_26,type,
    cancel1352612707id_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_27,type,
    linord219039673up_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_28,type,
    ordere779506340up_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_29,type,
    linord1659791738miring: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_30,type,
    canoni770627133id_add: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_31,type,
    ordere236663937imp_le: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_32,type,
    ordere516151231imp_le: 
      !>[X0: $tType] : ( itself(X0) > $o ) ).

thf(func_def_33,type,
    one_one: 
      !>[X0: $tType] : X0 ).

thf(func_def_34,type,
    plus_plus: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_35,type,
    zero_zero: 
      !>[X0: $tType] : X0 ).

thf(func_def_36,type,
    neg_numeral_dbl: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_37,type,
    bit0: num > num ).

thf(func_def_38,type,
    one2: num ).

thf(func_def_39,type,
    numeral_numeral: 
      !>[X0: $tType] : ( num > X0 ) ).

thf(func_def_40,type,
    ord_less: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_41,type,
    ord_less_eq: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_42,type,
    type: 
      !>[X0: $tType] : itself(X0) ).

thf(func_def_43,type,
    divide_divide: 
      !>[X0: $tType] : ( X0 > X0 > X0 ) ).

thf(func_def_44,type,
    na: nat ).

thf(func_def_48,type,
    vOR: $o > $o > $o ).

thf(func_def_49,type,
    vEQ: 
      !>[X0: $tType] : ( X0 > X0 > $o ) ).

thf(func_def_50,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_51,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_52,type,
    vAND: $o > $o > $o ).

thf(func_def_53,type,
    vNOT: $o > $o ).

thf(func_def_54,type,
    iCOMB: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_55,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_56,type,
    vSIGMA: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

thf(func_def_57,type,
    vIMP: $o > $o > $o ).

thf(func_def_58,type,
    sP0: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > $o ) ).

thf(func_def_59,type,
    sK1: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_60,type,
    sK2: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_61,type,
    sK3: nat > ( nat > $o ) > nat ).

thf(func_def_62,type,
    sK4: ( nat > $o ) > nat ).

thf(func_def_63,type,
    sK5: ( nat > $o ) > nat ).

thf(func_def_64,type,
    sK6: ( nat > $o ) > nat ).

thf(func_def_65,type,
    sK7: ( nat > nat ) > nat ).

thf(func_def_66,type,
    sK8: ( nat > nat ) > nat ).

thf(func_def_67,type,
    sK9: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).

thf(func_def_68,type,
    sK10: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).

thf(func_def_69,type,
    sK11: 
      !>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).

thf(func_def_70,type,
    sK12: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).

thf(func_def_71,type,
    sK13: 
      !>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).

thf(func_def_73,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(f11865,plain,
    $false,
    inference(trivial_inequality_removal,[],[f11864]) ).

thf(f11864,plain,
    $true = $false,
    inference(forward_demodulation,[],[f11863,f2099]) ).

thf(f2099,plain,
    ! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0) ),
    inference(trivial_inequality_removal,[],[f2098]) ).

thf(f2098,plain,
    ! [X0: nat] :
      ( ( $true != $true )
      | ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0) ) ),
    inference(superposition,[],[f1386,f304]) ).

thf(f304,plain,
    ! [X0: $o] :
      ( ( $true = X0 )
      | ( $false = X0 ) ),
    introduced(fool_axiom,[]) ).

thf(f1386,plain,
    ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0) ),
    inference(cnf_transformation,[],[f902]) ).

thf(f902,plain,
    ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0) ),
    inference(flattening,[],[f656]) ).

thf(f656,plain,
    ! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0) ),
    inference(fool_elimination,[],[f655]) ).

thf(f655,plain,
    ! [X0: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0),
    inference(rectify,[],[f107]) ).

thf(f107,axiom,
    ! [X2: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_less__irrefl__nat) ).

thf(f11863,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),zero_zero(nat)),
    inference(forward_demodulation,[],[f11861,f2265]) ).

thf(f2265,plain,
    zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2))),
    inference(trivial_inequality_removal,[],[f2255]) ).

thf(f2255,plain,
    ( ( $true = $false )
    | ( zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2))) ) ),
    inference(superposition,[],[f2061,f2091]) ).

thf(f2091,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) = $false,
    inference(trivial_inequality_removal,[],[f2090]) ).

thf(f2090,plain,
    ( ( $true != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) = $false ) ),
    inference(superposition,[],[f1202,f304]) ).

thf(f1202,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) != $true,
    inference(cnf_transformation,[],[f883]) ).

thf(f883,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) != $true,
    inference(flattening,[],[f306]) ).

thf(f306,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) != $true,
    inference(fool_elimination,[],[f305]) ).

thf(f305,plain,
    ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))),
    inference(rectify,[],[f302]) ).

thf(f302,negated_conjecture,
    ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))),
    inference(negated_conjecture,[],[f301]) ).

thf(f301,conjecture,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(f2061,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) )
      | ( zero_zero(nat) = X0 ) ),
    inference(equality_proxy_clausification,[],[f2060]) ).

thf(f2060,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0) ) ),
    inference(not_proxy_clausification,[],[f2056]) ).

thf(f2056,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) )
      | ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)) ) ),
    inference(binary_proxy_clausification,[],[f1214]) ).

thf(f1214,plain,
    ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)) ),
    inference(cnf_transformation,[],[f314]) ).

thf(f314,plain,
    ! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)) ),
    inference(fool_elimination,[],[f313]) ).

thf(f313,plain,
    ! [X0: nat] :
      ( ( zero_zero(nat) != X0 )
      = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) ),
    inference(rectify,[],[f6]) ).

thf(f6,axiom,
    ! [X2: nat] :
      ( ( zero_zero(nat) != X2 )
      = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_neq0__conv) ).

thf(f11861,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) = $true,
    inference(trivial_inequality_removal,[],[f11842]) ).

thf(f11842,plain,
    ( ( $true != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) = $true ) ),
    inference(superposition,[],[f1383,f3515]) ).

thf(f3515,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),na),
    inference(subsumption_resolution,[],[f3508,f1207]) ).

thf(f1207,plain,
    na != one_one(nat),
    inference(cnf_transformation,[],[f919]) ).

thf(f919,plain,
    ( ( na != one_one(nat) )
    & ( na != zero_zero(nat) ) ),
    inference(ennf_transformation,[],[f1]) ).

thf(f1,axiom,
    ~ ( ( na = one_one(nat) )
      | ( na = zero_zero(nat) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_ns) ).

thf(f3508,plain,
    ( ( na = one_one(nat) )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),na) ) ),
    inference(trivial_inequality_removal,[],[f3494]) ).

thf(f3494,plain,
    ( ( $true != $true )
    | ( na = one_one(nat) )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),na) ) ),
    inference(superposition,[],[f1423,f2979]) ).

thf(f2979,plain,
    $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),one_one(nat)),na),
    inference(trivial_inequality_removal,[],[f2928]) ).

thf(f2928,plain,
    ( ( $true = $false )
    | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),one_one(nat)),na) ) ),
    inference(superposition,[],[f1407,f2106]) ).

thf(f2106,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)) = $false,
    inference(trivial_inequality_removal,[],[f2105]) ).

thf(f2105,plain,
    ( ( $true != $true )
    | ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)) = $false ) ),
    inference(superposition,[],[f1208,f304]) ).

thf(f1208,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)) != $true,
    inference(cnf_transformation,[],[f884]) ).

thf(f884,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)) != $true,
    inference(flattening,[],[f312]) ).

thf(f312,plain,
    vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)) != $true,
    inference(fool_elimination,[],[f311]) ).

thf(f311,plain,
    ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_False) ).

thf(f1407,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
    inference(cnf_transformation,[],[f692]) ).

thf(f692,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
    inference(fool_elimination,[],[f691]) ).

thf(f691,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)
      | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ),
    inference(rectify,[],[f54]) ).

thf(f54,axiom,
    ! [X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X1)
      | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_nat__le__linear) ).

thf(f1423,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
      | ( X0 = X1 )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
    inference(cnf_transformation,[],[f1122]) ).

thf(f1122,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) )
      | ( X0 = X1 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
    inference(flattening,[],[f1121]) ).

thf(f1121,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) )
      | ( X0 = X1 )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
    inference(ennf_transformation,[],[f710]) ).

thf(f710,plain,
    ! [X0: nat,X1: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
     => ( ( X0 != X1 )
       => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ) ),
    inference(fool_elimination,[],[f709]) ).

thf(f709,plain,
    ! [X0: nat,X1: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)
     => ( ( X0 != X1 )
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
    inference(rectify,[],[f64]) ).

thf(f64,axiom,
    ! [X1: nat,X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)
     => ( ( X1 != X2 )
       => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_le__neq__implies__less) ).

thf(f1383,plain,
    ! [X0: nat] :
      ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),X0) )
      | ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) ) ),
    inference(cnf_transformation,[],[f1108]) ).

thf(f1108,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) )
      | ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),X0) ) ),
    inference(ennf_transformation,[],[f650]) ).

thf(f650,plain,
    ! [X0: nat] :
      ( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),X0) )
     => ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) ) ),
    inference(fool_elimination,[],[f649]) ).

thf(f649,plain,
    ! [X0: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),X0)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) ),
    inference(rectify,[],[f149]) ).

thf(f149,axiom,
    ! [X2: nat] :
      ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),X2)
     => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X2),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_div__2__gt__zero) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : DAT239^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n009.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   : Sun May 19 23:28:37 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (25002)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39  % (25005)WARNING: value z3 for option sas not known
% 0.14/0.39  % (25004)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39  % (25003)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39  % (25005)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)
% 0.14/0.39  % (25009)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)
% 0.14/0.39  % (25008)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)
% 0.14/0.39  % (25006)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40  % (25007)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)
% 0.21/0.41  % (25009)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.42  % Exception at run slice level
% 0.21/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.42  % Exception at run slice level
% 0.21/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.42  % Exception at run slice level
% 0.21/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43  % (25010)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.43  % (25011)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)
% 0.21/0.44  % (25012)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)
% 0.21/0.46  % (25011)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.46  % (25010)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.46  % Exception at run slice level
% 0.21/0.46  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.48  % (25013)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)
% 2.41/0.75  % (25012)First to succeed.
% 2.41/0.75  % (25012)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-25002"
% 2.41/0.76  % (25012)Refutation found. Thanks to Tanya!
% 2.41/0.76  % SZS status Theorem for theBenchmark
% 2.41/0.76  % SZS output start Proof for theBenchmark
% See solution above
% 2.41/0.76  % (25012)------------------------------
% 2.41/0.76  % (25012)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.41/0.76  % (25012)Termination reason: Refutation
% 2.41/0.76  
% 2.41/0.76  % (25012)Memory used [KB]: 3564
% 2.41/0.76  % (25012)Time elapsed: 0.339 s
% 2.41/0.76  % (25012)Instructions burned: 1024 (million)
% 2.41/0.76  % (25002)Success in time 0.373 s
%------------------------------------------------------------------------------