TSTP Solution File: ITP127^1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP127^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n014.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 22:52:36 EDT 2024

% Result   : Theorem 22.18s 3.61s
% Output   : Refutation 22.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :  124
% Syntax   : Number of formulae    :  147 (  25 unt; 117 typ;   0 def)
%            Number of atoms       :  181 (  34 equ;   0 cnn)
%            Maximal formula atoms :    2 (   6 avg)
%            Number of connectives :   14 (   9   ~;   2   |;   0   &;   0   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    6 (   5 usr)
%            Number of type conns  :  362 ( 361   >;   1   *;   0   +;   0  <<)
%            Number of symbols     :  110 ( 108 usr;   3 con; 0-6 aty)
%            Number of variables   :   69 (   0   ^  52   !;   2   ?;  69   :)
%                                         (  15  !>;   0  ?*;   0  @-;   0  @+)

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

thf(type_def_6,type,
    countable_Set_cset_c: $tType ).

thf(type_def_7,type,
    sTfun: ( $tType * $tType ) > $tType ).

thf(type_def_8,type,
    monomo197243225tT_a_m: $tType ).

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

thf(type_def_10,type,
    counta191869203tT_a_m: $tType ).

thf(func_def_0,type,
    counta191869203tT_a_m: $tType ).

thf(func_def_1,type,
    monomo197243225tT_a_m: $tType ).

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

thf(func_def_3,type,
    m: $tType ).

thf(func_def_4,type,
    c: $tType ).

thf(func_def_5,type,
    countable_Set_cin_c: c > countable_Set_cset_c > $o ).

thf(func_def_6,type,
    counta472291938sert_c: c > countable_Set_cset_c > countable_Set_cset_c ).

thf(func_def_7,type,
    comp_M864375327_a_m_c: ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > ( c > monomo197243225tT_a_m ) > c > monomo197243225tT_a_m ).

thf(func_def_8,type,
    comp_M1062614966_m_c_c: ( monomo197243225tT_a_m > c ) > ( c > monomo197243225tT_a_m ) > c > c ).

thf(func_def_9,type,
    comp_M1944986301tT_a_m: ( monomo197243225tT_a_m > m ) > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m > m ).

thf(func_def_10,type,
    comp_M750374444_m_m_c: ( monomo197243225tT_a_m > m ) > ( c > monomo197243225tT_a_m ) > c > m ).

thf(func_def_11,type,
    comp_M750374454_m_m_m: ( monomo197243225tT_a_m > m ) > ( m > monomo197243225tT_a_m ) > m > m ).

thf(func_def_12,type,
    comp_c1772230468_a_m_c: ( c > monomo197243225tT_a_m ) > ( c > c ) > c > monomo197243225tT_a_m ).

thf(func_def_13,type,
    comp_c_c_c: ( c > c ) > ( c > c ) > c > c ).

thf(func_def_14,type,
    comp_c997395372tT_a_m: ( c > m ) > ( monomo197243225tT_a_m > c ) > monomo197243225tT_a_m > m ).

thf(func_def_15,type,
    comp_c_m_c: ( c > m ) > ( c > c ) > c > m ).

thf(func_def_16,type,
    comp_c_m_m: ( c > m ) > ( m > c ) > m > m ).

thf(func_def_17,type,
    comp_m1038691662_a_m_c: ( m > monomo197243225tT_a_m ) > ( c > m ) > c > monomo197243225tT_a_m ).

thf(func_def_18,type,
    comp_m_c_c: ( m > c ) > ( c > m ) > c > c ).

thf(func_def_19,type,
    comp_m263856566tT_a_m: ( m > m ) > ( monomo197243225tT_a_m > m ) > monomo197243225tT_a_m > m ).

thf(func_def_20,type,
    comp_m_m_c: ( m > m ) > ( c > m ) > c > m ).

thf(func_def_21,type,
    comp_m_m_m: ( m > m ) > ( m > m ) > m > m ).

thf(func_def_22,type,
    minus_1646763425cset_c: countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).

thf(func_def_23,type,
    if_Cou1542198912cset_c: $o > countable_Set_cset_c > countable_Set_cset_c > countable_Set_cset_c ).

thf(func_def_24,type,
    if_c: $o > c > c > c ).

thf(func_def_25,type,
    monomo2081011572_m_m_a: ( counta191869203tT_a_m > ( monomo197243225tT_a_m > m ) > m ) > counta191869203tT_a_m > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).

thf(func_def_26,type,
    monomo463139869_c_m_a: ( countable_Set_cset_c > ( c > m ) > m ) > countable_Set_cset_c > ( c > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).

thf(func_def_27,type,
    monomo412532791tT_m_a: m > monomo197243225tT_a_m ).

thf(func_def_28,type,
    monomo624345106et_a_m: monomo197243225tT_a_m > m ).

thf(func_def_29,type,
    bot_bo1320844070cset_c: countable_Set_cset_c ).

thf(func_def_30,type,
    ord_le1587667814cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).

thf(func_def_31,type,
    ord_le1376176871cset_c: ( $o > countable_Set_cset_c ) > ( $o > countable_Set_cset_c ) > $o ).

thf(func_def_32,type,
    ord_le15364698cset_c: countable_Set_cset_c > countable_Set_cset_c > $o ).

thf(func_def_33,type,
    order_1683649299cset_c: ( countable_Set_cset_c > $o ) > countable_Set_cset_c ).

thf(func_def_34,type,
    f: c > monomo197243225tT_a_m ).

thf(func_def_35,type,
    mergec: countable_Set_cset_c > ( c > m ) > m ).

thf(func_def_36,type,
    x: c ).

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

thf(func_def_41,type,
    vAND: $o > $o > $o ).

thf(func_def_42,type,
    bCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_43,type,
    cCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).

thf(func_def_44,type,
    sCOMB: 
      !>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).

thf(func_def_45,type,
    iCOMB: 
      !>[X0: $tType] : ( X0 > X0 ) ).

thf(func_def_46,type,
    vNOT: $o > $o ).

thf(func_def_47,type,
    vOR: $o > $o > $o ).

thf(func_def_48,type,
    vPI: 
      !>[X0: $tType] : ( ( X0 > $o ) > $o ) ).

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

thf(func_def_50,type,
    vIMP: $o > $o > $o ).

thf(func_def_51,type,
    sP0: ( countable_Set_cset_c > $o ) > ( countable_Set_cset_c > $o ) > $o ).

thf(func_def_52,type,
    sK1: countable_Set_cset_c > c ).

thf(func_def_53,type,
    sK2: monomo197243225tT_a_m > m ).

thf(func_def_54,type,
    sK3: countable_Set_cset_c > countable_Set_cset_c > c ).

thf(func_def_55,type,
    sK4: countable_Set_cset_c > countable_Set_cset_c > c ).

thf(func_def_56,type,
    sK5: ( monomo197243225tT_a_m > $o ) > m ).

thf(func_def_57,type,
    sK6: countable_Set_cset_c > ( countable_Set_cset_c > $o ) > countable_Set_cset_c ).

thf(func_def_58,type,
    sK7: countable_Set_cset_c > countable_Set_cset_c > c ).

thf(func_def_59,type,
    sK8: countable_Set_cset_c > c > countable_Set_cset_c ).

thf(func_def_60,type,
    sK9: countable_Set_cset_c > c > countable_Set_cset_c ).

thf(func_def_61,type,
    sK10: ( countable_Set_cset_c > $o ) > ( countable_Set_cset_c > $o ) > countable_Set_cset_c ).

thf(func_def_62,type,
    sK11: countable_Set_cset_c > ( countable_Set_cset_c > $o ) > countable_Set_cset_c ).

thf(func_def_63,type,
    sK12: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_64,type,
    sK13: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_65,type,
    sK14: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_66,type,
    sK15: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_67,type,
    sK16: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_68,type,
    sK17: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_69,type,
    sK18: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_70,type,
    sK19: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_71,type,
    sK20: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_72,type,
    sK21: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_73,type,
    sK22: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_74,type,
    sK23: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_75,type,
    sK24: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_76,type,
    sK25: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_77,type,
    sK26: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_78,type,
    sK27: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_79,type,
    sK28: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_80,type,
    sK29: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_81,type,
    sK30: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_82,type,
    sK31: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_83,type,
    sK32: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_84,type,
    sK33: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_85,type,
    sK34: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_86,type,
    sK35: ( countable_Set_cset_c > countable_Set_cset_c ) > countable_Set_cset_c ).

thf(func_def_88,type,
    kCOMB: 
      !>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).

thf(func_def_89,type,
    sK37: ( c > m ) > ( c > c ) > c ).

thf(func_def_90,type,
    sK38: ( c > m ) > ( c > c ) > c > m ).

thf(func_def_91,type,
    sK39: ( c > monomo197243225tT_a_m ) > ( c > c ) > c ).

thf(func_def_92,type,
    sK40: ( c > monomo197243225tT_a_m ) > ( c > c ) > c > monomo197243225tT_a_m ).

thf(func_def_93,type,
    sK41: ( c > m ) > ( c > m ) > c ).

thf(func_def_94,type,
    sK42: ( c > m ) > ( c > m ) > m > m ).

thf(func_def_95,type,
    sK43: ( c > m ) > ( c > monomo197243225tT_a_m ) > c ).

thf(func_def_96,type,
    sK44: ( c > m ) > ( c > monomo197243225tT_a_m ) > monomo197243225tT_a_m > m ).

thf(func_def_97,type,
    sK45: ( monomo197243225tT_a_m > m ) > ( monomo197243225tT_a_m > m ) > monomo197243225tT_a_m ).

thf(func_def_98,type,
    sK46: ( monomo197243225tT_a_m > m ) > ( monomo197243225tT_a_m > m ) > m > m ).

thf(func_def_99,type,
    sK47: ( monomo197243225tT_a_m > m ) > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m ).

thf(func_def_100,type,
    sK48: ( monomo197243225tT_a_m > m ) > ( monomo197243225tT_a_m > monomo197243225tT_a_m ) > monomo197243225tT_a_m > m ).

thf(func_def_101,type,
    sK49: ( c > m ) > ( c > m ) > c ).

thf(func_def_102,type,
    sK50: ( c > m ) > ( c > m ) > c > c ).

thf(func_def_103,type,
    sK51: ( c > m ) > ( m > m ) > c ).

thf(func_def_104,type,
    sK52: ( c > m ) > ( m > m ) > c > m ).

thf(func_def_105,type,
    sK53: ( c > monomo197243225tT_a_m ) > ( c > monomo197243225tT_a_m ) > c ).

thf(func_def_106,type,
    sK54: ( c > monomo197243225tT_a_m ) > ( c > monomo197243225tT_a_m ) > c > c ).

thf(func_def_107,type,
    sK55: ( c > m ) > ( monomo197243225tT_a_m > m ) > c ).

thf(func_def_108,type,
    sK56: ( c > m ) > ( monomo197243225tT_a_m > m ) > c > monomo197243225tT_a_m ).

thf(func_def_109,type,
    sK57: ( monomo197243225tT_a_m > m ) > ( m > m ) > monomo197243225tT_a_m ).

thf(func_def_110,type,
    sK58: ( monomo197243225tT_a_m > m ) > ( m > m ) > monomo197243225tT_a_m > m ).

thf(func_def_111,type,
    sK59: ( monomo197243225tT_a_m > m ) > ( monomo197243225tT_a_m > m ) > monomo197243225tT_a_m ).

thf(func_def_112,type,
    sK60: ( monomo197243225tT_a_m > m ) > ( monomo197243225tT_a_m > m ) > monomo197243225tT_a_m > monomo197243225tT_a_m ).

thf(func_def_113,type,
    sK61: countable_Set_cset_c > c ).

thf(func_def_114,type,
    sK62: countable_Set_cset_c > c ).

thf(f52526,plain,
    $false,
    inference(subsumption_resolution,[],[f1156,f34304]) ).

thf(f34304,plain,
    ! [X0: c,X1: c > monomo197243225tT_a_m] : ( vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),vAPP(countable_Set_cset_c,countable_Set_cset_c,vAPP(c,sTfun(countable_Set_cset_c,countable_Set_cset_c),counta472291938sert_c,X0),bot_bo1320844070cset_c)),X1) = vAPP(c,monomo197243225tT_a_m,X1,X0) ),
    inference(forward_demodulation,[],[f34295,f1202]) ).

thf(f1202,plain,
    ! [X0: monomo197243225tT_a_m] : ( vAPP(m,monomo197243225tT_a_m,monomo412532791tT_m_a,vAPP(monomo197243225tT_a_m,m,sK2,X0)) = X0 ),
    inference(cnf_transformation,[],[f1111]) ).

thf(f1111,plain,
    ! [X0: monomo197243225tT_a_m] : ( vAPP(m,monomo197243225tT_a_m,monomo412532791tT_m_a,vAPP(monomo197243225tT_a_m,m,sK2,X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f835,f1110]) ).

thf(f1110,plain,
    ! [X0: monomo197243225tT_a_m] :
      ( ? [X1: m] : ( vAPP(m,monomo197243225tT_a_m,monomo412532791tT_m_a,X1) = X0 )
     => ( vAPP(m,monomo197243225tT_a_m,monomo412532791tT_m_a,vAPP(monomo197243225tT_a_m,m,sK2,X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

thf(f835,plain,
    ! [X0: monomo197243225tT_a_m] :
    ? [X1: m] : ( vAPP(m,monomo197243225tT_a_m,monomo412532791tT_m_a,X1) = X0 ),
    inference(ennf_transformation,[],[f675]) ).

thf(f675,plain,
    ! [X0: monomo197243225tT_a_m] :
      ~ ! [X1: m] : ( vAPP(m,monomo197243225tT_a_m,monomo412532791tT_m_a,X1) != X0 ),
    inference(rectify,[],[f85]) ).

thf(f85,axiom,
    ! [X7: monomo197243225tT_a_m] :
      ~ ! [X25: m] : ( vAPP(m,monomo197243225tT_a_m,monomo412532791tT_m_a,X25) != X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_nondetT_Oexhaust) ).

thf(f34295,plain,
    ! [X0: c,X1: c > monomo197243225tT_a_m] : ( vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),vAPP(countable_Set_cset_c,countable_Set_cset_c,vAPP(c,sTfun(countable_Set_cset_c,countable_Set_cset_c),counta472291938sert_c,X0),bot_bo1320844070cset_c)),X1) = vAPP(m,monomo197243225tT_a_m,monomo412532791tT_m_a,vAPP(monomo197243225tT_a_m,m,sK2,vAPP(c,monomo197243225tT_a_m,X1,X0))) ),
    inference(superposition,[],[f1202,f14200]) ).

thf(f14200,plain,
    ! [X0: c,X1: c > monomo197243225tT_a_m] : ( vAPP(monomo197243225tT_a_m,m,sK2,vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),vAPP(countable_Set_cset_c,countable_Set_cset_c,vAPP(c,sTfun(countable_Set_cset_c,countable_Set_cset_c),counta472291938sert_c,X0),bot_bo1320844070cset_c)),X1)) = vAPP(monomo197243225tT_a_m,m,sK2,vAPP(c,monomo197243225tT_a_m,X1,X0)) ),
    inference(forward_demodulation,[],[f14199,f1873]) ).

thf(f1873,plain,
    ! [X0: monomo197243225tT_a_m] : ( vAPP(monomo197243225tT_a_m,m,monomo624345106et_a_m,X0) = vAPP(monomo197243225tT_a_m,m,sK2,X0) ),
    inference(superposition,[],[f1188,f1202]) ).

thf(f1188,plain,
    ! [X0: m] : ( vAPP(monomo197243225tT_a_m,m,monomo624345106et_a_m,vAPP(m,monomo197243225tT_a_m,monomo412532791tT_m_a,X0)) = X0 ),
    inference(cnf_transformation,[],[f88]) ).

thf(f88,axiom,
    ! [X0: m] : ( vAPP(monomo197243225tT_a_m,m,monomo624345106et_a_m,vAPP(m,monomo197243225tT_a_m,monomo412532791tT_m_a,X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_nondetT_Osel) ).

thf(f14199,plain,
    ! [X0: c,X1: c > monomo197243225tT_a_m] : ( vAPP(monomo197243225tT_a_m,m,sK2,vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),vAPP(countable_Set_cset_c,countable_Set_cset_c,vAPP(c,sTfun(countable_Set_cset_c,countable_Set_cset_c),counta472291938sert_c,X0),bot_bo1320844070cset_c)),X1)) = vAPP(monomo197243225tT_a_m,m,monomo624345106et_a_m,vAPP(c,monomo197243225tT_a_m,X1,X0)) ),
    inference(forward_demodulation,[],[f14196,f1536]) ).

thf(f1536,plain,
    ! [X3: c,X0: monomo197243225tT_a_m > m,X1: c > monomo197243225tT_a_m] : ( vAPP(monomo197243225tT_a_m,m,X0,vAPP(c,monomo197243225tT_a_m,X1,X3)) = vAPP(c,m,vAPP(sTfun(c,monomo197243225tT_a_m),sTfun(c,m),vAPP(sTfun(monomo197243225tT_a_m,m),sTfun(sTfun(c,monomo197243225tT_a_m),sTfun(c,m)),comp_M750374444_m_m_c,X0),X1),X3) ),
    inference(equality_resolution,[],[f1392]) ).

thf(f1392,plain,
    ! [X2: c > m,X3: c,X0: monomo197243225tT_a_m > m,X1: c > monomo197243225tT_a_m] :
      ( ( vAPP(monomo197243225tT_a_m,m,X0,vAPP(c,monomo197243225tT_a_m,X1,X3)) = vAPP(c,m,X2,X3) )
      | ( vAPP(sTfun(c,monomo197243225tT_a_m),sTfun(c,m),vAPP(sTfun(monomo197243225tT_a_m,m),sTfun(sTfun(c,monomo197243225tT_a_m),sTfun(c,m)),comp_M750374444_m_m_c,X0),X1) != X2 ) ),
    inference(cnf_transformation,[],[f978]) ).

thf(f978,plain,
    ! [X0: monomo197243225tT_a_m > m,X1: c > monomo197243225tT_a_m,X2: c > m,X3: c] :
      ( ( vAPP(monomo197243225tT_a_m,m,X0,vAPP(c,monomo197243225tT_a_m,X1,X3)) = vAPP(c,m,X2,X3) )
      | ( vAPP(sTfun(c,monomo197243225tT_a_m),sTfun(c,m),vAPP(sTfun(monomo197243225tT_a_m,m),sTfun(sTfun(c,monomo197243225tT_a_m),sTfun(c,m)),comp_M750374444_m_m_c,X0),X1) != X2 ) ),
    inference(ennf_transformation,[],[f747]) ).

thf(f747,plain,
    ! [X0: monomo197243225tT_a_m > m,X1: c > monomo197243225tT_a_m,X2: c > m,X3: c] :
      ( ( vAPP(sTfun(c,monomo197243225tT_a_m),sTfun(c,m),vAPP(sTfun(monomo197243225tT_a_m,m),sTfun(sTfun(c,monomo197243225tT_a_m),sTfun(c,m)),comp_M750374444_m_m_c,X0),X1) = X2 )
     => ( vAPP(monomo197243225tT_a_m,m,X0,vAPP(c,monomo197243225tT_a_m,X1,X3)) = vAPP(c,m,X2,X3) ) ),
    inference(rectify,[],[f72]) ).

thf(f72,axiom,
    ! [X3: monomo197243225tT_a_m > m,X4: c > monomo197243225tT_a_m,X5: c > m,X18: c] :
      ( ( vAPP(sTfun(c,monomo197243225tT_a_m),sTfun(c,m),vAPP(sTfun(monomo197243225tT_a_m,m),sTfun(sTfun(c,monomo197243225tT_a_m),sTfun(c,m)),comp_M750374444_m_m_c,X3),X4) = X5 )
     => ( vAPP(monomo197243225tT_a_m,m,X3,vAPP(c,monomo197243225tT_a_m,X4,X18)) = vAPP(c,m,X5,X18) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_comp__eq__dest__lhs) ).

thf(f14196,plain,
    ! [X0: c,X1: c > monomo197243225tT_a_m] : ( vAPP(c,m,vAPP(sTfun(c,monomo197243225tT_a_m),sTfun(c,m),vAPP(sTfun(monomo197243225tT_a_m,m),sTfun(sTfun(c,monomo197243225tT_a_m),sTfun(c,m)),comp_M750374444_m_m_c,monomo624345106et_a_m),X1),X0) = vAPP(monomo197243225tT_a_m,m,sK2,vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),vAPP(countable_Set_cset_c,countable_Set_cset_c,vAPP(c,sTfun(countable_Set_cset_c,countable_Set_cset_c),counta472291938sert_c,X0),bot_bo1320844070cset_c)),X1)) ),
    inference(superposition,[],[f1874,f1215]) ).

thf(f1215,plain,
    ! [X0: c,X1: c > m] : ( vAPP(sTfun(c,m),m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,m),m),mergec,vAPP(countable_Set_cset_c,countable_Set_cset_c,vAPP(c,sTfun(countable_Set_cset_c,countable_Set_cset_c),counta472291938sert_c,X0),bot_bo1320844070cset_c)),X1) = vAPP(c,m,X1,X0) ),
    inference(cnf_transformation,[],[f1]) ).

thf(f1,axiom,
    ! [X0: c,X1: c > m] : ( vAPP(sTfun(c,m),m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,m),m),mergec,vAPP(countable_Set_cset_c,countable_Set_cset_c,vAPP(c,sTfun(countable_Set_cset_c,countable_Set_cset_c),counta472291938sert_c,X0),bot_bo1320844070cset_c)),X1) = vAPP(c,m,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_mergec__single) ).

thf(f1874,plain,
    ! [X0: countable_Set_cset_c,X1: c > monomo197243225tT_a_m] : ( vAPP(sTfun(c,m),m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,m),m),mergec,X0),vAPP(sTfun(c,monomo197243225tT_a_m),sTfun(c,m),vAPP(sTfun(monomo197243225tT_a_m,m),sTfun(sTfun(c,monomo197243225tT_a_m),sTfun(c,m)),comp_M750374444_m_m_c,monomo624345106et_a_m),X1)) = vAPP(monomo197243225tT_a_m,m,sK2,vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),X0),X1)) ),
    inference(backward_demodulation,[],[f1220,f1873]) ).

thf(f1220,plain,
    ! [X0: countable_Set_cset_c,X1: c > monomo197243225tT_a_m] : ( vAPP(sTfun(c,m),m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,m),m),mergec,X0),vAPP(sTfun(c,monomo197243225tT_a_m),sTfun(c,m),vAPP(sTfun(monomo197243225tT_a_m,m),sTfun(sTfun(c,monomo197243225tT_a_m),sTfun(c,m)),comp_M750374444_m_m_c,monomo624345106et_a_m),X1)) = vAPP(monomo197243225tT_a_m,m,monomo624345106et_a_m,vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),X0),X1)) ),
    inference(cnf_transformation,[],[f687]) ).

thf(f687,plain,
    ! [X0: countable_Set_cset_c,X1: c > monomo197243225tT_a_m] : ( vAPP(sTfun(c,m),m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,m),m),mergec,X0),vAPP(sTfun(c,monomo197243225tT_a_m),sTfun(c,m),vAPP(sTfun(monomo197243225tT_a_m,m),sTfun(sTfun(c,monomo197243225tT_a_m),sTfun(c,m)),comp_M750374444_m_m_c,monomo624345106et_a_m),X1)) = vAPP(monomo197243225tT_a_m,m,monomo624345106et_a_m,vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),X0),X1)) ),
    inference(rectify,[],[f8]) ).

thf(f8,axiom,
    ! [X2: countable_Set_cset_c,X1: c > monomo197243225tT_a_m] : ( vAPP(monomo197243225tT_a_m,m,monomo624345106et_a_m,vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),X2),X1)) = vAPP(sTfun(c,m),m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,m),m),mergec,X2),vAPP(sTfun(c,monomo197243225tT_a_m),sTfun(c,m),vAPP(sTfun(monomo197243225tT_a_m,m),sTfun(sTfun(c,monomo197243225tT_a_m),sTfun(c,m)),comp_M750374444_m_m_c,monomo624345106et_a_m),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_run__altc__nondet) ).

thf(f1156,plain,
    vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),vAPP(countable_Set_cset_c,countable_Set_cset_c,vAPP(c,sTfun(countable_Set_cset_c,countable_Set_cset_c),counta472291938sert_c,x),bot_bo1320844070cset_c)),f) != vAPP(c,monomo197243225tT_a_m,f,x),
    inference(cnf_transformation,[],[f668]) ).

thf(f668,plain,
    vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),vAPP(countable_Set_cset_c,countable_Set_cset_c,vAPP(c,sTfun(countable_Set_cset_c,countable_Set_cset_c),counta472291938sert_c,x),bot_bo1320844070cset_c)),f) != vAPP(c,monomo197243225tT_a_m,f,x),
    inference(flattening,[],[f317]) ).

thf(f317,negated_conjecture,
    vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),vAPP(countable_Set_cset_c,countable_Set_cset_c,vAPP(c,sTfun(countable_Set_cset_c,countable_Set_cset_c),counta472291938sert_c,x),bot_bo1320844070cset_c)),f) != vAPP(c,monomo197243225tT_a_m,f,x),
    inference(negated_conjecture,[],[f316]) ).

thf(f316,conjecture,
    vAPP(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m,vAPP(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m),vAPP(sTfun(countable_Set_cset_c,sTfun(sTfun(c,m),m)),sTfun(countable_Set_cset_c,sTfun(sTfun(c,monomo197243225tT_a_m),monomo197243225tT_a_m)),monomo463139869_c_m_a,mergec),vAPP(countable_Set_cset_c,countable_Set_cset_c,vAPP(c,sTfun(countable_Set_cset_c,countable_Set_cset_c),counta472291938sert_c,x),bot_bo1320844070cset_c)),f) = vAPP(c,monomo197243225tT_a_m,f,x),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : ITP127^1 : TPTP v8.2.0. Released v7.5.0.
% 0.10/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat May 18 18:07:23 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  % (10238)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38  % (10241)WARNING: value z3 for option sas not known
% 0.13/0.38  % (10242)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38  % (10239)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38  % (10241)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)
% 0.13/0.38  % (10240)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38  % (10244)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)
% 0.13/0.38  % (10243)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)
% 0.13/0.38  % (10245)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)
% 0.19/0.41  % (10245)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.42  % Exception at run slice level
% 0.19/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.42  % Exception at run slice level
% 0.19/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.42  % Exception at run slice level
% 0.19/0.42  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.43  % (10260)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.19/0.43  % (10261)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)
% 0.19/0.44  % (10262)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)
% 0.19/0.46  % (10260)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.47  % (10261)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.47  % Exception at run slice level
% 0.19/0.47  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.49  % (10294)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)
% 22.18/3.60  % (10262)First to succeed.
% 22.18/3.60  % (10262)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10238"
% 22.18/3.61  % (10262)Refutation found. Thanks to Tanya!
% 22.18/3.61  % SZS status Theorem for theBenchmark
% 22.18/3.61  % SZS output start Proof for theBenchmark
% See solution above
% 22.18/3.61  % (10262)------------------------------
% 22.18/3.61  % (10262)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 22.18/3.61  % (10262)Termination reason: Refutation
% 22.18/3.61  
% 22.18/3.61  % (10262)Memory used [KB]: 21529
% 22.18/3.61  % (10262)Time elapsed: 3.167 s
% 22.18/3.61  % (10262)Instructions burned: 13141 (million)
% 22.18/3.61  % (10238)Success in time 3.238 s
%------------------------------------------------------------------------------