TSTP Solution File: ITP004_3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP004_3 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n032.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 22:42:09 EDT 2024

% Result   : Theorem 213.35s 30.92s
% Output   : Refutation 213.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   47
% Syntax   : Number of formulae    :   82 (  16 unt;  39 typ;   0 def)
%            Number of atoms       :  106 (  23 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   98 (  35   ~;  34   |;  15   &)
%                                         (   7 <=>;   6  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   30 (  19   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   36 (  36 usr;   7 con; 0-4 aty)
%            Number of variables   :  135 (  99   !;   7   ?; 135   :)
%                                         (  29  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    tyop_2Emin_2Ebool: $tType ).

tff(type_def_6,type,
    tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).

tff(type_def_7,type,
    sK0: $tType ).

tff(func_def_0,type,
    app_2E2: 
      !>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X0 ) > X1 ) ).

tff(func_def_1,type,
    combin_i_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(X0,X0) ).

tff(func_def_2,type,
    combin_k_2E0: 
      !>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X0)) ).

tff(func_def_3,type,
    combin_s_2E0: 
      !>[X0: $tType,X1: $tType,X2: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2))) ).

tff(func_def_4,type,
    c_2Ebool_2E_21_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(func_def_5,type,
    c_2Ebool_2E_21_2E1: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(func_def_6,type,
    c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(func_def_7,type,
    c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(func_def_8,type,
    c_2Emin_2E_3D_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).

tff(func_def_9,type,
    c_2Emin_2E_3D_2E2: 
      !>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).

tff(func_def_10,type,
    c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(func_def_11,type,
    c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(func_def_12,type,
    c_2Ebool_2E_3F_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).

tff(func_def_13,type,
    c_2Ebool_2E_3F_2E1: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).

tff(func_def_14,type,
    c_2Epred__set_2ECHOICE_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X0) ).

tff(func_def_15,type,
    c_2Epred__set_2ECHOICE_2E1: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_16,type,
    c_2Epred__set_2EDELETE_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))) ).

tff(func_def_17,type,
    c_2Epred__set_2EDELETE_2E2: 
      !>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * X0 ) > tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) ).

tff(func_def_18,type,
    c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).

tff(func_def_19,type,
    c_2Ebool_2EIN_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(func_def_20,type,
    c_2Ebool_2EIN_2E2: 
      !>[X0: $tType] : ( ( X0 * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(func_def_21,type,
    c_2Epred__set_2EREST_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).

tff(func_def_22,type,
    c_2Epred__set_2EREST_2E1: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) ).

tff(func_def_23,type,
    c_2Epred__set_2ESUBSET_2E0: 
      !>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).

tff(func_def_24,type,
    c_2Epred__set_2ESUBSET_2E2: 
      !>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).

tff(func_def_25,type,
    c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).

tff(func_def_26,type,
    c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).

tff(func_def_27,type,
    c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).

tff(func_def_28,type,
    c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).

tff(func_def_29,type,
    c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).

tff(func_def_30,type,
    sK1: tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool) ).

tff(func_def_31,type,
    sK2: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_32,type,
    sK3: 
      !>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > X0 ) ).

tff(func_def_33,type,
    sK4: 
      !>[X0: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) ) > X0 ) ).

tff(func_def_34,type,
    sK5: 
      !>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).

tff(pred_def_1,type,
    p: tyop_2Emin_2Ebool > $o ).

tff(f250850,plain,
    $false,
    inference(subsumption_resolution,[],[f250754,f104]) ).

tff(f104,plain,
    p(c_2Ebool_2ET_2E0),
    inference(cnf_transformation,[],[f3]) ).

tff(f3,axiom,
    p(c_2Ebool_2ET_2E0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Etruth) ).

tff(f250754,plain,
    ~ p(c_2Ebool_2ET_2E0),
    inference(superposition,[],[f102,f250469]) ).

tff(f250469,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ET_2E0 = c_2Epred__set_2ESUBSET_2E2(X0,c_2Epred__set_2EREST_2E1(X0,X1),X1) ),
    inference(superposition,[],[f250352,f114]) ).

tff(f114,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EREST_2E1(X0,X1) = c_2Epred__set_2EDELETE_2E2(X0,X1,c_2Epred__set_2ECHOICE_2E1(X0,X1)) ),
    inference(cnf_transformation,[],[f41]) ).

tff(f41,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EREST_2E1(X0,X1) = c_2Epred__set_2EDELETE_2E2(X0,X1,c_2Epred__set_2ECHOICE_2E1(X0,X1)) ),
    inference(rectify,[],[f30]) ).

tff(f30,axiom,
    ! [X0: $tType,X14: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EREST_2E1(X0,X14) = c_2Epred__set_2EDELETE_2E2(X0,X14,c_2Epred__set_2ECHOICE_2E1(X0,X14)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__DEF) ).

tff(f250352,plain,
    ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ( c_2Ebool_2ET_2E0 = c_2Epred__set_2ESUBSET_2E2(X0,c_2Epred__set_2EDELETE_2E2(X0,X1,X2),X1) ),
    inference(subsumption_resolution,[],[f250254,f102]) ).

tff(f250254,plain,
    ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(sK0,c_2Epred__set_2EREST_2E1(sK0,sK1),sK1))
      | ( c_2Ebool_2ET_2E0 = c_2Epred__set_2ESUBSET_2E2(X0,c_2Epred__set_2EDELETE_2E2(X0,X1,X2),X1) ) ),
    inference(superposition,[],[f67700,f629]) ).

tff(f629,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ( c_2Epred__set_2ESUBSET_2E2(sK0,c_2Epred__set_2EREST_2E1(sK0,sK1),sK1) = X0 )
      | ( c_2Ebool_2ET_2E0 = X0 ) ),
    inference(resolution,[],[f230,f102]) ).

tff(f230,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X1)
      | ( c_2Ebool_2ET_2E0 = X0 )
      | ( X0 = X1 ) ),
    inference(resolution,[],[f226,f116]) ).

tff(f116,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( p(X1)
      | p(X0)
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f71]) ).

tff(f71,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( X0 = X1 )
      | ( ( ~ p(X1)
          | ~ p(X0) )
        & ( p(X1)
          | p(X0) ) ) ),
    inference(nnf_transformation,[],[f62]) ).

tff(f62,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( X0 = X1 )
      | ( p(X0)
      <~> p(X1) ) ),
    inference(ennf_transformation,[],[f43]) ).

tff(f43,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ( p(X0)
      <=> p(X1) )
     => ( X0 = X1 ) ),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X6: tyop_2Emin_2Ebool,X7: tyop_2Emin_2Ebool] :
      ( ( p(X6)
      <=> p(X7) )
     => ( X6 = X7 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eboolext) ).

tff(f226,plain,
    ! [X0: tyop_2Emin_2Ebool] :
      ( ~ p(X0)
      | ( c_2Ebool_2ET_2E0 = X0 ) ),
    inference(resolution,[],[f117,f104]) ).

tff(f117,plain,
    ! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
      ( ~ p(X1)
      | ( X0 = X1 )
      | ~ p(X0) ),
    inference(cnf_transformation,[],[f71]) ).

tff(f67700,plain,
    ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(X0,c_2Epred__set_2EDELETE_2E2(X0,X1,X2),X1)),
    inference(duplicate_literal_removal,[],[f67525]) ).

tff(f67525,plain,
    ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(X0,c_2Epred__set_2EDELETE_2E2(X0,X1,X2),X1))
      | p(c_2Epred__set_2ESUBSET_2E2(X0,c_2Epred__set_2EDELETE_2E2(X0,X1,X2),X1)) ),
    inference(resolution,[],[f1687,f149]) ).

tff(f149,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Ebool_2EIN_2E2(X0,sK4(X0,X1,X2),X2))
      | p(c_2Epred__set_2ESUBSET_2E2(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f97]) ).

tff(f97,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2ESUBSET_2E2(X0,X1,X2))
        | ( ~ p(c_2Ebool_2EIN_2E2(X0,sK4(X0,X1,X2),X2))
          & p(c_2Ebool_2EIN_2E2(X0,sK4(X0,X1,X2),X1)) ) )
      & ( ! [X4: X0] :
            ( p(c_2Ebool_2EIN_2E2(X0,X4,X2))
            | ~ p(c_2Ebool_2EIN_2E2(X0,X4,X1)) )
        | ~ p(c_2Epred__set_2ESUBSET_2E2(X0,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f95,f96]) ).

tff(f96,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ? [X3: X0] :
          ( ~ p(c_2Ebool_2EIN_2E2(X0,X3,X2))
          & p(c_2Ebool_2EIN_2E2(X0,X3,X1)) )
     => ( ~ p(c_2Ebool_2EIN_2E2(X0,sK4(X0,X1,X2),X2))
        & p(c_2Ebool_2EIN_2E2(X0,sK4(X0,X1,X2),X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f95,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2ESUBSET_2E2(X0,X1,X2))
        | ? [X3: X0] :
            ( ~ p(c_2Ebool_2EIN_2E2(X0,X3,X2))
            & p(c_2Ebool_2EIN_2E2(X0,X3,X1)) ) )
      & ( ! [X4: X0] :
            ( p(c_2Ebool_2EIN_2E2(X0,X4,X2))
            | ~ p(c_2Ebool_2EIN_2E2(X0,X4,X1)) )
        | ~ p(c_2Epred__set_2ESUBSET_2E2(X0,X1,X2)) ) ),
    inference(rectify,[],[f94]) ).

tff(f94,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ( p(c_2Epred__set_2ESUBSET_2E2(X0,X1,X2))
        | ? [X3: X0] :
            ( ~ p(c_2Ebool_2EIN_2E2(X0,X3,X2))
            & p(c_2Ebool_2EIN_2E2(X0,X3,X1)) ) )
      & ( ! [X3: X0] :
            ( p(c_2Ebool_2EIN_2E2(X0,X3,X2))
            | ~ p(c_2Ebool_2EIN_2E2(X0,X3,X1)) )
        | ~ p(c_2Epred__set_2ESUBSET_2E2(X0,X1,X2)) ) ),
    inference(nnf_transformation,[],[f65]) ).

tff(f65,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(X0,X1,X2))
    <=> ! [X3: X0] :
          ( p(c_2Ebool_2EIN_2E2(X0,X3,X2))
          | ~ p(c_2Ebool_2EIN_2E2(X0,X3,X1)) ) ),
    inference(ennf_transformation,[],[f57]) ).

tff(f57,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(X0,X1,X2))
    <=> ! [X3: X0] :
          ( p(c_2Ebool_2EIN_2E2(X0,X3,X1))
         => p(c_2Ebool_2EIN_2E2(X0,X3,X2)) ) ),
    inference(rectify,[],[f28]) ).

tff(f28,axiom,
    ! [X0: $tType,X14: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X15: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Epred__set_2ESUBSET_2E2(X0,X14,X15))
    <=> ! [X5: X0] :
          ( p(c_2Ebool_2EIN_2E2(X0,X5,X14))
         => p(c_2Ebool_2EIN_2E2(X0,X5,X15)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DEF) ).

tff(f1687,plain,
    ! [X0: $tType,X2: X0,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2EIN_2E2(X0,sK4(X0,c_2Epred__set_2EDELETE_2E2(X0,X1,X2),X3),X1))
      | p(c_2Epred__set_2ESUBSET_2E2(X0,c_2Epred__set_2EDELETE_2E2(X0,X1,X2),X3)) ),
    inference(resolution,[],[f152,f148]) ).

tff(f148,plain,
    ! [X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( p(c_2Ebool_2EIN_2E2(X0,sK4(X0,X1,X2),X1))
      | p(c_2Epred__set_2ESUBSET_2E2(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f97]) ).

tff(f152,plain,
    ! [X0: $tType,X2: X0,X3: X0,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] :
      ( ~ p(c_2Ebool_2EIN_2E2(X0,X2,c_2Epred__set_2EDELETE_2E2(X0,X1,X3)))
      | p(c_2Ebool_2EIN_2E2(X0,X2,X1)) ),
    inference(cnf_transformation,[],[f101]) ).

tff(f101,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: X0,X3: X0] :
      ( ( p(c_2Ebool_2EIN_2E2(X0,X2,c_2Epred__set_2EDELETE_2E2(X0,X1,X3)))
        | ( X2 = X3 )
        | ~ p(c_2Ebool_2EIN_2E2(X0,X2,X1)) )
      & ( ( ( X2 != X3 )
          & p(c_2Ebool_2EIN_2E2(X0,X2,X1)) )
        | ~ p(c_2Ebool_2EIN_2E2(X0,X2,c_2Epred__set_2EDELETE_2E2(X0,X1,X3))) ) ),
    inference(flattening,[],[f100]) ).

tff(f100,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: X0,X3: X0] :
      ( ( p(c_2Ebool_2EIN_2E2(X0,X2,c_2Epred__set_2EDELETE_2E2(X0,X1,X3)))
        | ( X2 = X3 )
        | ~ p(c_2Ebool_2EIN_2E2(X0,X2,X1)) )
      & ( ( ( X2 != X3 )
          & p(c_2Ebool_2EIN_2E2(X0,X2,X1)) )
        | ~ p(c_2Ebool_2EIN_2E2(X0,X2,c_2Epred__set_2EDELETE_2E2(X0,X1,X3))) ) ),
    inference(nnf_transformation,[],[f60]) ).

tff(f60,plain,
    ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2: X0,X3: X0] :
      ( p(c_2Ebool_2EIN_2E2(X0,X2,c_2Epred__set_2EDELETE_2E2(X0,X1,X3)))
    <=> ( ( X2 != X3 )
        & p(c_2Ebool_2EIN_2E2(X0,X2,X1)) ) ),
    inference(rectify,[],[f29]) ).

tff(f29,axiom,
    ! [X0: $tType,X14: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X11: X0,X16: X0] :
      ( p(c_2Ebool_2EIN_2E2(X0,X11,c_2Epred__set_2EDELETE_2E2(X0,X14,X16)))
    <=> ( ( X11 != X16 )
        & p(c_2Ebool_2EIN_2E2(X0,X11,X14)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EIN__DELETE) ).

tff(f102,plain,
    ~ p(c_2Epred__set_2ESUBSET_2E2(sK0,c_2Epred__set_2EREST_2E1(sK0,sK1),sK1)),
    inference(cnf_transformation,[],[f68]) ).

tff(f68,plain,
    ~ p(c_2Epred__set_2ESUBSET_2E2(sK0,c_2Epred__set_2EREST_2E1(sK0,sK1),sK1)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f61,f67]) ).

tff(f67,plain,
    ( ? [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ~ p(c_2Epred__set_2ESUBSET_2E2(X0,c_2Epred__set_2EREST_2E1(X0,X1),X1))
   => ~ p(c_2Epred__set_2ESUBSET_2E2(sK0,c_2Epred__set_2EREST_2E1(sK0,sK1),sK1)) ),
    introduced(choice_axiom,[]) ).

tff(f61,plain,
    ? [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : ~ p(c_2Epred__set_2ESUBSET_2E2(X0,c_2Epred__set_2EREST_2E1(X0,X1),X1)),
    inference(ennf_transformation,[],[f33]) ).

tff(f33,plain,
    ~ ! [X0: $tType,X1: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(X0,c_2Epred__set_2EREST_2E1(X0,X1),X1)),
    inference(rectify,[],[f32]) ).

tff(f32,negated_conjecture,
    ~ ! [X0: $tType,X14: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(X0,c_2Epred__set_2EREST_2E1(X0,X14),X14)),
    inference(negated_conjecture,[],[f31]) ).

tff(f31,conjecture,
    ! [X0: $tType,X14: tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)] : p(c_2Epred__set_2ESUBSET_2E2(X0,c_2Epred__set_2EREST_2E1(X0,X14),X14)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2EREST__SUBSET) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : ITP004_3 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.11/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.32  % Computer : n032.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit   : 300
% 0.13/0.32  % WCLimit    : 300
% 0.13/0.32  % DateTime   : Sat May 18 15:29:37 EDT 2024
% 0.13/0.32  % CPUTime    : 
% 0.13/0.32  % (4315)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.33  % (4318)WARNING: value z3 for option sas not known
% 0.13/0.34  % (4318)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)
% 0.13/0.34  % (4323)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)
% 0.13/0.34  % (4317)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.34  % (4323)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.34  % Exception at run slice level
% 0.13/0.34  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.35  % (4322)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)
% 0.13/0.35  % (4316)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.35  % (4324)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.35  % (4324)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.35  % Exception at run slice level
% 0.13/0.35  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.35  % Exception at run slice level
% 0.13/0.35  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.35  % (4320)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.35  % (4321)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)
% 0.13/0.35  % Exception at run slice level
% 0.13/0.35  User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.36  % (4325)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)
% 0.13/0.36  % (4325)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37  % (4326)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)
% 0.13/0.37  % (4327)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)
% 212.69/30.89  % (4318)First to succeed.
% 212.69/30.89  % (4318)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4315"
% 213.35/30.92  % (4318)Refutation found. Thanks to Tanya!
% 213.35/30.92  % SZS status Theorem for theBenchmark
% 213.35/30.92  % SZS output start Proof for theBenchmark
% See solution above
% 213.35/30.92  % (4318)------------------------------
% 213.35/30.92  % (4318)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 213.35/30.92  % (4318)Termination reason: Refutation
% 213.35/30.92  
% 213.35/30.92  % (4318)Memory used [KB]: 437547
% 213.35/30.92  % (4318)Time elapsed: 30.562 s
% 213.35/30.92  % (4318)Instructions burned: 69311 (million)
% 213.35/30.92  % (4315)Success in time 30.391 s
%------------------------------------------------------------------------------