TSTP Solution File: ITP004+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP004+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.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 06:56:30 EDT 2024

% Result   : Theorem 176.70s 25.77s
% Output   : Refutation 176.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   46 (  17 unt;   0 def)
%            Number of atoms       :  112 (  21 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  109 (  43   ~;  37   |;  15   &)
%                                         (   7 <=>;   6  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   5 con; 0-3 aty)
%            Number of variables   :   94 (  87   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f236337,plain,
    $false,
    inference(resolution,[],[f236175,f104]) ).

fof(f104,plain,
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Etruth) ).

fof(f236175,plain,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
    inference(resolution,[],[f236165,f103]) ).

fof(f103,plain,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Enotfalse) ).

fof(f236165,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
    | ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
    inference(forward_demodulation,[],[f235976,f325]) ).

fof(f325,plain,
    s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),
    inference(resolution,[],[f281,f102]) ).

fof(f102,plain,
    ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f61,f67]) ).

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

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

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

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

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

fof(f281,plain,
    ! [X0] :
      ( p(s(tyop_2Emin_2Ebool,X0))
      | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,X0) ),
    inference(resolution,[],[f116,f103]) ).

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

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

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

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

fof(f2,axiom,
    ! [X5,X6] :
      ( ( p(s(tyop_2Emin_2Ebool,X5))
      <=> p(s(tyop_2Emin_2Ebool,X6)) )
     => s(tyop_2Emin_2Ebool,X5) = s(tyop_2Emin_2Ebool,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reserved_2Eho_2Eboolext) ).

fof(f235976,plain,
    ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
    | p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)))) ),
    inference(resolution,[],[f235330,f149]) ).

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

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

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

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

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

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

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

fof(f28,axiom,
    ! [X0,X14,X15] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X14),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X15))))
    <=> ! [X4] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X14))))
         => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X4),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X15)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Epred__set_2ESUBSET__DEF) ).

fof(f235330,plain,
    ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK4(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))
    | ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
    inference(superposition,[],[f33626,f234863]) ).

fof(f234863,plain,
    s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK4(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))),
    inference(resolution,[],[f234561,f104]) ).

fof(f234561,plain,
    ! [X0] :
      ( ~ p(s(tyop_2Emin_2Ebool,X0))
      | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK4(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))) ),
    inference(resolution,[],[f231600,f103]) ).

fof(f231600,plain,
    ! [X0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
      | ~ p(s(tyop_2Emin_2Ebool,X0))
      | s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(sK0,sK4(sK0,c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1)),sK1)),s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK1))))) ),
    inference(superposition,[],[f24315,f325]) ).

fof(f24315,plain,
    ! [X2,X3,X0,X1] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X2))))
      | ~ p(s(tyop_2Emin_2Ebool,X3))
      | s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,sK4(X0,X1,X2)),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))) = s(tyop_2Emin_2Ebool,X3) ),
    inference(resolution,[],[f148,f117]) ).

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

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

fof(f33626,plain,
    ! [X2,X0,X1] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EREST_2E1(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1))))))
      | p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))) ),
    inference(superposition,[],[f152,f114]) ).

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

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

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

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

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

fof(f100,plain,
    ! [X0,X1,X2,X3] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3))))))
        | s(X0,X2) = s(X0,X3)
        | ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))) )
      & ( ( s(X0,X2) != s(X0,X3)
          & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))) )
        | ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3)))))) ) ),
    inference(nnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1,X2,X3] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),c_2Epred__set_2EDELETE_2E2(s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1),s(X0,X3))))))
    <=> ( s(X0,X2) != s(X0,X3)
        & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(X0,X2),s(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X1)))) ) ),
    inference(rectify,[],[f29]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.15  % Problem    : ITP004+1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.04/0.17  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.38  % Computer : n008.cluster.edu
% 0.15/0.38  % Model    : x86_64 x86_64
% 0.15/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38  % Memory   : 8042.1875MB
% 0.15/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38  % CPULimit   : 300
% 0.15/0.38  % WCLimit    : 300
% 0.15/0.38  % DateTime   : Fri May  3 19:04:23 EDT 2024
% 0.15/0.38  % CPUTime    : 
% 0.15/0.39  % (7841)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.40  % (7848)WARNING: value z3 for option sas not known
% 0.22/0.41  % (7846)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.41  % (7848)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)
% 0.22/0.41  % (7850)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)
% 0.22/0.41  % (7851)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)
% 0.22/0.41  % (7849)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.41  % (7847)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.41  % (7852)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)
% 0.22/0.44  TRYING [1]
% 0.22/0.44  TRYING [1]
% 0.22/0.44  TRYING [2]
% 0.22/0.45  TRYING [2]
% 0.22/0.51  TRYING [3]
% 0.22/0.52  TRYING [3]
% 2.45/0.76  TRYING [4]
% 3.94/0.96  TRYING [4]
% 8.15/1.53  TRYING [1]
% 8.15/1.54  TRYING [2]
% 8.15/1.58  TRYING [3]
% 12.24/2.12  TRYING [4]
% 38.50/5.89  TRYING [5]
% 176.70/25.75  % (7851)First to succeed.
% 176.70/25.76  % (7851)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-7841"
% 176.70/25.77  % (7851)Refutation found. Thanks to Tanya!
% 176.70/25.77  % SZS status Theorem for theBenchmark
% 176.70/25.77  % SZS output start Proof for theBenchmark
% See solution above
% 176.70/25.77  % (7851)------------------------------
% 176.70/25.77  % (7851)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 176.70/25.77  % (7851)Termination reason: Refutation
% 176.70/25.77  
% 176.70/25.77  % (7851)Memory used [KB]: 57916
% 176.70/25.77  % (7851)Time elapsed: 25.362 s
% 176.70/25.77  % (7851)Instructions burned: 81277 (million)
% 176.70/25.77  % (7841)Success in time 25.259 s
%------------------------------------------------------------------------------