TSTP Solution File: ITP004+2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : ITP004+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n020.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 : Fri May  3 02:28:59 EDT 2024

% Result   : Theorem 4.03s 1.19s
% Output   : CNFRefutation 4.03s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0,X1,X2] :
      ( mem(X2,arr(X0,X1))
     => ! [X3] :
          ( mem(X3,X0)
         => mem(ap(X2,X3),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_tp) ).

fof(f17,axiom,
    ! [X8] :
      ( ne(X8)
     => mem(c_2Epred__set_2ECHOICE(X8),arr(arr(X8,bool),X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECHOICE) ).

fof(f19,axiom,
    ! [X8] :
      ( ne(X8)
     => mem(c_2Epred__set_2EREST(X8),arr(arr(X8,bool),arr(X8,bool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2EREST) ).

fof(f24,axiom,
    ! [X8] :
      ( ne(X8)
     => ! [X9] :
          ( mem(X9,arr(X8,bool))
         => ! [X10] :
              ( mem(X10,arr(X8,bool))
             => ( p(ap(ap(c_2Epred__set_2ESUBSET(X8),X9),X10))
              <=> ! [X11] :
                    ( mem(X11,X8)
                   => ( p(ap(ap(c_2Ebool_2EIN(X8),X11),X9))
                     => p(ap(ap(c_2Ebool_2EIN(X8),X11),X10)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2ESUBSET__DEF) ).

fof(f25,axiom,
    ! [X8] :
      ( ne(X8)
     => ! [X9] :
          ( mem(X9,arr(X8,bool))
         => ! [X12] :
              ( mem(X12,X8)
             => ! [X13] :
                  ( mem(X13,X8)
                 => ( p(ap(ap(c_2Ebool_2EIN(X8),X12),ap(ap(c_2Epred__set_2EDELETE(X8),X9),X13)))
                  <=> ( X12 != X13
                      & p(ap(ap(c_2Ebool_2EIN(X8),X12),X9)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EIN__DELETE) ).

fof(f26,axiom,
    ! [X8] :
      ( ne(X8)
     => ! [X9] :
          ( mem(X9,arr(X8,bool))
         => ap(c_2Epred__set_2EREST(X8),X9) = ap(ap(c_2Epred__set_2EDELETE(X8),X9),ap(c_2Epred__set_2ECHOICE(X8),X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF) ).

fof(f27,conjecture,
    ! [X8] :
      ( ne(X8)
     => ! [X9] :
          ( mem(X9,arr(X8,bool))
         => p(ap(ap(c_2Epred__set_2ESUBSET(X8),ap(c_2Epred__set_2EREST(X8),X9)),X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET) ).

fof(f28,negated_conjecture,
    ~ ! [X8] :
        ( ne(X8)
       => ! [X9] :
            ( mem(X9,arr(X8,bool))
           => p(ap(ap(c_2Epred__set_2ESUBSET(X8),ap(c_2Epred__set_2EREST(X8),X9)),X9)) ) ),
    inference(negated_conjecture,[],[f27]) ).

fof(f38,plain,
    ! [X0] :
      ( ne(X0)
     => mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)) ),
    inference(rectify,[],[f17]) ).

fof(f40,plain,
    ! [X0] :
      ( ne(X0)
     => mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool))) ),
    inference(rectify,[],[f19]) ).

fof(f45,plain,
    ! [X0] :
      ( ne(X0)
     => ! [X1] :
          ( mem(X1,arr(X0,bool))
         => ! [X2] :
              ( mem(X2,arr(X0,bool))
             => ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
              <=> ! [X3] :
                    ( mem(X3,X0)
                   => ( p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
                     => p(ap(ap(c_2Ebool_2EIN(X0),X3),X2)) ) ) ) ) ) ),
    inference(rectify,[],[f24]) ).

fof(f46,plain,
    ! [X0] :
      ( ne(X0)
     => ! [X1] :
          ( mem(X1,arr(X0,bool))
         => ! [X2] :
              ( mem(X2,X0)
             => ! [X3] :
                  ( mem(X3,X0)
                 => ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
                  <=> ( X2 != X3
                      & p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) ) ) ) ) ) ),
    inference(rectify,[],[f25]) ).

fof(f47,plain,
    ! [X0] :
      ( ne(X0)
     => ! [X1] :
          ( mem(X1,arr(X0,bool))
         => ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1)) ) ),
    inference(rectify,[],[f26]) ).

fof(f48,plain,
    ~ ! [X0] :
        ( ne(X0)
       => ! [X1] :
            ( mem(X1,arr(X0,bool))
           => p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1)) ) ),
    inference(rectify,[],[f28]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( mem(ap(X2,X3),X1)
          | ~ mem(X3,X0) )
      | ~ mem(X2,arr(X0,X1)) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f62,plain,
    ! [X0] :
      ( mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0))
      | ~ ne(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f64,plain,
    ! [X0] :
      ( mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool)))
      | ~ ne(X0) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f69,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
              <=> ! [X3] :
                    ( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
                    | ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
                    | ~ mem(X3,X0) ) )
              | ~ mem(X2,arr(X0,bool)) )
          | ~ mem(X1,arr(X0,bool)) )
      | ~ ne(X0) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f70,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
              <=> ! [X3] :
                    ( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
                    | ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
                    | ~ mem(X3,X0) ) )
              | ~ mem(X2,arr(X0,bool)) )
          | ~ mem(X1,arr(X0,bool)) )
      | ~ ne(X0) ),
    inference(flattening,[],[f69]) ).

fof(f71,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
                  <=> ( X2 != X3
                      & p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) ) )
                  | ~ mem(X3,X0) )
              | ~ mem(X2,X0) )
          | ~ mem(X1,arr(X0,bool)) )
      | ~ ne(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f72,plain,
    ! [X0] :
      ( ! [X1] :
          ( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1))
          | ~ mem(X1,arr(X0,bool)) )
      | ~ ne(X0) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f73,plain,
    ? [X0] :
      ( ? [X1] :
          ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1))
          & mem(X1,arr(X0,bool)) )
      & ne(X0) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f87,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
                  | ? [X3] :
                      ( ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
                      & p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
                      & mem(X3,X0) ) )
                & ( ! [X3] :
                      ( p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
                      | ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
                      | ~ mem(X3,X0) )
                  | ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) )
              | ~ mem(X2,arr(X0,bool)) )
          | ~ mem(X1,arr(X0,bool)) )
      | ~ ne(X0) ),
    inference(nnf_transformation,[],[f70]) ).

fof(f88,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
                  | ? [X3] :
                      ( ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
                      & p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
                      & mem(X3,X0) ) )
                & ( ! [X4] :
                      ( p(ap(ap(c_2Ebool_2EIN(X0),X4),X2))
                      | ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
                      | ~ mem(X4,X0) )
                  | ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) )
              | ~ mem(X2,arr(X0,bool)) )
          | ~ mem(X1,arr(X0,bool)) )
      | ~ ne(X0) ),
    inference(rectify,[],[f87]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ~ p(ap(ap(c_2Ebool_2EIN(X0),X3),X2))
          & p(ap(ap(c_2Ebool_2EIN(X0),X3),X1))
          & mem(X3,X0) )
     => ( ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X2))
        & p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X1))
        & mem(sK2(X0,X1,X2),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f90,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
                  | ( ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X2))
                    & p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X1))
                    & mem(sK2(X0,X1,X2),X0) ) )
                & ( ! [X4] :
                      ( p(ap(ap(c_2Ebool_2EIN(X0),X4),X2))
                      | ~ p(ap(ap(c_2Ebool_2EIN(X0),X4),X1))
                      | ~ mem(X4,X0) )
                  | ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ) )
              | ~ mem(X2,arr(X0,bool)) )
          | ~ mem(X1,arr(X0,bool)) )
      | ~ ne(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f88,f89]) ).

fof(f91,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
                      | X2 = X3
                      | ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) )
                    & ( ( X2 != X3
                        & p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) )
                      | ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ) )
                  | ~ mem(X3,X0) )
              | ~ mem(X2,X0) )
          | ~ mem(X1,arr(X0,bool)) )
      | ~ ne(X0) ),
    inference(nnf_transformation,[],[f71]) ).

fof(f92,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
                      | X2 = X3
                      | ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) )
                    & ( ( X2 != X3
                        & p(ap(ap(c_2Ebool_2EIN(X0),X2),X1)) )
                      | ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3))) ) )
                  | ~ mem(X3,X0) )
              | ~ mem(X2,X0) )
          | ~ mem(X1,arr(X0,bool)) )
      | ~ ne(X0) ),
    inference(flattening,[],[f91]) ).

fof(f93,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(X0),ap(c_2Epred__set_2EREST(X0),X1)),X1))
            & mem(X1,arr(X0,bool)) )
        & ne(X0) )
   => ( ? [X1] :
          ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),X1)),X1))
          & mem(X1,arr(sK3,bool)) )
      & ne(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ( ? [X1] :
        ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),X1)),X1))
        & mem(X1,arr(sK3,bool)) )
   => ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4))
      & mem(sK4,arr(sK3,bool)) ) ),
    introduced(choice_axiom,[]) ).

fof(f95,plain,
    ( ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4))
    & mem(sK4,arr(sK3,bool))
    & ne(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f73,f94,f93]) ).

fof(f99,plain,
    ! [X2,X3,X0,X1] :
      ( mem(ap(X2,X3),X1)
      | ~ mem(X3,X0)
      | ~ mem(X2,arr(X0,X1)) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f119,plain,
    ! [X0] :
      ( mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0))
      | ~ ne(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f121,plain,
    ! [X0] :
      ( mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool)))
      | ~ ne(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f130,plain,
    ! [X2,X0,X1] :
      ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
      | mem(sK2(X0,X1,X2),X0)
      | ~ mem(X2,arr(X0,bool))
      | ~ mem(X1,arr(X0,bool))
      | ~ ne(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f131,plain,
    ! [X2,X0,X1] :
      ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
      | p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X1))
      | ~ mem(X2,arr(X0,bool))
      | ~ mem(X1,arr(X0,bool))
      | ~ ne(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f132,plain,
    ! [X2,X0,X1] :
      ( p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2))
      | ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X2))
      | ~ mem(X2,arr(X0,bool))
      | ~ mem(X1,arr(X0,bool))
      | ~ ne(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f133,plain,
    ! [X2,X3,X0,X1] :
      ( p(ap(ap(c_2Ebool_2EIN(X0),X2),X1))
      | ~ p(ap(ap(c_2Ebool_2EIN(X0),X2),ap(ap(c_2Epred__set_2EDELETE(X0),X1),X3)))
      | ~ mem(X3,X0)
      | ~ mem(X2,X0)
      | ~ mem(X1,arr(X0,bool))
      | ~ ne(X0) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( ap(c_2Epred__set_2EREST(X0),X1) = ap(ap(c_2Epred__set_2EDELETE(X0),X1),ap(c_2Epred__set_2ECHOICE(X0),X1))
      | ~ mem(X1,arr(X0,bool))
      | ~ ne(X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f137,plain,
    ne(sK3),
    inference(cnf_transformation,[],[f95]) ).

fof(f138,plain,
    mem(sK4,arr(sK3,bool)),
    inference(cnf_transformation,[],[f95]) ).

fof(f139,plain,
    ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4)),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_52,plain,
    ( ~ mem(X0,arr(X1,X2))
    | ~ mem(X3,X1)
    | mem(ap(X0,X3),X2) ),
    inference(cnf_transformation,[],[f99]) ).

cnf(c_72,plain,
    ( ~ ne(X0)
    | mem(c_2Epred__set_2ECHOICE(X0),arr(arr(X0,bool),X0)) ),
    inference(cnf_transformation,[],[f119]) ).

cnf(c_74,plain,
    ( ~ ne(X0)
    | mem(c_2Epred__set_2EREST(X0),arr(arr(X0,bool),arr(X0,bool))) ),
    inference(cnf_transformation,[],[f121]) ).

cnf(c_82,plain,
    ( ~ p(ap(ap(c_2Ebool_2EIN(X0),sK2(X0,X1,X2)),X2))
    | ~ mem(X1,arr(X0,bool))
    | ~ mem(X2,arr(X0,bool))
    | ~ ne(X0)
    | p(ap(ap(c_2Epred__set_2ESUBSET(X0),X1),X2)) ),
    inference(cnf_transformation,[],[f132]) ).

cnf(c_83,plain,
    ( ~ mem(X0,arr(X1,bool))
    | ~ mem(X2,arr(X1,bool))
    | ~ ne(X1)
    | p(ap(ap(c_2Ebool_2EIN(X1),sK2(X1,X0,X2)),X0))
    | p(ap(ap(c_2Epred__set_2ESUBSET(X1),X0),X2)) ),
    inference(cnf_transformation,[],[f131]) ).

cnf(c_84,plain,
    ( ~ mem(X0,arr(X1,bool))
    | ~ mem(X2,arr(X1,bool))
    | ~ ne(X1)
    | p(ap(ap(c_2Epred__set_2ESUBSET(X1),X0),X2))
    | mem(sK2(X1,X0,X2),X1) ),
    inference(cnf_transformation,[],[f130]) ).

cnf(c_88,plain,
    ( ~ p(ap(ap(c_2Ebool_2EIN(X0),X1),ap(ap(c_2Epred__set_2EDELETE(X0),X2),X3)))
    | ~ mem(X2,arr(X0,bool))
    | ~ mem(X1,X0)
    | ~ mem(X3,X0)
    | ~ ne(X0)
    | p(ap(ap(c_2Ebool_2EIN(X0),X1),X2)) ),
    inference(cnf_transformation,[],[f133]) ).

cnf(c_89,plain,
    ( ~ mem(X0,arr(X1,bool))
    | ~ ne(X1)
    | ap(ap(c_2Epred__set_2EDELETE(X1),X0),ap(c_2Epred__set_2ECHOICE(X1),X0)) = ap(c_2Epred__set_2EREST(X1),X0) ),
    inference(cnf_transformation,[],[f136]) ).

cnf(c_90,negated_conjecture,
    ~ p(ap(ap(c_2Epred__set_2ESUBSET(sK3),ap(c_2Epred__set_2EREST(sK3),sK4)),sK4)),
    inference(cnf_transformation,[],[f139]) ).

cnf(c_91,negated_conjecture,
    mem(sK4,arr(sK3,bool)),
    inference(cnf_transformation,[],[f138]) ).

cnf(c_92,negated_conjecture,
    ne(sK3),
    inference(cnf_transformation,[],[f137]) ).

cnf(c_696,plain,
    arr(sK3,bool) = sP0_iProver_def,
    definition ).

cnf(c_697,plain,
    c_2Epred__set_2ESUBSET(sK3) = sP1_iProver_def,
    definition ).

cnf(c_698,plain,
    c_2Epred__set_2EREST(sK3) = sP2_iProver_def,
    definition ).

cnf(c_699,plain,
    ap(sP2_iProver_def,sK4) = sP3_iProver_def,
    definition ).

cnf(c_700,plain,
    ap(sP1_iProver_def,sP3_iProver_def) = sP4_iProver_def,
    definition ).

cnf(c_701,plain,
    ap(sP4_iProver_def,sK4) = sP5_iProver_def,
    definition ).

cnf(c_702,negated_conjecture,
    ne(sK3),
    inference(demodulation,[status(thm)],[c_92]) ).

cnf(c_703,negated_conjecture,
    mem(sK4,sP0_iProver_def),
    inference(demodulation,[status(thm)],[c_91,c_696]) ).

cnf(c_704,negated_conjecture,
    ~ p(sP5_iProver_def),
    inference(demodulation,[status(thm)],[c_90,c_698,c_699,c_697,c_700,c_701]) ).

cnf(c_1446,plain,
    ( ~ ne(sK3)
    | mem(c_2Epred__set_2ECHOICE(sK3),arr(sP0_iProver_def,sK3)) ),
    inference(superposition,[status(thm)],[c_696,c_72]) ).

cnf(c_1448,plain,
    mem(c_2Epred__set_2ECHOICE(sK3),arr(sP0_iProver_def,sK3)),
    inference(forward_subsumption_resolution,[status(thm)],[c_1446,c_702]) ).

cnf(c_1534,plain,
    ( ~ ne(sK3)
    | mem(c_2Epred__set_2EREST(sK3),arr(sP0_iProver_def,sP0_iProver_def)) ),
    inference(superposition,[status(thm)],[c_696,c_74]) ).

cnf(c_1538,plain,
    ( ~ ne(sK3)
    | mem(sP2_iProver_def,arr(sP0_iProver_def,sP0_iProver_def)) ),
    inference(light_normalisation,[status(thm)],[c_1534,c_698]) ).

cnf(c_1539,plain,
    mem(sP2_iProver_def,arr(sP0_iProver_def,sP0_iProver_def)),
    inference(forward_subsumption_resolution,[status(thm)],[c_1538,c_702]) ).

cnf(c_1568,plain,
    ( ~ mem(X0,sP0_iProver_def)
    | mem(ap(c_2Epred__set_2ECHOICE(sK3),X0),sK3) ),
    inference(superposition,[status(thm)],[c_1448,c_52]) ).

cnf(c_1642,plain,
    ( ~ mem(X0,sP0_iProver_def)
    | mem(ap(sP2_iProver_def,X0),sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_1539,c_52]) ).

cnf(c_1688,plain,
    ( ~ mem(sK4,sP0_iProver_def)
    | mem(sP3_iProver_def,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_699,c_1642]) ).

cnf(c_1691,plain,
    mem(sP3_iProver_def,sP0_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_1688,c_703]) ).

cnf(c_3155,plain,
    ( ~ mem(X0,sP0_iProver_def)
    | ~ ne(sK3)
    | ap(ap(c_2Epred__set_2EDELETE(sK3),X0),ap(c_2Epred__set_2ECHOICE(sK3),X0)) = ap(c_2Epred__set_2EREST(sK3),X0) ),
    inference(superposition,[status(thm)],[c_696,c_89]) ).

cnf(c_3159,plain,
    ( ~ mem(X0,sP0_iProver_def)
    | ~ ne(sK3)
    | ap(ap(c_2Epred__set_2EDELETE(sK3),X0),ap(c_2Epred__set_2ECHOICE(sK3),X0)) = ap(sP2_iProver_def,X0) ),
    inference(light_normalisation,[status(thm)],[c_3155,c_698]) ).

cnf(c_3160,plain,
    ( ~ mem(X0,sP0_iProver_def)
    | ap(ap(c_2Epred__set_2EDELETE(sK3),X0),ap(c_2Epred__set_2ECHOICE(sK3),X0)) = ap(sP2_iProver_def,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3159,c_702]) ).

cnf(c_3340,plain,
    ap(ap(c_2Epred__set_2EDELETE(sK3),sK4),ap(c_2Epred__set_2ECHOICE(sK3),sK4)) = ap(sP2_iProver_def,sK4),
    inference(superposition,[status(thm)],[c_703,c_3160]) ).

cnf(c_3349,plain,
    ap(ap(c_2Epred__set_2EDELETE(sK3),sK4),ap(c_2Epred__set_2ECHOICE(sK3),sK4)) = sP3_iProver_def,
    inference(light_normalisation,[status(thm)],[c_3340,c_699]) ).

cnf(c_3508,plain,
    ( ~ mem(X0,arr(sK3,bool))
    | ~ mem(X1,arr(sK3,bool))
    | ~ ne(sK3)
    | mem(sK2(sK3,X0,X1),sK3)
    | p(ap(ap(sP1_iProver_def,X0),X1)) ),
    inference(superposition,[status(thm)],[c_697,c_84]) ).

cnf(c_3523,plain,
    ( ~ mem(X0,sP0_iProver_def)
    | ~ mem(X1,sP0_iProver_def)
    | ~ ne(sK3)
    | mem(sK2(sK3,X0,X1),sK3)
    | p(ap(ap(sP1_iProver_def,X0),X1)) ),
    inference(light_normalisation,[status(thm)],[c_3508,c_696]) ).

cnf(c_3524,plain,
    ( ~ mem(X0,sP0_iProver_def)
    | ~ mem(X1,sP0_iProver_def)
    | mem(sK2(sK3,X0,X1),sK3)
    | p(ap(ap(sP1_iProver_def,X0),X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3523,c_702]) ).

cnf(c_3788,plain,
    ( ~ mem(X0,sP0_iProver_def)
    | ~ mem(sP3_iProver_def,sP0_iProver_def)
    | mem(sK2(sK3,sP3_iProver_def,X0),sK3)
    | p(ap(sP4_iProver_def,X0)) ),
    inference(superposition,[status(thm)],[c_700,c_3524]) ).

cnf(c_3790,plain,
    ( ~ mem(X0,sP0_iProver_def)
    | mem(sK2(sK3,sP3_iProver_def,X0),sK3)
    | p(ap(sP4_iProver_def,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3788,c_1691]) ).

cnf(c_4357,plain,
    ( ~ p(ap(ap(c_2Ebool_2EIN(sK3),X0),sP3_iProver_def))
    | ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
    | ~ mem(sK4,arr(sK3,bool))
    | ~ mem(X0,sK3)
    | ~ ne(sK3)
    | p(ap(ap(c_2Ebool_2EIN(sK3),X0),sK4)) ),
    inference(superposition,[status(thm)],[c_3349,c_88]) ).

cnf(c_4359,plain,
    ( ~ p(ap(ap(c_2Ebool_2EIN(sK3),X0),sP3_iProver_def))
    | ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
    | ~ mem(X0,sK3)
    | ~ mem(sK4,sP0_iProver_def)
    | ~ ne(sK3)
    | p(ap(ap(c_2Ebool_2EIN(sK3),X0),sK4)) ),
    inference(light_normalisation,[status(thm)],[c_4357,c_696]) ).

cnf(c_4360,plain,
    ( ~ p(ap(ap(c_2Ebool_2EIN(sK3),X0),sP3_iProver_def))
    | ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
    | ~ mem(X0,sK3)
    | p(ap(ap(c_2Ebool_2EIN(sK3),X0),sK4)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4359,c_702,c_703]) ).

cnf(c_4715,plain,
    ( ~ mem(sK2(sK3,sP3_iProver_def,X0),sK3)
    | ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
    | ~ mem(X0,arr(sK3,bool))
    | ~ mem(sP3_iProver_def,arr(sK3,bool))
    | ~ ne(sK3)
    | p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,sP3_iProver_def,X0)),sK4))
    | p(ap(ap(c_2Epred__set_2ESUBSET(sK3),sP3_iProver_def),X0)) ),
    inference(superposition,[status(thm)],[c_83,c_4360]) ).

cnf(c_4723,plain,
    ( ~ mem(sK2(sK3,sP3_iProver_def,X0),sK3)
    | ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
    | ~ mem(X0,sP0_iProver_def)
    | ~ mem(sP3_iProver_def,sP0_iProver_def)
    | ~ ne(sK3)
    | p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,sP3_iProver_def,X0)),sK4))
    | p(ap(sP4_iProver_def,X0)) ),
    inference(light_normalisation,[status(thm)],[c_4715,c_696,c_697,c_700]) ).

cnf(c_4724,plain,
    ( ~ mem(sK2(sK3,sP3_iProver_def,X0),sK3)
    | ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
    | ~ mem(X0,sP0_iProver_def)
    | p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,sP3_iProver_def,X0)),sK4))
    | p(ap(sP4_iProver_def,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4723,c_702,c_1691]) ).

cnf(c_4758,plain,
    ( ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
    | ~ mem(X0,sP0_iProver_def)
    | p(ap(ap(c_2Ebool_2EIN(sK3),sK2(sK3,sP3_iProver_def,X0)),sK4))
    | p(ap(sP4_iProver_def,X0)) ),
    inference(global_subsumption_just,[status(thm)],[c_4724,c_3790,c_4724]) ).

cnf(c_4769,plain,
    ( ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
    | ~ mem(sK4,arr(sK3,bool))
    | ~ mem(sP3_iProver_def,arr(sK3,bool))
    | ~ mem(sK4,sP0_iProver_def)
    | ~ ne(sK3)
    | p(ap(ap(c_2Epred__set_2ESUBSET(sK3),sP3_iProver_def),sK4))
    | p(ap(sP4_iProver_def,sK4)) ),
    inference(superposition,[status(thm)],[c_4758,c_82]) ).

cnf(c_4770,plain,
    ( ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3)
    | ~ mem(sK4,sP0_iProver_def)
    | ~ mem(sP3_iProver_def,sP0_iProver_def)
    | ~ ne(sK3)
    | p(sP5_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_4769,c_696,c_697,c_700,c_701]) ).

cnf(c_4771,plain,
    ~ mem(ap(c_2Epred__set_2ECHOICE(sK3),sK4),sK3),
    inference(forward_subsumption_resolution,[status(thm)],[c_4770,c_704,c_702,c_1691,c_703]) ).

cnf(c_4773,plain,
    ~ mem(sK4,sP0_iProver_def),
    inference(superposition,[status(thm)],[c_1568,c_4771]) ).

cnf(c_4774,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_4773,c_703]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ITP004+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n020.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May  2 21:50:01 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.03/1.19  % SZS status Started for theBenchmark.p
% 4.03/1.19  % SZS status Theorem for theBenchmark.p
% 4.03/1.19  
% 4.03/1.19  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.03/1.19  
% 4.03/1.19  ------  iProver source info
% 4.03/1.19  
% 4.03/1.19  git: date: 2024-05-02 19:28:25 +0000
% 4.03/1.19  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.03/1.19  git: non_committed_changes: false
% 4.03/1.19  
% 4.03/1.19  ------ Parsing...
% 4.03/1.19  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.03/1.19  
% 4.03/1.19  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 4.03/1.19  
% 4.03/1.19  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.03/1.19  
% 4.03/1.19  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.03/1.19  ------ Proving...
% 4.03/1.19  ------ Problem Properties 
% 4.03/1.19  
% 4.03/1.19  
% 4.03/1.19  clauses                                 50
% 4.03/1.19  conjectures                             3
% 4.03/1.19  EPR                                     7
% 4.03/1.19  Horn                                    42
% 4.03/1.19  unary                                   14
% 4.03/1.19  binary                                  9
% 4.03/1.19  lits                                    151
% 4.03/1.19  lits eq                                 16
% 4.03/1.19  fd_pure                                 0
% 4.03/1.19  fd_pseudo                               0
% 4.03/1.19  fd_cond                                 0
% 4.03/1.19  fd_pseudo_cond                          6
% 4.03/1.19  AC symbols                              0
% 4.03/1.19  
% 4.03/1.19  ------ Schedule dynamic 5 is on 
% 4.03/1.19  
% 4.03/1.19  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.03/1.19  
% 4.03/1.19  
% 4.03/1.19  ------ 
% 4.03/1.19  Current options:
% 4.03/1.19  ------ 
% 4.03/1.19  
% 4.03/1.19  
% 4.03/1.19  
% 4.03/1.19  
% 4.03/1.19  ------ Proving...
% 4.03/1.19  
% 4.03/1.19  
% 4.03/1.19  % SZS status Theorem for theBenchmark.p
% 4.03/1.19  
% 4.03/1.19  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.03/1.20  
% 4.03/1.20  
%------------------------------------------------------------------------------