TSTP Solution File: NUM388+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUM388+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% 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 : Thu Aug 31 11:30:15 EDT 2023

% Result   : Theorem 1.84s 1.16s
% Output   : CNFRefutation 1.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   58 (  13 unt;   0 def)
%            Number of atoms       :  180 (   1 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  184 (  62   ~;  49   |;  54   &)
%                                         (   3 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-1 aty)
%            Number of variables   :   92 (   1 sgn;  54   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] :
      ( ordinal(X0)
     => ( epsilon_connected(X0)
        & epsilon_transitive(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).

fof(f7,axiom,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( in(X1,X0)
         => subset(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).

fof(f24,conjecture,
    ! [X0] :
      ( ordinal(X0)
     => ! [X1] :
          ( ordinal(X1)
         => ! [X2] :
              ( epsilon_transitive(X2)
             => ( ( in(X0,X1)
                  & in(X2,X0) )
               => in(X2,X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_ordinal1) ).

fof(f25,negated_conjecture,
    ~ ! [X0] :
        ( ordinal(X0)
       => ! [X1] :
            ( ordinal(X1)
           => ! [X2] :
                ( epsilon_transitive(X2)
               => ( ( in(X0,X1)
                    & in(X2,X0) )
                 => in(X2,X1) ) ) ) ),
    inference(negated_conjecture,[],[f24]) ).

fof(f27,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(f28,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

fof(f29,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

fof(f32,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

fof(f43,plain,
    ! [X0] :
      ( ( epsilon_connected(X0)
        & epsilon_transitive(X0) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f49,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( subset(X1,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f50,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ in(X2,X1)
              & in(X0,X1)
              & in(X2,X0)
              & epsilon_transitive(X2) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f51,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ in(X2,X1)
              & in(X0,X1)
              & in(X2,X0)
              & epsilon_transitive(X2) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(flattening,[],[f50]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f53]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f55]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f61,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X1] :
            ( subset(X1,X0)
            | ~ in(X1,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(nnf_transformation,[],[f49]) ).

fof(f62,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(rectify,[],[f61]) ).

fof(f63,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ subset(X1,X0)
          & in(X1,X0) )
     => ( ~ subset(sK0(X0),X0)
        & in(sK0(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ( ~ subset(sK0(X0),X0)
          & in(sK0(X0),X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f62,f63]) ).

fof(f89,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ~ in(X2,X1)
                & in(X0,X1)
                & in(X2,X0)
                & epsilon_transitive(X2) )
            & ordinal(X1) )
        & ordinal(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ~ in(X2,X1)
              & in(sK13,X1)
              & in(X2,sK13)
              & epsilon_transitive(X2) )
          & ordinal(X1) )
      & ordinal(sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f90,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ~ in(X2,X1)
            & in(sK13,X1)
            & in(X2,sK13)
            & epsilon_transitive(X2) )
        & ordinal(X1) )
   => ( ? [X2] :
          ( ~ in(X2,sK14)
          & in(sK13,sK14)
          & in(X2,sK13)
          & epsilon_transitive(X2) )
      & ordinal(sK14) ) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ( ? [X2] :
        ( ~ in(X2,sK14)
        & in(sK13,sK14)
        & in(X2,sK13)
        & epsilon_transitive(X2) )
   => ( ~ in(sK15,sK14)
      & in(sK13,sK14)
      & in(sK15,sK13)
      & epsilon_transitive(sK15) ) ),
    introduced(choice_axiom,[]) ).

fof(f92,plain,
    ( ~ in(sK15,sK14)
    & in(sK13,sK14)
    & in(sK15,sK13)
    & epsilon_transitive(sK15)
    & ordinal(sK14)
    & ordinal(sK13) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f51,f91,f90,f89]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f28]) ).

fof(f96,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f102,plain,
    ! [X2,X0] :
      ( subset(X2,X0)
      | ~ in(X2,X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f134,plain,
    ordinal(sK14),
    inference(cnf_transformation,[],[f92]) ).

fof(f136,plain,
    in(sK15,sK13),
    inference(cnf_transformation,[],[f92]) ).

fof(f137,plain,
    in(sK13,sK14),
    inference(cnf_transformation,[],[f92]) ).

fof(f138,plain,
    ~ in(sK15,sK14),
    inference(cnf_transformation,[],[f92]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(c_52,plain,
    ( ~ ordinal(X0)
    | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f96]) ).

cnf(c_57,plain,
    ( ~ in(X0,X1)
    | ~ epsilon_transitive(X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f102]) ).

cnf(c_86,negated_conjecture,
    ~ in(sK15,sK14),
    inference(cnf_transformation,[],[f138]) ).

cnf(c_87,negated_conjecture,
    in(sK13,sK14),
    inference(cnf_transformation,[],[f137]) ).

cnf(c_88,negated_conjecture,
    in(sK15,sK13),
    inference(cnf_transformation,[],[f136]) ).

cnf(c_90,negated_conjecture,
    ordinal(sK14),
    inference(cnf_transformation,[],[f134]) ).

cnf(c_93,plain,
    ( ~ element(X0,X1)
    | in(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f140]) ).

cnf(c_94,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f142]) ).

cnf(c_96,plain,
    ( ~ element(X0,powerset(X1))
    | ~ in(X2,X0)
    | element(X2,X1) ),
    inference(cnf_transformation,[],[f143]) ).

cnf(c_99,plain,
    ( ~ in(X0,X1)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_116,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_94]) ).

cnf(c_136,plain,
    ( ~ ordinal(X0)
    | epsilon_transitive(X0) ),
    inference(prop_impl_just,[status(thm)],[c_52]) ).

cnf(c_218,plain,
    ( ~ in(X0,X1)
    | ~ subset(X1,X2)
    | element(X0,X2) ),
    inference(bin_hyper_res,[status(thm)],[c_96,c_116]) ).

cnf(c_466,plain,
    ( X0 != sK14
    | epsilon_transitive(X0) ),
    inference(resolution_lifted,[status(thm)],[c_136,c_90]) ).

cnf(c_467,plain,
    epsilon_transitive(sK14),
    inference(unflattening,[status(thm)],[c_466]) ).

cnf(c_1700,plain,
    ~ empty(sK14),
    inference(superposition,[status(thm)],[c_87,c_99]) ).

cnf(c_1770,plain,
    ( ~ subset(sK13,X0)
    | element(sK15,X0) ),
    inference(superposition,[status(thm)],[c_88,c_218]) ).

cnf(c_1791,plain,
    ( ~ epsilon_transitive(sK14)
    | subset(sK13,sK14) ),
    inference(superposition,[status(thm)],[c_87,c_57]) ).

cnf(c_1795,plain,
    subset(sK13,sK14),
    inference(forward_subsumption_resolution,[status(thm)],[c_1791,c_467]) ).

cnf(c_1816,plain,
    element(sK15,sK14),
    inference(superposition,[status(thm)],[c_1795,c_1770]) ).

cnf(c_1817,plain,
    ( in(sK15,sK14)
    | empty(sK14) ),
    inference(superposition,[status(thm)],[c_1816,c_93]) ).

cnf(c_1818,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1817,c_1700,c_86]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM388+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 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 : Fri Aug 25 15:38:33 EDT 2023
% 0.13/0.34  % 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 --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.84/1.16  % SZS status Started for theBenchmark.p
% 1.84/1.16  % SZS status Theorem for theBenchmark.p
% 1.84/1.16  
% 1.84/1.16  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.84/1.16  
% 1.84/1.16  ------  iProver source info
% 1.84/1.16  
% 1.84/1.16  git: date: 2023-05-31 18:12:56 +0000
% 1.84/1.16  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.84/1.16  git: non_committed_changes: false
% 1.84/1.16  git: last_make_outside_of_git: false
% 1.84/1.16  
% 1.84/1.16  ------ Parsing...
% 1.84/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.84/1.16  
% 1.84/1.16  ------ Preprocessing... sup_sim: 0  sf_s  rm: 19 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 5 0s  sf_e  pe_s  pe_e 
% 1.84/1.16  
% 1.84/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.84/1.16  
% 1.84/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.84/1.16  ------ Proving...
% 1.84/1.16  ------ Problem Properties 
% 1.84/1.16  
% 1.84/1.16  
% 1.84/1.16  clauses                                 28
% 1.84/1.16  conjectures                             4
% 1.84/1.16  EPR                                     23
% 1.84/1.16  Horn                                    26
% 1.84/1.16  unary                                   15
% 1.84/1.16  binary                                  8
% 1.84/1.16  lits                                    46
% 1.84/1.16  lits eq                                 2
% 1.84/1.16  fd_pure                                 0
% 1.84/1.16  fd_pseudo                               0
% 1.84/1.16  fd_cond                                 1
% 1.84/1.16  fd_pseudo_cond                          1
% 1.84/1.16  AC symbols                              0
% 1.84/1.16  
% 1.84/1.16  ------ Schedule dynamic 5 is on 
% 1.84/1.16  
% 1.84/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.84/1.16  
% 1.84/1.16  
% 1.84/1.16  ------ 
% 1.84/1.16  Current options:
% 1.84/1.16  ------ 
% 1.84/1.16  
% 1.84/1.16  
% 1.84/1.16  
% 1.84/1.16  
% 1.84/1.16  ------ Proving...
% 1.84/1.16  
% 1.84/1.16  
% 1.84/1.16  % SZS status Theorem for theBenchmark.p
% 1.84/1.16  
% 1.84/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.84/1.16  
% 1.84/1.16  
%------------------------------------------------------------------------------