TSTP Solution File: SET947+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n031.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 15:10:46 EDT 2023

% Result   : Theorem 0.49s 1.20s
% Output   : CNFRefutation 0.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   37 (   8 unt;   0 def)
%            Number of atoms       :  115 (  10 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  130 (  52   ~;  50   |;  19   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   74 (   0 sgn;  48   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] :
      ( powerset(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> subset(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => subset(X0,union(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).

fof(f8,conjecture,
    ! [X0] : subset(X0,powerset(union(X0))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).

fof(f9,negated_conjecture,
    ~ ! [X0] : subset(X0,powerset(union(X0))),
    inference(negated_conjecture,[],[f8]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f14,plain,
    ? [X0] : ~ subset(X0,powerset(union(X0))),
    inference(ennf_transformation,[],[f9]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | ~ subset(X2,X0) )
            & ( subset(X2,X0)
              | ~ in(X2,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ? [X2] :
            ( ( ~ subset(X2,X0)
              | ~ in(X2,X1) )
            & ( subset(X2,X0)
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(rectify,[],[f15]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ subset(X2,X0)
            | ~ in(X2,X1) )
          & ( subset(X2,X0)
            | in(X2,X1) ) )
     => ( ( ~ subset(sK0(X0,X1),X0)
          | ~ in(sK0(X0,X1),X1) )
        & ( subset(sK0(X0,X1),X0)
          | in(sK0(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( powerset(X0) = X1
        | ( ( ~ subset(sK0(X0,X1),X0)
            | ~ in(sK0(X0,X1),X1) )
          & ( subset(sK0(X0,X1),X0)
            | in(sK0(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ~ subset(X3,X0) )
            & ( subset(X3,X0)
              | ~ in(X3,X1) ) )
        | powerset(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f19]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK1(X0,X1),X1)
        & in(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK1(X0,X1),X1)
          & in(sK1(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f20,f21]) ).

fof(f27,plain,
    ( ? [X0] : ~ subset(X0,powerset(union(X0)))
   => ~ subset(sK4,powerset(union(sK4))) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ~ subset(sK4,powerset(union(sK4))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f14,f27]) ).

fof(f31,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | ~ subset(X3,X0)
      | powerset(X0) != X1 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ in(sK1(X0,X1),X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( subset(X0,union(X1))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f41,plain,
    ~ subset(sK4,powerset(union(sK4))),
    inference(cnf_transformation,[],[f28]) ).

fof(f42,plain,
    ! [X3,X0] :
      ( in(X3,powerset(X0))
      | ~ subset(X3,X0) ),
    inference(equality_resolution,[],[f31]) ).

cnf(c_52,plain,
    ( ~ subset(X0,X1)
    | in(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_54,plain,
    ( ~ in(sK1(X0,X1),X1)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_55,plain,
    ( in(sK1(X0,X1),X0)
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

cnf(c_57,plain,
    ( ~ in(X0,X1)
    | subset(X0,union(X1)) ),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_61,negated_conjecture,
    ~ subset(sK4,powerset(union(sK4))),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_80,plain,
    ( subset(X0,X1)
    | in(sK1(X0,X1),X0) ),
    inference(prop_impl_just,[status(thm)],[c_55]) ).

cnf(c_81,plain,
    ( in(sK1(X0,X1),X0)
    | subset(X0,X1) ),
    inference(renaming,[status(thm)],[c_80]) ).

cnf(c_396,plain,
    ( powerset(union(sK4)) != X1
    | X0 != sK4
    | in(sK1(X0,X1),X0) ),
    inference(resolution_lifted,[status(thm)],[c_81,c_61]) ).

cnf(c_397,plain,
    in(sK1(sK4,powerset(union(sK4))),sK4),
    inference(unflattening,[status(thm)],[c_396]) ).

cnf(c_1226,plain,
    ( ~ subset(sK1(X0,powerset(X1)),X1)
    | subset(X0,powerset(X1)) ),
    inference(superposition,[status(thm)],[c_52,c_54]) ).

cnf(c_1315,plain,
    ( ~ in(sK1(X0,powerset(union(X1))),X1)
    | subset(X0,powerset(union(X1))) ),
    inference(superposition,[status(thm)],[c_57,c_1226]) ).

cnf(c_1319,plain,
    ( ~ in(sK1(sK4,powerset(union(sK4))),sK4)
    | subset(sK4,powerset(union(sK4))) ),
    inference(instantiation,[status(thm)],[c_1315]) ).

cnf(c_1320,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_1319,c_397,c_61]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET947+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.34  % Computer : n031.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat Aug 26 15:09:23 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.49/1.20  % SZS status Started for theBenchmark.p
% 0.49/1.20  % SZS status Theorem for theBenchmark.p
% 0.49/1.20  
% 0.49/1.20  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.49/1.20  
% 0.49/1.20  ------  iProver source info
% 0.49/1.20  
% 0.49/1.20  git: date: 2023-05-31 18:12:56 +0000
% 0.49/1.20  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.49/1.20  git: non_committed_changes: false
% 0.49/1.20  git: last_make_outside_of_git: false
% 0.49/1.20  
% 0.49/1.20  ------ Parsing...
% 0.49/1.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.49/1.20  
% 0.49/1.20  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 0.49/1.20  
% 0.49/1.20  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.49/1.20  
% 0.49/1.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.49/1.20  ------ Proving...
% 0.49/1.20  ------ Problem Properties 
% 0.49/1.20  
% 0.49/1.20  
% 0.49/1.20  clauses                                 12
% 0.49/1.20  conjectures                             1
% 0.49/1.20  EPR                                     4
% 0.49/1.20  Horn                                    10
% 0.49/1.20  unary                                   3
% 0.49/1.20  binary                                  6
% 0.49/1.20  lits                                    24
% 0.49/1.20  lits eq                                 3
% 0.49/1.20  fd_pure                                 0
% 0.49/1.20  fd_pseudo                               0
% 0.49/1.20  fd_cond                                 0
% 0.49/1.20  fd_pseudo_cond                          2
% 0.49/1.20  AC symbols                              0
% 0.49/1.20  
% 0.49/1.20  ------ Schedule dynamic 5 is on 
% 0.49/1.20  
% 0.49/1.20  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.49/1.20  
% 0.49/1.20  
% 0.49/1.20  ------ 
% 0.49/1.20  Current options:
% 0.49/1.20  ------ 
% 0.49/1.20  
% 0.49/1.20  
% 0.49/1.20  
% 0.49/1.20  
% 0.49/1.20  ------ Proving...
% 0.49/1.20  
% 0.49/1.20  
% 0.49/1.20  % SZS status Theorem for theBenchmark.p
% 0.49/1.20  
% 0.49/1.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.49/1.20  
% 0.49/1.20  
%------------------------------------------------------------------------------