TSTP Solution File: SET880+1 by iProver---3.8

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%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET880+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% 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 : Thu Aug 31 15:10:27 EDT 2023

% Result   : Theorem 1.76s 1.13s
% Output   : CNFRefutation 1.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   24 (   7 unt;   0 def)
%            Number of atoms       :   77 (  50 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :   87 (  34   ~;  30   |;  16   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   40 (   0 sgn;  29   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( empty_set = set_difference(singleton(X0),X1)
    <=> in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).

fof(f7,conjecture,
    ! [X0,X1] :
      ( empty_set = set_difference(singleton(X0),singleton(X1))
     => X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1] :
        ( empty_set = set_difference(singleton(X0),singleton(X1))
       => X0 = X1 ),
    inference(negated_conjecture,[],[f7]) ).

fof(f10,plain,
    ? [X0,X1] :
      ( X0 != X1
      & empty_set = set_difference(singleton(X0),singleton(X1)) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f11]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK0(X0,X1) != X0
          | ~ in(sK0(X0,X1),X1) )
        & ( sK0(X0,X1) = X0
          | in(sK0(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK0(X0,X1) != X0
            | ~ in(sK0(X0,X1),X1) )
          & ( sK0(X0,X1) = X0
            | in(sK0(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f12,f13]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( empty_set = set_difference(singleton(X0),X1)
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | empty_set != set_difference(singleton(X0),X1) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f20,plain,
    ( ? [X0,X1] :
        ( X0 != X1
        & empty_set = set_difference(singleton(X0),singleton(X1)) )
   => ( sK3 != sK4
      & empty_set = set_difference(singleton(sK3),singleton(sK4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ( sK3 != sK4
    & empty_set = set_difference(singleton(sK3),singleton(sK4)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f10,f20]) ).

fof(f23,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f14]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty_set != set_difference(singleton(X0),X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f32,plain,
    empty_set = set_difference(singleton(sK3),singleton(sK4)),
    inference(cnf_transformation,[],[f21]) ).

fof(f33,plain,
    sK3 != sK4,
    inference(cnf_transformation,[],[f21]) ).

fof(f36,plain,
    ! [X3,X0] :
      ( X0 = X3
      | ~ in(X3,singleton(X0)) ),
    inference(equality_resolution,[],[f23]) ).

cnf(c_53,plain,
    ( ~ in(X0,singleton(X1))
    | X0 = X1 ),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_56,plain,
    ( set_difference(singleton(X0),X1) != empty_set
    | in(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

cnf(c_59,negated_conjecture,
    sK3 != sK4,
    inference(cnf_transformation,[],[f33]) ).

cnf(c_60,negated_conjecture,
    set_difference(singleton(sK3),singleton(sK4)) = empty_set,
    inference(cnf_transformation,[],[f32]) ).

cnf(c_459,plain,
    in(sK3,singleton(sK4)),
    inference(superposition,[status(thm)],[c_60,c_56]) ).

cnf(c_483,plain,
    sK3 = sK4,
    inference(superposition,[status(thm)],[c_459,c_53]) ).

cnf(c_484,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_483,c_59]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET880+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n008.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Aug 26 10:37:02 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.76/1.13  % SZS status Started for theBenchmark.p
% 1.76/1.13  % SZS status Theorem for theBenchmark.p
% 1.76/1.13  
% 1.76/1.13  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.76/1.13  
% 1.76/1.13  ------  iProver source info
% 1.76/1.13  
% 1.76/1.13  git: date: 2023-05-31 18:12:56 +0000
% 1.76/1.13  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.76/1.13  git: non_committed_changes: false
% 1.76/1.13  git: last_make_outside_of_git: false
% 1.76/1.13  
% 1.76/1.13  ------ Parsing...
% 1.76/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.76/1.13  
% 1.76/1.13  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 1.76/1.13  
% 1.76/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.76/1.13  
% 1.76/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.76/1.13  ------ Proving...
% 1.76/1.13  ------ Problem Properties 
% 1.76/1.13  
% 1.76/1.13  
% 1.76/1.13  clauses                                 12
% 1.76/1.13  conjectures                             2
% 1.76/1.13  EPR                                     5
% 1.76/1.13  Horn                                    11
% 1.76/1.13  unary                                   6
% 1.76/1.13  binary                                  4
% 1.76/1.13  lits                                    20
% 1.76/1.13  lits eq                                 9
% 1.76/1.13  fd_pure                                 0
% 1.76/1.13  fd_pseudo                               0
% 1.76/1.13  fd_cond                                 0
% 1.76/1.13  fd_pseudo_cond                          2
% 1.76/1.13  AC symbols                              0
% 1.76/1.13  
% 1.76/1.13  ------ Schedule dynamic 5 is on 
% 1.76/1.13  
% 1.76/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.76/1.13  
% 1.76/1.13  
% 1.76/1.13  ------ 
% 1.76/1.13  Current options:
% 1.76/1.13  ------ 
% 1.76/1.13  
% 1.76/1.13  
% 1.76/1.13  
% 1.76/1.13  
% 1.76/1.13  ------ Proving...
% 1.76/1.13  
% 1.76/1.13  
% 1.76/1.13  % SZS status Theorem for theBenchmark.p
% 1.76/1.13  
% 1.76/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.76/1.13  
% 1.76/1.13  
%------------------------------------------------------------------------------