TSTP Solution File: SET924+1 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET924+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n029.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 : Mon Jun 24 14:36:35 EDT 2024

% Result   : Theorem 1.62s 1.15s
% Output   : CNFRefutation 1.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   25 (   4 unt;   0 def)
%            Number of atoms       :   58 (  28 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   60 (  27   ~;  23   |;   5   &)
%                                         (   3 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   26 (   0 sgn  12   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,conjecture,
    ! [X0,X1] :
      ( singleton(X0) = set_difference(singleton(X0),X1)
    <=> ~ in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t67_zfmisc_1) ).

fof(f5,negated_conjecture,
    ~ ! [X0,X1] :
        ( singleton(X0) = set_difference(singleton(X0),X1)
      <=> ~ in(X0,X1) ),
    inference(negated_conjecture,[],[f4]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( singleton(X0) = set_difference(singleton(X0),X1)
    <=> ~ in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).

fof(f8,plain,
    ? [X0,X1] :
      ( singleton(X0) = set_difference(singleton(X0),X1)
    <~> ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f13,plain,
    ? [X0,X1] :
      ( ( in(X0,X1)
        | singleton(X0) != set_difference(singleton(X0),X1) )
      & ( ~ in(X0,X1)
        | singleton(X0) = set_difference(singleton(X0),X1) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f14,plain,
    ( ? [X0,X1] :
        ( ( in(X0,X1)
          | singleton(X0) != set_difference(singleton(X0),X1) )
        & ( ~ in(X0,X1)
          | singleton(X0) = set_difference(singleton(X0),X1) ) )
   => ( ( in(sK2,sK3)
        | singleton(sK2) != set_difference(singleton(sK2),sK3) )
      & ( ~ in(sK2,sK3)
        | singleton(sK2) = set_difference(singleton(sK2),sK3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ( ( in(sK2,sK3)
      | singleton(sK2) != set_difference(singleton(sK2),sK3) )
    & ( ~ in(sK2,sK3)
      | singleton(sK2) = set_difference(singleton(sK2),sK3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f13,f14]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = set_difference(singleton(X0),X1)
        | in(X0,X1) )
      & ( ~ in(X0,X1)
        | singleton(X0) != set_difference(singleton(X0),X1) ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f20,plain,
    ( ~ in(sK2,sK3)
    | singleton(sK2) = set_difference(singleton(sK2),sK3) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f21,plain,
    ( in(sK2,sK3)
    | singleton(sK2) != set_difference(singleton(sK2),sK3) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | singleton(X0) != set_difference(singleton(X0),X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( singleton(X0) = set_difference(singleton(X0),X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f16]) ).

cnf(c_52,negated_conjecture,
    ( set_difference(singleton(sK2),sK3) != singleton(sK2)
    | in(sK2,sK3) ),
    inference(cnf_transformation,[],[f21]) ).

cnf(c_53,negated_conjecture,
    ( ~ in(sK2,sK3)
    | set_difference(singleton(sK2),sK3) = singleton(sK2) ),
    inference(cnf_transformation,[],[f20]) ).

cnf(c_54,plain,
    ( set_difference(singleton(X0),X1) = singleton(X0)
    | in(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

cnf(c_55,plain,
    ( set_difference(singleton(X0),X1) != singleton(X0)
    | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

cnf(c_58,plain,
    ( in(sK2,sK3)
    | set_difference(singleton(sK2),sK3) != singleton(sK2) ),
    inference(prop_impl_just,[status(thm)],[c_52]) ).

cnf(c_59,plain,
    ( set_difference(singleton(sK2),sK3) != singleton(sK2)
    | in(sK2,sK3) ),
    inference(renaming,[status(thm)],[c_58]) ).

cnf(c_60,plain,
    ( ~ in(sK2,sK3)
    | set_difference(singleton(sK2),sK3) = singleton(sK2) ),
    inference(prop_impl_just,[status(thm)],[c_53]) ).

cnf(c_64,plain,
    ( in(X0,X1)
    | set_difference(singleton(X0),X1) = singleton(X0) ),
    inference(prop_impl_just,[status(thm)],[c_54]) ).

cnf(c_65,plain,
    ( set_difference(singleton(X0),X1) = singleton(X0)
    | in(X0,X1) ),
    inference(renaming,[status(thm)],[c_64]) ).

cnf(c_96,plain,
    in(sK2,sK3),
    inference(backward_subsumption_resolution,[status(thm)],[c_59,c_65]) ).

cnf(c_98,plain,
    set_difference(singleton(sK2),sK3) = singleton(sK2),
    inference(backward_subsumption_resolution,[status(thm)],[c_60,c_65]) ).

cnf(c_375,plain,
    ~ in(sK2,sK3),
    inference(superposition,[status(thm)],[c_98,c_55]) ).

cnf(c_379,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_375,c_96]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET924+1 : TPTP v8.2.0. Released v3.2.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Jun 23 15:00:39 EDT 2024
% 0.12/0.33  % 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 --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.62/1.15  % SZS status Started for theBenchmark.p
% 1.62/1.15  % SZS status Theorem for theBenchmark.p
% 1.62/1.15  
% 1.62/1.15  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 1.62/1.15  
% 1.62/1.15  ------  iProver source info
% 1.62/1.15  
% 1.62/1.15  git: date: 2024-06-12 09:56:46 +0000
% 1.62/1.15  git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 1.62/1.15  git: non_committed_changes: false
% 1.62/1.15  
% 1.62/1.15  ------ Parsing...
% 1.62/1.15  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.62/1.15  
% 1.62/1.15  ------ 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 
% 1.62/1.15  
% 1.62/1.15  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.62/1.15  
% 1.62/1.15  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.62/1.15  ------ Proving...
% 1.62/1.15  ------ Problem Properties 
% 1.62/1.15  
% 1.62/1.15  
% 1.62/1.15  clauses                                 6
% 1.62/1.15  conjectures                             0
% 1.62/1.15  EPR                                     3
% 1.62/1.15  Horn                                    5
% 1.62/1.15  unary                                   3
% 1.62/1.15  binary                                  3
% 1.62/1.15  lits                                    9
% 1.62/1.15  lits eq                                 4
% 1.62/1.15  fd_pure                                 0
% 1.62/1.15  fd_pseudo                               0
% 1.62/1.15  fd_cond                                 0
% 1.62/1.15  fd_pseudo_cond                          0
% 1.62/1.15  AC symbols                              0
% 1.62/1.15  
% 1.62/1.15  ------ Schedule dynamic 5 is on 
% 1.62/1.15  
% 1.62/1.15  ------ no conjectures: strip conj schedule 
% 1.62/1.15  
% 1.62/1.15  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.62/1.15  
% 1.62/1.15  
% 1.62/1.15  ------ 
% 1.62/1.15  Current options:
% 1.62/1.15  ------ 
% 1.62/1.15  
% 1.62/1.15  
% 1.62/1.15  
% 1.62/1.15  
% 1.62/1.15  ------ Proving...
% 1.62/1.15  
% 1.62/1.15  
% 1.62/1.15  % SZS status Theorem for theBenchmark.p
% 1.62/1.15  
% 1.62/1.15  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.62/1.15  
% 1.62/1.15  
%------------------------------------------------------------------------------