TSTP Solution File: SET020+1 by iProver---3.8

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%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SET020+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n005.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 15:05:36 EDT 2023

% Result   : Theorem 3.65s 1.16s
% Output   : CNFRefutation 3.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   38 (  18 unt;   0 def)
%            Number of atoms       :   96 (  55 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   93 (  35   ~;  25   |;  28   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   46 (   0 sgn;  31   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).

fof(f7,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ( member(X1,universal_class)
        & member(X0,universal_class) )
     => ( second(ordered_pair(X0,X1)) = X1
        & first(ordered_pair(X0,X1)) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_second) ).

fof(f44,conjecture,
    ! [X2,X3,X0] :
      ( ( ordered_pair(X2,X3) = X0
        & member(X3,universal_class)
        & member(X2,universal_class) )
     => ( second(X0) = X3
        & first(X0) = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).

fof(f45,negated_conjecture,
    ~ ! [X2,X3,X0] :
        ( ( ordered_pair(X2,X3) = X0
          & member(X3,universal_class)
          & member(X2,universal_class) )
       => ( second(X0) = X3
          & first(X0) = X2 ) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f70,plain,
    ~ ! [X0,X1,X2] :
        ( ( ordered_pair(X0,X1) = X2
          & member(X1,universal_class)
          & member(X0,universal_class) )
       => ( second(X2) = X1
          & first(X2) = X0 ) ),
    inference(rectify,[],[f45]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ( second(ordered_pair(X0,X1)) = X1
        & first(ordered_pair(X0,X1)) = X0 )
      | ~ member(X1,universal_class)
      | ~ member(X0,universal_class) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ( second(ordered_pair(X0,X1)) = X1
        & first(ordered_pair(X0,X1)) = X0 )
      | ~ member(X1,universal_class)
      | ~ member(X0,universal_class) ),
    inference(flattening,[],[f73]) ).

fof(f85,plain,
    ? [X0,X1,X2] :
      ( ( second(X2) != X1
        | first(X2) != X0 )
      & ordered_pair(X0,X1) = X2
      & member(X1,universal_class)
      & member(X0,universal_class) ),
    inference(ennf_transformation,[],[f70]) ).

fof(f86,plain,
    ? [X0,X1,X2] :
      ( ( second(X2) != X1
        | first(X2) != X0 )
      & ordered_pair(X0,X1) = X2
      & member(X1,universal_class)
      & member(X0,universal_class) ),
    inference(flattening,[],[f85]) ).

fof(f135,plain,
    ( ? [X0,X1,X2] :
        ( ( second(X2) != X1
          | first(X2) != X0 )
        & ordered_pair(X0,X1) = X2
        & member(X1,universal_class)
        & member(X0,universal_class) )
   => ( ( sK7 != second(sK8)
        | sK6 != first(sK8) )
      & sK8 = ordered_pair(sK6,sK7)
      & member(sK7,universal_class)
      & member(sK6,universal_class) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ( ( sK7 != second(sK8)
      | sK6 != first(sK8) )
    & sK8 = ordered_pair(sK6,sK7)
    & member(sK7,universal_class)
    & member(sK6,universal_class) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f86,f135]) ).

fof(f149,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f150,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
    inference(cnf_transformation,[],[f7]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( first(ordered_pair(X0,X1)) = X0
      | ~ member(X1,universal_class)
      | ~ member(X0,universal_class) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( second(ordered_pair(X0,X1)) = X1
      | ~ member(X1,universal_class)
      | ~ member(X0,universal_class) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f224,plain,
    member(sK6,universal_class),
    inference(cnf_transformation,[],[f136]) ).

fof(f225,plain,
    member(sK7,universal_class),
    inference(cnf_transformation,[],[f136]) ).

fof(f226,plain,
    sK8 = ordered_pair(sK6,sK7),
    inference(cnf_transformation,[],[f136]) ).

fof(f227,plain,
    ( sK7 != second(sK8)
    | sK6 != first(sK8) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f228,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
    inference(definition_unfolding,[],[f150,f149,f149]) ).

fof(f236,plain,
    ! [X0,X1] :
      ( second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
      | ~ member(X1,universal_class)
      | ~ member(X0,universal_class) ),
    inference(definition_unfolding,[],[f155,f228]) ).

fof(f237,plain,
    ! [X0,X1] :
      ( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0
      | ~ member(X1,universal_class)
      | ~ member(X0,universal_class) ),
    inference(definition_unfolding,[],[f154,f228]) ).

fof(f265,plain,
    sK8 = unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7))),
    inference(definition_unfolding,[],[f226,f228]) ).

cnf(c_64,plain,
    ( ~ member(X0,universal_class)
    | ~ member(X1,universal_class)
    | second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1 ),
    inference(cnf_transformation,[],[f236]) ).

cnf(c_65,plain,
    ( ~ member(X0,universal_class)
    | ~ member(X1,universal_class)
    | first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0 ),
    inference(cnf_transformation,[],[f237]) ).

cnf(c_128,negated_conjecture,
    ( second(sK8) != sK7
    | first(sK8) != sK6 ),
    inference(cnf_transformation,[],[f227]) ).

cnf(c_129,negated_conjecture,
    unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7))) = sK8,
    inference(cnf_transformation,[],[f265]) ).

cnf(c_130,negated_conjecture,
    member(sK7,universal_class),
    inference(cnf_transformation,[],[f225]) ).

cnf(c_131,negated_conjecture,
    member(sK6,universal_class),
    inference(cnf_transformation,[],[f224]) ).

cnf(c_5706,plain,
    ( ~ member(X0,universal_class)
    | second(unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(X0,X0)))) = X0 ),
    inference(superposition,[status(thm)],[c_131,c_64]) ).

cnf(c_5862,plain,
    ( ~ member(X0,universal_class)
    | first(unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(X0,X0)))) = sK6 ),
    inference(superposition,[status(thm)],[c_131,c_65]) ).

cnf(c_6487,plain,
    second(unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))) = sK7,
    inference(superposition,[status(thm)],[c_130,c_5706]) ).

cnf(c_6508,plain,
    second(sK8) = sK7,
    inference(light_normalisation,[status(thm)],[c_6487,c_129]) ).

cnf(c_6546,plain,
    first(sK8) != sK6,
    inference(backward_subsumption_resolution,[status(thm)],[c_128,c_6508]) ).

cnf(c_7210,plain,
    first(unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7)))) = sK6,
    inference(superposition,[status(thm)],[c_130,c_5862]) ).

cnf(c_7231,plain,
    first(sK8) = sK6,
    inference(light_normalisation,[status(thm)],[c_7210,c_129]) ).

cnf(c_7232,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_7231,c_6546]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem  : SET020+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.13/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n005.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 : Sat Aug 26 14:43:38 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.65/1.16  % SZS status Started for theBenchmark.p
% 3.65/1.16  % SZS status Theorem for theBenchmark.p
% 3.65/1.16  
% 3.65/1.16  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.65/1.16  
% 3.65/1.16  ------  iProver source info
% 3.65/1.16  
% 3.65/1.16  git: date: 2023-05-31 18:12:56 +0000
% 3.65/1.16  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.65/1.16  git: non_committed_changes: false
% 3.65/1.16  git: last_make_outside_of_git: false
% 3.65/1.16  
% 3.65/1.16  ------ Parsing...
% 3.65/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.65/1.16  
% 3.65/1.16  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e 
% 3.65/1.16  
% 3.65/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.65/1.16  
% 3.65/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.65/1.16  ------ Proving...
% 3.65/1.16  ------ Problem Properties 
% 3.65/1.16  
% 3.65/1.16  
% 3.65/1.16  clauses                                 78
% 3.65/1.16  conjectures                             4
% 3.65/1.16  EPR                                     9
% 3.65/1.16  Horn                                    70
% 3.65/1.16  unary                                   17
% 3.65/1.16  binary                                  40
% 3.65/1.16  lits                                    161
% 3.65/1.16  lits eq                                 17
% 3.65/1.16  fd_pure                                 0
% 3.65/1.16  fd_pseudo                               0
% 3.65/1.16  fd_cond                                 4
% 3.65/1.16  fd_pseudo_cond                          3
% 3.65/1.16  AC symbols                              0
% 3.65/1.16  
% 3.65/1.16  ------ Schedule dynamic 5 is on 
% 3.65/1.16  
% 3.65/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.65/1.16  
% 3.65/1.16  
% 3.65/1.16  ------ 
% 3.65/1.16  Current options:
% 3.65/1.16  ------ 
% 3.65/1.16  
% 3.65/1.16  
% 3.65/1.16  
% 3.65/1.16  
% 3.65/1.16  ------ Proving...
% 3.65/1.16  
% 3.65/1.16  
% 3.65/1.16  % SZS status Theorem for theBenchmark.p
% 3.65/1.16  
% 3.65/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.65/1.16  
% 3.65/1.16  
%------------------------------------------------------------------------------