TSTP Solution File: SET108+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SET108+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : Fri May  3 02:59:56 EDT 2024

% Result   : Theorem 3.28s 1.11s
% Output   : CNFRefutation 3.28s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% 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(f44,conjecture,
    ! [X0] :
    ? [X2,X3] :
      ( ( X0 = X3
        & X0 = X2
        & ~ ? [X1,X4] :
              ( ordered_pair(X1,X4) = X0
              & member(X4,universal_class)
              & member(X1,universal_class) ) )
      | ( ordered_pair(X2,X3) = X0
        & member(X3,universal_class)
        & member(X2,universal_class) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_first_and_second) ).

fof(f45,negated_conjecture,
    ~ ! [X0] :
      ? [X2,X3] :
        ( ( X0 = X3
          & X0 = X2
          & ~ ? [X1,X4] :
                ( ordered_pair(X1,X4) = X0
                & member(X4,universal_class)
                & member(X1,universal_class) ) )
        | ( ordered_pair(X2,X3) = X0
          & member(X3,universal_class)
          & member(X2,universal_class) ) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f70,plain,
    ~ ! [X0] :
      ? [X1,X2] :
        ( ( X0 = X2
          & X0 = X1
          & ~ ? [X3,X4] :
                ( ordered_pair(X3,X4) = X0
                & member(X4,universal_class)
                & member(X3,universal_class) ) )
        | ( ordered_pair(X1,X2) = X0
          & member(X2,universal_class)
          & member(X1,universal_class) ) ),
    inference(rectify,[],[f45]) ).

fof(f85,plain,
    ? [X0] :
    ! [X1,X2] :
      ( ( X0 != X2
        | X0 != X1
        | ? [X3,X4] :
            ( ordered_pair(X3,X4) = X0
            & member(X4,universal_class)
            & member(X3,universal_class) ) )
      & ( ordered_pair(X1,X2) != X0
        | ~ member(X2,universal_class)
        | ~ member(X1,universal_class) ) ),
    inference(ennf_transformation,[],[f70]) ).

fof(f134,plain,
    ( ? [X0] :
      ! [X1,X2] :
        ( ( X0 != X2
          | X0 != X1
          | ? [X3,X4] :
              ( ordered_pair(X3,X4) = X0
              & member(X4,universal_class)
              & member(X3,universal_class) ) )
        & ( ordered_pair(X1,X2) != X0
          | ~ member(X2,universal_class)
          | ~ member(X1,universal_class) ) )
   => ! [X2,X1] :
        ( ( sK6 != X2
          | sK6 != X1
          | ? [X4,X3] :
              ( ordered_pair(X3,X4) = sK6
              & member(X4,universal_class)
              & member(X3,universal_class) ) )
        & ( ordered_pair(X1,X2) != sK6
          | ~ member(X2,universal_class)
          | ~ member(X1,universal_class) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f135,plain,
    ( ? [X4,X3] :
        ( ordered_pair(X3,X4) = sK6
        & member(X4,universal_class)
        & member(X3,universal_class) )
   => ( sK6 = ordered_pair(sK7,sK8)
      & member(sK8,universal_class)
      & member(sK7,universal_class) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ! [X1,X2] :
      ( ( sK6 != X2
        | sK6 != X1
        | ( sK6 = ordered_pair(sK7,sK8)
          & member(sK8,universal_class)
          & member(sK7,universal_class) ) )
      & ( ordered_pair(X1,X2) != sK6
        | ~ member(X2,universal_class)
        | ~ member(X1,universal_class) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f85,f135,f134]) ).

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(f224,plain,
    ! [X2,X1] :
      ( ordered_pair(X1,X2) != sK6
      | ~ member(X2,universal_class)
      | ~ member(X1,universal_class) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f225,plain,
    ! [X2,X1] :
      ( sK6 != X2
      | sK6 != X1
      | member(sK7,universal_class) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f226,plain,
    ! [X2,X1] :
      ( sK6 != X2
      | sK6 != X1
      | member(sK8,universal_class) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f227,plain,
    ! [X2,X1] :
      ( sK6 != X2
      | sK6 != X1
      | sK6 = ordered_pair(sK7,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(f265,plain,
    ! [X2,X1] :
      ( sK6 != X2
      | sK6 != X1
      | sK6 = unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK8,sK8))) ),
    inference(definition_unfolding,[],[f227,f228]) ).

fof(f266,plain,
    ! [X2,X1] :
      ( sK6 != unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))
      | ~ member(X2,universal_class)
      | ~ member(X1,universal_class) ),
    inference(definition_unfolding,[],[f224,f228]) ).

fof(f273,plain,
    ! [X1] :
      ( sK6 != X1
      | sK6 = unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK8,sK8))) ),
    inference(equality_resolution,[],[f265]) ).

fof(f274,plain,
    sK6 = unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK8,sK8))),
    inference(equality_resolution,[],[f273]) ).

fof(f275,plain,
    ! [X1] :
      ( sK6 != X1
      | member(sK8,universal_class) ),
    inference(equality_resolution,[],[f226]) ).

fof(f276,plain,
    member(sK8,universal_class),
    inference(equality_resolution,[],[f275]) ).

fof(f277,plain,
    ! [X1] :
      ( sK6 != X1
      | member(sK7,universal_class) ),
    inference(equality_resolution,[],[f225]) ).

fof(f278,plain,
    member(sK7,universal_class),
    inference(equality_resolution,[],[f277]) ).

cnf(c_128,negated_conjecture,
    unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK8,sK8))) = sK6,
    inference(cnf_transformation,[],[f274]) ).

cnf(c_129,negated_conjecture,
    member(sK8,universal_class),
    inference(cnf_transformation,[],[f276]) ).

cnf(c_130,negated_conjecture,
    member(sK7,universal_class),
    inference(cnf_transformation,[],[f278]) ).

cnf(c_131,negated_conjecture,
    ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) != sK6
    | ~ member(X0,universal_class)
    | ~ member(X1,universal_class) ),
    inference(cnf_transformation,[],[f266]) ).

cnf(c_1588,plain,
    unordered_pair(sK7,sK7) = sP0_iProver_def,
    definition ).

cnf(c_1589,plain,
    unordered_pair(sK8,sK8) = sP1_iProver_def,
    definition ).

cnf(c_1590,plain,
    unordered_pair(sK7,sP1_iProver_def) = sP2_iProver_def,
    definition ).

cnf(c_1591,plain,
    unordered_pair(sP0_iProver_def,sP2_iProver_def) = sP3_iProver_def,
    definition ).

cnf(c_1592,negated_conjecture,
    ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) != sK6
    | ~ member(X0,universal_class)
    | ~ member(X1,universal_class) ),
    inference(demodulation,[status(thm)],[c_131]) ).

cnf(c_1593,negated_conjecture,
    member(sK7,universal_class),
    inference(demodulation,[status(thm)],[c_130]) ).

cnf(c_1594,negated_conjecture,
    member(sK8,universal_class),
    inference(demodulation,[status(thm)],[c_129]) ).

cnf(c_1595,negated_conjecture,
    sP3_iProver_def = sK6,
    inference(demodulation,[status(thm)],[c_128,c_1589,c_1590,c_1588,c_1591]) ).

cnf(c_2433,plain,
    ( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) != sP3_iProver_def
    | ~ member(X0,universal_class)
    | ~ member(X1,universal_class) ),
    inference(light_normalisation,[status(thm)],[c_1592,c_1595]) ).

cnf(c_2437,plain,
    ( unordered_pair(sP0_iProver_def,unordered_pair(sK7,unordered_pair(X0,X0))) != sP3_iProver_def
    | ~ member(X0,universal_class)
    | ~ member(sK7,universal_class) ),
    inference(superposition,[status(thm)],[c_1588,c_2433]) ).

cnf(c_2442,plain,
    ( unordered_pair(sP0_iProver_def,unordered_pair(sK7,unordered_pair(X0,X0))) != sP3_iProver_def
    | ~ member(X0,universal_class) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2437,c_1593]) ).

cnf(c_2472,plain,
    ( unordered_pair(sP0_iProver_def,unordered_pair(sK7,sP1_iProver_def)) != sP3_iProver_def
    | ~ member(sK8,universal_class) ),
    inference(superposition,[status(thm)],[c_1589,c_2442]) ).

cnf(c_2473,plain,
    ( sP3_iProver_def != sP3_iProver_def
    | ~ member(sK8,universal_class) ),
    inference(light_normalisation,[status(thm)],[c_2472,c_1590,c_1591]) ).

cnf(c_2474,plain,
    ~ member(sK8,universal_class),
    inference(equality_resolution_simp,[status(thm)],[c_2473]) ).

cnf(c_2475,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_2474,c_1594]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : SET108+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.09/0.11  % Command  : run_iprover %s %d THM
% 0.10/0.32  % Computer : n031.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Thu May  2 21:14:31 EDT 2024
% 0.10/0.32  % CPUTime  : 
% 0.17/0.43  Running first-order theorem proving
% 0.17/0.43  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
% 3.28/1.11  % SZS status Started for theBenchmark.p
% 3.28/1.11  % SZS status Theorem for theBenchmark.p
% 3.28/1.11  
% 3.28/1.11  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.28/1.11  
% 3.28/1.11  ------  iProver source info
% 3.28/1.11  
% 3.28/1.11  git: date: 2024-05-02 19:28:25 +0000
% 3.28/1.11  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.28/1.11  git: non_committed_changes: false
% 3.28/1.11  
% 3.28/1.11  ------ Parsing...
% 3.28/1.11  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.28/1.11  
% 3.28/1.11  ------ 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 
% 3.28/1.11  
% 3.28/1.11  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.28/1.11  
% 3.28/1.11  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.28/1.11  ------ Proving...
% 3.28/1.11  ------ Problem Properties 
% 3.28/1.11  
% 3.28/1.11  
% 3.28/1.11  clauses                                 82
% 3.28/1.11  conjectures                             4
% 3.28/1.11  EPR                                     10
% 3.28/1.11  Horn                                    74
% 3.28/1.11  unary                                   21
% 3.28/1.11  binary                                  39
% 3.28/1.11  lits                                    166
% 3.28/1.11  lits eq                                 20
% 3.28/1.12  fd_pure                                 0
% 3.28/1.12  fd_pseudo                               0
% 3.28/1.12  fd_cond                                 4
% 3.28/1.12  fd_pseudo_cond                          3
% 3.28/1.12  AC symbols                              0
% 3.28/1.12  
% 3.28/1.12  ------ Schedule dynamic 5 is on 
% 3.28/1.12  
% 3.28/1.12  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.28/1.12  
% 3.28/1.12  
% 3.28/1.12  ------ 
% 3.28/1.12  Current options:
% 3.28/1.12  ------ 
% 3.28/1.12  
% 3.28/1.12  
% 3.28/1.12  
% 3.28/1.12  
% 3.28/1.12  ------ Proving...
% 3.28/1.12  
% 3.28/1.12  
% 3.28/1.12  % SZS status Theorem for theBenchmark.p
% 3.28/1.12  
% 3.28/1.12  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.28/1.12  
% 3.28/1.12  
%------------------------------------------------------------------------------