TSTP Solution File: SWC406+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC406+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n015.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 03:12:22 EDT 2024

% Result   : Theorem 4.05s 1.22s
% Output   : CNFRefutation 4.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   30 (  14 unt;   0 def)
%            Number of atoms       :  335 (  60 equ)
%            Maximal formula atoms :   44 (  11 avg)
%            Number of connectives :  434 ( 129   ~; 108   |; 173   &)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-1 aty)
%            Number of variables   :   96 (   0 sgn  42   !;  52   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ! [X6] :
                        ( ssItem(X6)
                       => ( memberP(X1,X6)
                          | ~ memberP(X0,X6) ) )
                    | ? [X4] :
                        ( ( ( ( ? [X5] :
                                  ( leq(X5,X4)
                                  & memberP(X3,X5)
                                  & X4 != X5
                                  & ssItem(X5) )
                              | ~ memberP(X3,X4) )
                            & memberP(X2,X4) )
                          | ( memberP(X3,X4)
                            & ! [X5] :
                                ( ssItem(X5)
                               => ( X4 = X5
                                  | ~ leq(X5,X4)
                                  | ~ memberP(X3,X5) ) )
                            & ~ memberP(X2,X4) ) )
                        & ssItem(X4) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ! [X6] :
                          ( ssItem(X6)
                         => ( memberP(X1,X6)
                            | ~ memberP(X0,X6) ) )
                      | ? [X4] :
                          ( ( ( ( ? [X5] :
                                    ( leq(X5,X4)
                                    & memberP(X3,X5)
                                    & X4 != X5
                                    & ssItem(X5) )
                                | ~ memberP(X3,X4) )
                              & memberP(X2,X4) )
                            | ( memberP(X3,X4)
                              & ! [X5] :
                                  ( ssItem(X5)
                                 => ( X4 = X5
                                    | ~ leq(X5,X4)
                                    | ~ memberP(X3,X5) ) )
                              & ~ memberP(X2,X4) ) )
                          & ssItem(X4) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ! [X4] :
                          ( ssItem(X4)
                         => ( memberP(X1,X4)
                            | ~ memberP(X0,X4) ) )
                      | ? [X5] :
                          ( ( ( ( ? [X6] :
                                    ( leq(X6,X5)
                                    & memberP(X3,X6)
                                    & X5 != X6
                                    & ssItem(X6) )
                                | ~ memberP(X3,X5) )
                              & memberP(X2,X5) )
                            | ( memberP(X3,X5)
                              & ! [X7] :
                                  ( ssItem(X7)
                                 => ( X5 = X7
                                    | ~ leq(X7,X5)
                                    | ~ memberP(X3,X7) ) )
                              & ~ memberP(X2,X5) ) )
                          & ssItem(X5) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ~ memberP(X1,X4)
                      & memberP(X0,X4)
                      & ssItem(X4) )
                  & ! [X5] :
                      ( ( ( ( ! [X6] :
                                ( ~ leq(X6,X5)
                                | ~ memberP(X3,X6)
                                | X5 = X6
                                | ~ ssItem(X6) )
                            & memberP(X3,X5) )
                          | ~ memberP(X2,X5) )
                        & ( ~ memberP(X3,X5)
                          | ? [X7] :
                              ( X5 != X7
                              & leq(X7,X5)
                              & memberP(X3,X7)
                              & ssItem(X7) )
                          | memberP(X2,X5) ) )
                      | ~ ssItem(X5) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ~ memberP(X1,X4)
                      & memberP(X0,X4)
                      & ssItem(X4) )
                  & ! [X5] :
                      ( ( ( ( ! [X6] :
                                ( ~ leq(X6,X5)
                                | ~ memberP(X3,X6)
                                | X5 = X6
                                | ~ ssItem(X6) )
                            & memberP(X3,X5) )
                          | ~ memberP(X2,X5) )
                        & ( ~ memberP(X3,X5)
                          | ? [X7] :
                              ( X5 != X7
                              & leq(X7,X5)
                              & memberP(X3,X7)
                              & ssItem(X7) )
                          | memberP(X2,X5) ) )
                      | ~ ssItem(X5) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f344,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ~ memberP(X1,X4)
                        & memberP(X0,X4)
                        & ssItem(X4) )
                    & ! [X5] :
                        ( ( ( ( ! [X6] :
                                  ( ~ leq(X6,X5)
                                  | ~ memberP(X3,X6)
                                  | X5 = X6
                                  | ~ ssItem(X6) )
                              & memberP(X3,X5) )
                            | ~ memberP(X2,X5) )
                          & ( ~ memberP(X3,X5)
                            | ? [X7] :
                                ( X5 != X7
                                & leq(X7,X5)
                                & memberP(X3,X7)
                                & ssItem(X7) )
                            | memberP(X2,X5) ) )
                        | ~ ssItem(X5) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ~ memberP(X1,X4)
                      & memberP(sK53,X4)
                      & ssItem(X4) )
                  & ! [X5] :
                      ( ( ( ( ! [X6] :
                                ( ~ leq(X6,X5)
                                | ~ memberP(X3,X6)
                                | X5 = X6
                                | ~ ssItem(X6) )
                            & memberP(X3,X5) )
                          | ~ memberP(X2,X5) )
                        & ( ~ memberP(X3,X5)
                          | ? [X7] :
                              ( X5 != X7
                              & leq(X7,X5)
                              & memberP(X3,X7)
                              & ssItem(X7) )
                          | memberP(X2,X5) ) )
                      | ~ ssItem(X5) )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ~ memberP(X1,X4)
                    & memberP(sK53,X4)
                    & ssItem(X4) )
                & ! [X5] :
                    ( ( ( ( ! [X6] :
                              ( ~ leq(X6,X5)
                              | ~ memberP(X3,X6)
                              | X5 = X6
                              | ~ ssItem(X6) )
                          & memberP(X3,X5) )
                        | ~ memberP(X2,X5) )
                      & ( ~ memberP(X3,X5)
                        | ? [X7] :
                            ( X5 != X7
                            & leq(X7,X5)
                            & memberP(X3,X7)
                            & ssItem(X7) )
                        | memberP(X2,X5) ) )
                    | ~ ssItem(X5) )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ~ memberP(sK54,X4)
                  & memberP(sK53,X4)
                  & ssItem(X4) )
              & ! [X5] :
                  ( ( ( ( ! [X6] :
                            ( ~ leq(X6,X5)
                            | ~ memberP(X3,X6)
                            | X5 = X6
                            | ~ ssItem(X6) )
                        & memberP(X3,X5) )
                      | ~ memberP(X2,X5) )
                    & ( ~ memberP(X3,X5)
                      | ? [X7] :
                          ( X5 != X7
                          & leq(X7,X5)
                          & memberP(X3,X7)
                          & ssItem(X7) )
                      | memberP(X2,X5) ) )
                  | ~ ssItem(X5) )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ? [X4] :
                ( ~ memberP(sK54,X4)
                & memberP(sK53,X4)
                & ssItem(X4) )
            & ! [X5] :
                ( ( ( ( ! [X6] :
                          ( ~ leq(X6,X5)
                          | ~ memberP(X3,X6)
                          | X5 = X6
                          | ~ ssItem(X6) )
                      & memberP(X3,X5) )
                    | ~ memberP(X2,X5) )
                  & ( ~ memberP(X3,X5)
                    | ? [X7] :
                        ( X5 != X7
                        & leq(X7,X5)
                        & memberP(X3,X7)
                        & ssItem(X7) )
                    | memberP(X2,X5) ) )
                | ~ ssItem(X5) )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ? [X4] :
              ( ~ memberP(sK54,X4)
              & memberP(sK53,X4)
              & ssItem(X4) )
          & ! [X5] :
              ( ( ( ( ! [X6] :
                        ( ~ leq(X6,X5)
                        | ~ memberP(X3,X6)
                        | X5 = X6
                        | ~ ssItem(X6) )
                    & memberP(X3,X5) )
                  | ~ memberP(sK55,X5) )
                & ( ~ memberP(X3,X5)
                  | ? [X7] :
                      ( X5 != X7
                      & leq(X7,X5)
                      & memberP(X3,X7)
                      & ssItem(X7) )
                  | memberP(sK55,X5) ) )
              | ~ ssItem(X5) )
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X3] :
        ( ? [X4] :
            ( ~ memberP(sK54,X4)
            & memberP(sK53,X4)
            & ssItem(X4) )
        & ! [X5] :
            ( ( ( ( ! [X6] :
                      ( ~ leq(X6,X5)
                      | ~ memberP(X3,X6)
                      | X5 = X6
                      | ~ ssItem(X6) )
                  & memberP(X3,X5) )
                | ~ memberP(sK55,X5) )
              & ( ~ memberP(X3,X5)
                | ? [X7] :
                    ( X5 != X7
                    & leq(X7,X5)
                    & memberP(X3,X7)
                    & ssItem(X7) )
                | memberP(sK55,X5) ) )
            | ~ ssItem(X5) )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ? [X4] :
          ( ~ memberP(sK54,X4)
          & memberP(sK53,X4)
          & ssItem(X4) )
      & ! [X5] :
          ( ( ( ( ! [X6] :
                    ( ~ leq(X6,X5)
                    | ~ memberP(sK56,X6)
                    | X5 = X6
                    | ~ ssItem(X6) )
                & memberP(sK56,X5) )
              | ~ memberP(sK55,X5) )
            & ( ~ memberP(sK56,X5)
              | ? [X7] :
                  ( X5 != X7
                  & leq(X7,X5)
                  & memberP(sK56,X7)
                  & ssItem(X7) )
              | memberP(sK55,X5) ) )
          | ~ ssItem(X5) )
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ? [X4] :
        ( ~ memberP(sK54,X4)
        & memberP(sK53,X4)
        & ssItem(X4) )
   => ( ~ memberP(sK54,sK57)
      & memberP(sK53,sK57)
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ! [X5] :
      ( ? [X7] :
          ( X5 != X7
          & leq(X7,X5)
          & memberP(sK56,X7)
          & ssItem(X7) )
     => ( sK58(X5) != X5
        & leq(sK58(X5),X5)
        & memberP(sK56,sK58(X5))
        & ssItem(sK58(X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ( ~ memberP(sK54,sK57)
    & memberP(sK53,sK57)
    & ssItem(sK57)
    & ! [X5] :
        ( ( ( ( ! [X6] :
                  ( ~ leq(X6,X5)
                  | ~ memberP(sK56,X6)
                  | X5 = X6
                  | ~ ssItem(X6) )
              & memberP(sK56,X5) )
            | ~ memberP(sK55,X5) )
          & ( ~ memberP(sK56,X5)
            | ( sK58(X5) != X5
              & leq(sK58(X5),X5)
              & memberP(sK56,sK58(X5))
              & ssItem(sK58(X5)) )
            | memberP(sK55,X5) ) )
        | ~ ssItem(X5) )
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58])],[f223,f349,f348,f347,f346,f345,f344]) ).

fof(f554,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f350]) ).

fof(f555,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f350]) ).

fof(f560,plain,
    ! [X5] :
      ( memberP(sK56,X5)
      | ~ memberP(sK55,X5)
      | ~ ssItem(X5) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f562,plain,
    ssItem(sK57),
    inference(cnf_transformation,[],[f350]) ).

fof(f563,plain,
    memberP(sK53,sK57),
    inference(cnf_transformation,[],[f350]) ).

fof(f564,plain,
    ~ memberP(sK54,sK57),
    inference(cnf_transformation,[],[f350]) ).

fof(f565,plain,
    ~ memberP(sK56,sK57),
    inference(definition_unfolding,[],[f564,f554]) ).

fof(f566,plain,
    memberP(sK55,sK57),
    inference(definition_unfolding,[],[f563,f555]) ).

cnf(c_246,negated_conjecture,
    ~ memberP(sK56,sK57),
    inference(cnf_transformation,[],[f565]) ).

cnf(c_247,negated_conjecture,
    memberP(sK55,sK57),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_248,negated_conjecture,
    ssItem(sK57),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_250,negated_conjecture,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | memberP(sK56,X0) ),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_8996,negated_conjecture,
    ( ~ memberP(sK55,X0)
    | ~ ssItem(X0)
    | memberP(sK56,X0) ),
    inference(demodulation,[status(thm)],[c_250]) ).

cnf(c_8998,negated_conjecture,
    ssItem(sK57),
    inference(demodulation,[status(thm)],[c_248]) ).

cnf(c_8999,negated_conjecture,
    memberP(sK55,sK57),
    inference(demodulation,[status(thm)],[c_247]) ).

cnf(c_9000,negated_conjecture,
    ~ memberP(sK56,sK57),
    inference(demodulation,[status(thm)],[c_246]) ).

cnf(c_11899,plain,
    ( ~ ssItem(sK57)
    | memberP(sK56,sK57) ),
    inference(superposition,[status(thm)],[c_8999,c_8996]) ).

cnf(c_11900,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_11899,c_9000,c_8998]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SWC406+1 : TPTP v8.1.2. Released v2.4.0.
% 0.08/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.34  % Computer : n015.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May  2 23:56:36 EDT 2024
% 0.14/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  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
% 4.05/1.22  % SZS status Started for theBenchmark.p
% 4.05/1.22  % SZS status Theorem for theBenchmark.p
% 4.05/1.22  
% 4.05/1.22  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.05/1.22  
% 4.05/1.22  ------  iProver source info
% 4.05/1.22  
% 4.05/1.22  git: date: 2024-05-02 19:28:25 +0000
% 4.05/1.22  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.05/1.22  git: non_committed_changes: false
% 4.05/1.22  
% 4.05/1.22  ------ Parsing...
% 4.05/1.22  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.05/1.22  
% 4.05/1.22  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 4 0s  sf_e  pe_s  pe_e 
% 4.05/1.22  
% 4.05/1.22  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.05/1.22  
% 4.05/1.22  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.05/1.22  ------ Proving...
% 4.05/1.22  ------ Problem Properties 
% 4.05/1.22  
% 4.05/1.22  
% 4.05/1.22  clauses                                 191
% 4.05/1.22  conjectures                             11
% 4.05/1.22  EPR                                     56
% 4.05/1.22  Horn                                    120
% 4.05/1.22  unary                                   21
% 4.05/1.22  binary                                  40
% 4.05/1.22  lits                                    648
% 4.05/1.22  lits eq                                 80
% 4.05/1.22  fd_pure                                 0
% 4.05/1.22  fd_pseudo                               0
% 4.05/1.22  fd_cond                                 21
% 4.05/1.22  fd_pseudo_cond                          15
% 4.05/1.22  AC symbols                              0
% 4.05/1.22  
% 4.05/1.22  ------ Schedule dynamic 5 is on 
% 4.05/1.22  
% 4.05/1.22  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.05/1.22  
% 4.05/1.22  
% 4.05/1.22  ------ 
% 4.05/1.22  Current options:
% 4.05/1.22  ------ 
% 4.05/1.22  
% 4.05/1.22  
% 4.05/1.22  
% 4.05/1.22  
% 4.05/1.22  ------ Proving...
% 4.05/1.22  
% 4.05/1.22  
% 4.05/1.22  % SZS status Theorem for theBenchmark.p
% 4.05/1.22  
% 4.05/1.22  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.05/1.22  
% 4.05/1.23  
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