TSTP Solution File: SWC097+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC097+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n024.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 03:11:12 EDT 2024

% Result   : Theorem 0.46s 1.16s
% Output   : CNFRefutation 0.46s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

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

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ! [X5] :
                              ( ssItem(X5)
                             => app(X2,cons(X5,nil)) != X3 )
                          | ? [X4] :
                              ( app(X0,cons(X4,nil)) = X1
                              & ssItem(X4) )
                          | ~ neq(X1,nil) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ! [X4] :
                              ( ssItem(X4)
                             => app(X2,cons(X4,nil)) != X3 )
                          | ? [X5] :
                              ( app(X0,cons(X5,nil)) = X1
                              & ssItem(X5) )
                          | ~ neq(X1,nil) ) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( app(X2,cons(X4,nil)) = X3
                          & ssItem(X4) )
                      & ! [X5] :
                          ( app(X0,cons(X5,nil)) != X1
                          | ~ ssItem(X5) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( app(X2,cons(X4,nil)) = X3
                          & ssItem(X4) )
                      & ! [X5] :
                          ( app(X0,cons(X5,nil)) != X1
                          | ~ ssItem(X5) )
                      & neq(X1,nil) ) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f344,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ~ neq(X3,nil)
                        & neq(X1,nil) )
                      | ( ? [X4] :
                            ( app(X2,cons(X4,nil)) = X3
                            & ssItem(X4) )
                        & ! [X5] :
                            ( app(X0,cons(X5,nil)) != X1
                            | ~ ssItem(X5) )
                        & neq(X1,nil) ) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( app(X2,cons(X4,nil)) = X3
                          & ssItem(X4) )
                      & ! [X5] :
                          ( app(sK53,cons(X5,nil)) != X1
                          | ~ ssItem(X5) )
                      & neq(X1,nil) ) )
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ~ neq(X3,nil)
                    & neq(X1,nil) )
                  | ( ? [X4] :
                        ( app(X2,cons(X4,nil)) = X3
                        & ssItem(X4) )
                    & ! [X5] :
                        ( app(sK53,cons(X5,nil)) != X1
                        | ~ ssItem(X5) )
                    & neq(X1,nil) ) )
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ~ neq(X3,nil)
                  & neq(sK54,nil) )
                | ( ? [X4] :
                      ( app(X2,cons(X4,nil)) = X3
                      & ssItem(X4) )
                  & ! [X5] :
                      ( app(sK53,cons(X5,nil)) != sK54
                      | ~ ssItem(X5) )
                  & neq(sK54,nil) ) )
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ~ neq(X3,nil)
                & neq(sK54,nil) )
              | ( ? [X4] :
                    ( app(X2,cons(X4,nil)) = X3
                    & ssItem(X4) )
                & ! [X5] :
                    ( app(sK53,cons(X5,nil)) != sK54
                    | ~ ssItem(X5) )
                & neq(sK54,nil) ) )
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ~ neq(X3,nil)
              & neq(sK54,nil) )
            | ( ? [X4] :
                  ( app(sK55,cons(X4,nil)) = X3
                  & ssItem(X4) )
              & ! [X5] :
                  ( app(sK53,cons(X5,nil)) != sK54
                  | ~ ssItem(X5) )
              & neq(sK54,nil) ) )
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X3] :
        ( ( ( ~ neq(X3,nil)
            & neq(sK54,nil) )
          | ( ? [X4] :
                ( app(sK55,cons(X4,nil)) = X3
                & ssItem(X4) )
            & ! [X5] :
                ( app(sK53,cons(X5,nil)) != sK54
                | ~ ssItem(X5) )
            & neq(sK54,nil) ) )
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ( ~ neq(sK56,nil)
          & neq(sK54,nil) )
        | ( ? [X4] :
              ( app(sK55,cons(X4,nil)) = sK56
              & ssItem(X4) )
          & ! [X5] :
              ( app(sK53,cons(X5,nil)) != sK54
              | ~ ssItem(X5) )
          & neq(sK54,nil) ) )
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ? [X4] :
        ( app(sK55,cons(X4,nil)) = sK56
        & ssItem(X4) )
   => ( sK56 = app(sK55,cons(sK57,nil))
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ( ( ~ neq(sK56,nil)
        & neq(sK54,nil) )
      | ( sK56 = app(sK55,cons(sK57,nil))
        & ssItem(sK57)
        & ! [X5] :
            ( app(sK53,cons(X5,nil)) != sK54
            | ~ ssItem(X5) )
        & neq(sK54,nil) ) )
    & sK53 = sK55
    & sK54 = sK56
    & ssList(sK56)
    & ssList(sK55)
    & ssList(sK54)
    & ssList(sK53) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57])],[f223,f348,f347,f346,f345,f344]) ).

fof(f553,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f349]) ).

fof(f554,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f349]) ).

fof(f560,plain,
    ! [X5] :
      ( ~ neq(sK56,nil)
      | app(sK53,cons(X5,nil)) != sK54
      | ~ ssItem(X5) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f561,plain,
    ( ~ neq(sK56,nil)
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f562,plain,
    ( ~ neq(sK56,nil)
    | sK56 = app(sK55,cons(sK57,nil)) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f563,plain,
    ! [X5] :
      ( ~ neq(sK56,nil)
      | sK56 != app(sK55,cons(X5,nil))
      | ~ ssItem(X5) ),
    inference(definition_unfolding,[],[f560,f554,f553]) ).

cnf(c_246,negated_conjecture,
    ( ~ neq(sK56,nil)
    | app(sK55,cons(sK57,nil)) = sK56 ),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_247,negated_conjecture,
    ( ~ neq(sK56,nil)
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f561]) ).

cnf(c_248,negated_conjecture,
    ( app(sK55,cons(X0,nil)) != sK56
    | ~ neq(sK56,nil)
    | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f563]) ).

cnf(c_252,negated_conjecture,
    neq(sK56,nil),
    inference(cnf_transformation,[],[f605]) ).

cnf(c_366,negated_conjecture,
    ssItem(sK57),
    inference(global_subsumption_just,[status(thm)],[c_247,c_252,c_247]) ).

cnf(c_382,negated_conjecture,
    app(sK55,cons(sK57,nil)) = sK56,
    inference(global_subsumption_just,[status(thm)],[c_246,c_252,c_246]) ).

cnf(c_386,negated_conjecture,
    ( app(sK55,cons(X0,nil)) != sK56
    | ~ ssItem(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_248,c_252,c_248]) ).

cnf(c_8823,plain,
    cons(sK57,nil) = sP0_iProver_def,
    definition ).

cnf(c_8824,plain,
    app(sK55,sP0_iProver_def) = sP1_iProver_def,
    definition ).

cnf(c_8825,negated_conjecture,
    ( app(sK55,cons(X0,nil)) != sK56
    | ~ ssItem(X0) ),
    inference(demodulation,[status(thm)],[c_386]) ).

cnf(c_8826,negated_conjecture,
    sP1_iProver_def = sK56,
    inference(demodulation,[status(thm)],[c_382,c_8823,c_8824]) ).

cnf(c_8827,negated_conjecture,
    ssItem(sK57),
    inference(demodulation,[status(thm)],[c_366]) ).

cnf(c_11638,plain,
    ( app(sK55,cons(X0,nil)) != sP1_iProver_def
    | ~ ssItem(X0) ),
    inference(light_normalisation,[status(thm)],[c_8825,c_8826]) ).

cnf(c_11654,plain,
    ( app(sK55,sP0_iProver_def) != sP1_iProver_def
    | ~ ssItem(sK57) ),
    inference(superposition,[status(thm)],[c_8823,c_11638]) ).

cnf(c_11655,plain,
    app(sK55,sP0_iProver_def) != sP1_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_11654,c_8827]) ).

cnf(c_11656,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_11655,c_8824]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC097+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n024.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 : Thu May  2 23:35:50 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.18/0.46  Running first-order theorem proving
% 0.18/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.46/1.16  % SZS status Started for theBenchmark.p
% 0.46/1.16  % SZS status Theorem for theBenchmark.p
% 0.46/1.16  
% 0.46/1.16  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.46/1.16  
% 0.46/1.16  ------  iProver source info
% 0.46/1.16  
% 0.46/1.16  git: date: 2024-05-02 19:28:25 +0000
% 0.46/1.16  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.46/1.16  git: non_committed_changes: false
% 0.46/1.16  
% 0.46/1.16  ------ Parsing...
% 0.46/1.16  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.46/1.16  
% 0.46/1.16  ------ 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: 5 0s  sf_e  pe_s  pe_e 
% 0.46/1.16  
% 0.46/1.16  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.46/1.16  
% 0.46/1.16  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 0.46/1.16  ------ Proving...
% 0.46/1.16  ------ Problem Properties 
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  clauses                                 188
% 0.46/1.16  conjectures                             5
% 0.46/1.16  EPR                                     54
% 0.46/1.16  Horn                                    120
% 0.46/1.16  unary                                   23
% 0.46/1.16  binary                                  41
% 0.46/1.16  lits                                    627
% 0.46/1.16  lits eq                                 83
% 0.46/1.16  fd_pure                                 0
% 0.46/1.16  fd_pseudo                               0
% 0.46/1.16  fd_cond                                 21
% 0.46/1.16  fd_pseudo_cond                          14
% 0.46/1.16  AC symbols                              0
% 0.46/1.16  
% 0.46/1.16  ------ Schedule dynamic 5 is on 
% 0.46/1.16  
% 0.46/1.16  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  ------ 
% 0.46/1.16  Current options:
% 0.46/1.16  ------ 
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  ------ Proving...
% 0.46/1.16  
% 0.46/1.16  
% 0.46/1.16  % SZS status Theorem for theBenchmark.p
% 0.46/1.16  
% 0.46/1.16  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.16  
% 0.46/1.16  
%------------------------------------------------------------------------------