TSTP Solution File: SWC256+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC256+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n014.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 03:11:46 EDT 2024

% Result   : Theorem 4.18s 1.23s
% Output   : CNFRefutation 4.18s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f595)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( nil != X2
                        | nil != X3 )
                      & ! [X4] :
                          ( ssItem(X4)
                         => ( ~ memberP(X3,X4)
                            | cons(X4,nil) != X2 ) ) )
                    | singletonP(X0)
                    | ~ neq(X1,nil)
                    | 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)
                   => ( ( ( nil != X2
                          | nil != X3 )
                        & ! [X4] :
                            ( ssItem(X4)
                           => ( ~ memberP(X3,X4)
                              | cons(X4,nil) != X2 ) ) )
                      | singletonP(X0)
                      | ~ neq(X1,nil)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f100,plain,
    ! [X0] :
      ( ( singletonP(X0)
      <=> ? [X1] :
            ( cons(X1,nil) = X0
            & ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f221,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ~ singletonP(X0)
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ~ singletonP(X0)
                  & neq(X1,nil)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f221]) ).

fof(f241,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X1] :
              ( cons(X1,nil) = X0
              & ssItem(X1) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f100]) ).

fof(f242,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ? [X2] :
              ( cons(X2,nil) = X0
              & ssItem(X2) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f241]) ).

fof(f243,plain,
    ! [X0] :
      ( ? [X2] :
          ( cons(X2,nil) = X0
          & ssItem(X2) )
     => ( cons(sK10(X0),nil) = X0
        & ssItem(sK10(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f244,plain,
    ! [X0] :
      ( ( ( singletonP(X0)
          | ! [X1] :
              ( cons(X1,nil) != X0
              | ~ ssItem(X1) ) )
        & ( ( cons(sK10(X0),nil) = X0
            & ssItem(sK10(X0)) )
          | ~ singletonP(X0) ) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f242,f243]) ).

fof(f343,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil = X2
                        & nil = X3 )
                      | ? [X4] :
                          ( memberP(X3,X4)
                          & cons(X4,nil) = X2
                          & ssItem(X4) ) )
                    & ~ singletonP(X0)
                    & neq(X1,nil)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ~ singletonP(sK53)
                  & neq(X1,nil)
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f344,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil = X2
                    & nil = X3 )
                  | ? [X4] :
                      ( memberP(X3,X4)
                      & cons(X4,nil) = X2
                      & ssItem(X4) ) )
                & ~ singletonP(sK53)
                & neq(X1,nil)
                & sK53 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( nil = X2
                  & nil = X3 )
                | ? [X4] :
                    ( memberP(X3,X4)
                    & cons(X4,nil) = X2
                    & ssItem(X4) ) )
              & ~ singletonP(sK53)
              & neq(sK54,nil)
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil = X2
                & nil = X3 )
              | ? [X4] :
                  ( memberP(X3,X4)
                  & cons(X4,nil) = X2
                  & ssItem(X4) ) )
            & ~ singletonP(sK53)
            & neq(sK54,nil)
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK55
              & nil = X3 )
            | ? [X4] :
                ( memberP(X3,X4)
                & cons(X4,nil) = sK55
                & ssItem(X4) ) )
          & ~ singletonP(sK53)
          & neq(sK54,nil)
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X3] :
        ( ( ( nil = sK55
            & nil = X3 )
          | ? [X4] :
              ( memberP(X3,X4)
              & cons(X4,nil) = sK55
              & ssItem(X4) ) )
        & ~ singletonP(sK53)
        & neq(sK54,nil)
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ( nil = sK55
          & nil = sK56 )
        | ? [X4] :
            ( memberP(sK56,X4)
            & cons(X4,nil) = sK55
            & ssItem(X4) ) )
      & ~ singletonP(sK53)
      & neq(sK54,nil)
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X4] :
        ( memberP(sK56,X4)
        & cons(X4,nil) = sK55
        & ssItem(X4) )
   => ( memberP(sK56,sK57)
      & sK55 = cons(sK57,nil)
      & ssItem(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f348,plain,
    ( ( ( nil = sK55
        & nil = sK56 )
      | ( memberP(sK56,sK57)
        & sK55 = cons(sK57,nil)
        & ssItem(sK57) ) )
    & ~ singletonP(sK53)
    & 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])],[f222,f347,f346,f345,f344,f343]) ).

fof(f360,plain,
    ! [X0,X1] :
      ( singletonP(X0)
      | cons(X1,nil) != X0
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f244]) ).

fof(f441,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f548,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f348]) ).

fof(f552,plain,
    sK54 = sK56,
    inference(cnf_transformation,[],[f348]) ).

fof(f553,plain,
    sK53 = sK55,
    inference(cnf_transformation,[],[f348]) ).

fof(f554,plain,
    neq(sK54,nil),
    inference(cnf_transformation,[],[f348]) ).

fof(f555,plain,
    ~ singletonP(sK53),
    inference(cnf_transformation,[],[f348]) ).

fof(f556,plain,
    ( nil = sK56
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f557,plain,
    ( nil = sK56
    | sK55 = cons(sK57,nil) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f562,plain,
    ~ singletonP(sK55),
    inference(definition_unfolding,[],[f555,f553]) ).

fof(f563,plain,
    neq(sK56,nil),
    inference(definition_unfolding,[],[f554,f552]) ).

fof(f565,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f548,f553]) ).

fof(f568,plain,
    ! [X1] :
      ( singletonP(cons(X1,nil))
      | ~ ssItem(X1)
      | ~ ssList(cons(X1,nil)) ),
    inference(equality_resolution,[],[f360]) ).

cnf(c_58,plain,
    ( ~ ssList(cons(X0,nil))
    | ~ ssItem(X0)
    | singletonP(cons(X0,nil)) ),
    inference(cnf_transformation,[],[f568]) ).

cnf(c_139,plain,
    ( ~ neq(X0,X0)
    | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f595]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f441]) ).

cnf(c_250,negated_conjecture,
    ( cons(sK57,nil) = sK55
    | nil = sK56 ),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_251,negated_conjecture,
    ( nil = sK56
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_252,negated_conjecture,
    ~ singletonP(sK55),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_253,negated_conjecture,
    neq(sK56,nil),
    inference(cnf_transformation,[],[f563]) ).

cnf(c_257,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f565]) ).

cnf(c_408,plain,
    ( ~ neq(X0,X0)
    | ~ ssList(X0) ),
    inference(prop_impl_just,[status(thm)],[c_139]) ).

cnf(c_532,plain,
    ( nil = sK56
    | cons(sK57,nil) = sK55 ),
    inference(prop_impl_just,[status(thm)],[c_250]) ).

cnf(c_533,plain,
    ( cons(sK57,nil) = sK55
    | nil = sK56 ),
    inference(renaming,[status(thm)],[c_532]) ).

cnf(c_826,plain,
    ( X0 != nil
    | X0 != sK56
    | ~ ssList(X0) ),
    inference(resolution_lifted,[status(thm)],[c_408,c_253]) ).

cnf(c_827,plain,
    ( nil != sK56
    | ~ ssList(nil) ),
    inference(unflattening,[status(thm)],[c_826]) ).

cnf(c_828,plain,
    nil != sK56,
    inference(global_subsumption_just,[status(thm)],[c_827,c_141,c_827]) ).

cnf(c_836,plain,
    cons(sK57,nil) = sK55,
    inference(backward_subsumption_resolution,[status(thm)],[c_533,c_828]) ).

cnf(c_5858,plain,
    cons(sK57,nil) = sK55,
    inference(subtyping,[status(esa)],[c_836]) ).

cnf(c_6035,plain,
    ( ~ ssList(cons(X0_14,nil))
    | ~ ssItem(X0_14)
    | singletonP(cons(X0_14,nil)) ),
    inference(subtyping,[status(esa)],[c_58]) ).

cnf(c_7520,plain,
    ( ~ ssItem(sK57)
    | ~ ssList(sK55)
    | singletonP(cons(sK57,nil)) ),
    inference(superposition,[status(thm)],[c_5858,c_6035]) ).

cnf(c_7527,plain,
    ( ~ ssItem(sK57)
    | ~ ssList(sK55)
    | singletonP(sK55) ),
    inference(demodulation,[status(thm)],[c_7520,c_5858]) ).

cnf(c_7537,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_7527,c_827,c_251,c_252,c_141,c_257]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWC256+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May  2 23:25:32 EDT 2024
% 0.13/0.35  % 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
% 4.18/1.23  % SZS status Started for theBenchmark.p
% 4.18/1.23  % SZS status Theorem for theBenchmark.p
% 4.18/1.23  
% 4.18/1.23  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.18/1.23  
% 4.18/1.23  ------  iProver source info
% 4.18/1.23  
% 4.18/1.23  git: date: 2024-05-02 19:28:25 +0000
% 4.18/1.23  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.18/1.23  git: non_committed_changes: false
% 4.18/1.23  
% 4.18/1.23  ------ Parsing...
% 4.18/1.23  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.18/1.23  
% 4.18/1.23  ------ Preprocessing... sup_sim: 0  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  pe_s  pe_e  sup_sim: 0  pe_s  pe_e 
% 4.18/1.23  
% 4.18/1.23  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  scvd_s sp: 0 0s scvd_e  snvd_s sp: 0 0s snvd_e 
% 4.18/1.23  
% 4.18/1.23  ------ Preprocessing...
% 4.18/1.23  ------ Proving...
% 4.18/1.23  ------ Problem Properties 
% 4.18/1.23  
% 4.18/1.23  
% 4.18/1.23  clauses                                 187
% 4.18/1.23  conjectures                             3
% 4.18/1.23  EPR                                     55
% 4.18/1.23  Horn                                    119
% 4.18/1.23  unary                                   23
% 4.18/1.23  binary                                  40
% 4.18/1.23  lits                                    625
% 4.18/1.23  lits eq                                 80
% 4.18/1.23  fd_pure                                 0
% 4.18/1.23  fd_pseudo                               0
% 4.18/1.23  fd_cond                                 21
% 4.18/1.23  fd_pseudo_cond                          14
% 4.18/1.23  AC symbols                              0
% 4.18/1.23  
% 4.18/1.23  ------ Input Options Time Limit: Unbounded
% 4.18/1.23  
% 4.18/1.23  
% 4.18/1.23  ------ 
% 4.18/1.23  Current options:
% 4.18/1.23  ------ 
% 4.18/1.23  
% 4.18/1.23  
% 4.18/1.23  
% 4.18/1.23  
% 4.18/1.23  ------ Proving...
% 4.18/1.23  
% 4.18/1.23  
% 4.18/1.23  % SZS status Theorem for theBenchmark.p
% 4.18/1.23  
% 4.18/1.23  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.18/1.23  
% 4.18/1.23  
%------------------------------------------------------------------------------