TSTP Solution File: SWC252+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC252+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 03:11:45 EDT 2024

% Result   : Theorem 4.32s 1.17s
% Output   : CNFRefutation 4.32s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).

fof(f38,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ~ memberP(nil,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax84) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( nil != X2
                        | nil != X3 )
                      & ! [X8] :
                          ( ssItem(X8)
                         => ( ~ memberP(X3,X8)
                            | cons(X8,nil) != X2 ) ) )
                    | ? [X4] :
                        ( ? [X5] :
                            ( ? [X6] :
                                ( ! [X7] :
                                    ( ssItem(X7)
                                   => ( leq(X4,X7)
                                      | ~ lt(X4,X7)
                                      | ~ memberP(X6,X7)
                                      | ~ memberP(X5,X7) ) )
                                & app(app(X5,cons(X4,nil)),X6) = X0
                                & ssList(X6) )
                            & ssList(X5) )
                        & ssItem(X4) )
                    | nil = X0
                    | 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)
                   => ( ( ( nil != X2
                          | nil != X3 )
                        & ! [X8] :
                            ( ssItem(X8)
                           => ( ~ memberP(X3,X8)
                              | cons(X8,nil) != X2 ) ) )
                      | ? [X4] :
                          ( ? [X5] :
                              ( ? [X6] :
                                  ( ! [X7] :
                                      ( ssItem(X7)
                                     => ( leq(X4,X7)
                                        | ~ lt(X4,X7)
                                        | ~ memberP(X6,X7)
                                        | ~ memberP(X5,X7) ) )
                                  & app(app(X5,cons(X4,nil)),X6) = X0
                                  & ssList(X6) )
                              & ssList(X5) )
                          & ssItem(X4) )
                      | nil = X0
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f98,plain,
    ~ ! [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 ) ) )
                      | ? [X5] :
                          ( ? [X6] :
                              ( ? [X7] :
                                  ( ! [X8] :
                                      ( ssItem(X8)
                                     => ( leq(X5,X8)
                                        | ~ lt(X5,X8)
                                        | ~ memberP(X7,X8)
                                        | ~ memberP(X6,X8) ) )
                                  & app(app(X6,cons(X5,nil)),X7) = X0
                                  & ssList(X7) )
                              & ssList(X6) )
                          & ssItem(X5) )
                      | nil = X0
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f135,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f149,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f202,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ! [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ? [X8] :
                                  ( ~ leq(X5,X8)
                                  & lt(X5,X8)
                                  & memberP(X7,X8)
                                  & memberP(X6,X8)
                                  & ssItem(X8) )
                              | app(app(X6,cons(X5,nil)),X7) != X0
                              | ~ ssList(X7) )
                          | ~ ssList(X6) )
                      | ~ ssItem(X5) )
                  & nil != X0
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f223,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( nil = X2
                      & nil = X3 )
                    | ? [X4] :
                        ( memberP(X3,X4)
                        & cons(X4,nil) = X2
                        & ssItem(X4) ) )
                  & ! [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ? [X8] :
                                  ( ~ leq(X5,X8)
                                  & lt(X5,X8)
                                  & memberP(X7,X8)
                                  & memberP(X6,X8)
                                  & ssItem(X8) )
                              | app(app(X6,cons(X5,nil)),X7) != X0
                              | ~ ssList(X7) )
                          | ~ ssList(X6) )
                      | ~ ssItem(X5) )
                  & nil != X0
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f222]) ).

fof(f344,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( nil = X2
                        & nil = X3 )
                      | ? [X4] :
                          ( memberP(X3,X4)
                          & cons(X4,nil) = X2
                          & ssItem(X4) ) )
                    & ! [X5] :
                        ( ! [X6] :
                            ( ! [X7] :
                                ( ? [X8] :
                                    ( ~ leq(X5,X8)
                                    & lt(X5,X8)
                                    & memberP(X7,X8)
                                    & memberP(X6,X8)
                                    & ssItem(X8) )
                                | app(app(X6,cons(X5,nil)),X7) != X0
                                | ~ ssList(X7) )
                            | ~ ssList(X6) )
                        | ~ ssItem(X5) )
                    & nil != X0
                    & 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) ) )
                  & ! [X5] :
                      ( ! [X6] :
                          ( ! [X7] :
                              ( ? [X8] :
                                  ( ~ leq(X5,X8)
                                  & lt(X5,X8)
                                  & memberP(X7,X8)
                                  & memberP(X6,X8)
                                  & ssItem(X8) )
                              | app(app(X6,cons(X5,nil)),X7) != sK53
                              | ~ ssList(X7) )
                          | ~ ssList(X6) )
                      | ~ ssItem(X5) )
                  & nil != sK53
                  & sK53 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK53) ) ),
    introduced(choice_axiom,[]) ).

fof(f345,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( nil = X2
                    & nil = X3 )
                  | ? [X4] :
                      ( memberP(X3,X4)
                      & cons(X4,nil) = X2
                      & ssItem(X4) ) )
                & ! [X5] :
                    ( ! [X6] :
                        ( ! [X7] :
                            ( ? [X8] :
                                ( ~ leq(X5,X8)
                                & lt(X5,X8)
                                & memberP(X7,X8)
                                & memberP(X6,X8)
                                & ssItem(X8) )
                            | app(app(X6,cons(X5,nil)),X7) != sK53
                            | ~ ssList(X7) )
                        | ~ ssList(X6) )
                    | ~ ssItem(X5) )
                & nil != sK53
                & 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) ) )
              & ! [X5] :
                  ( ! [X6] :
                      ( ! [X7] :
                          ( ? [X8] :
                              ( ~ leq(X5,X8)
                              & lt(X5,X8)
                              & memberP(X7,X8)
                              & memberP(X6,X8)
                              & ssItem(X8) )
                          | app(app(X6,cons(X5,nil)),X7) != sK53
                          | ~ ssList(X7) )
                      | ~ ssList(X6) )
                  | ~ ssItem(X5) )
              & nil != sK53
              & sK53 = X2
              & sK54 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK54) ) ),
    introduced(choice_axiom,[]) ).

fof(f346,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( nil = X2
                & nil = X3 )
              | ? [X4] :
                  ( memberP(X3,X4)
                  & cons(X4,nil) = X2
                  & ssItem(X4) ) )
            & ! [X5] :
                ( ! [X6] :
                    ( ! [X7] :
                        ( ? [X8] :
                            ( ~ leq(X5,X8)
                            & lt(X5,X8)
                            & memberP(X7,X8)
                            & memberP(X6,X8)
                            & ssItem(X8) )
                        | app(app(X6,cons(X5,nil)),X7) != sK53
                        | ~ ssList(X7) )
                    | ~ ssList(X6) )
                | ~ ssItem(X5) )
            & nil != sK53
            & sK53 = X2
            & sK54 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( nil = sK55
              & nil = X3 )
            | ? [X4] :
                ( memberP(X3,X4)
                & cons(X4,nil) = sK55
                & ssItem(X4) ) )
          & ! [X5] :
              ( ! [X6] :
                  ( ! [X7] :
                      ( ? [X8] :
                          ( ~ leq(X5,X8)
                          & lt(X5,X8)
                          & memberP(X7,X8)
                          & memberP(X6,X8)
                          & ssItem(X8) )
                      | app(app(X6,cons(X5,nil)),X7) != sK53
                      | ~ ssList(X7) )
                  | ~ ssList(X6) )
              | ~ ssItem(X5) )
          & nil != sK53
          & sK53 = sK55
          & sK54 = X3
          & ssList(X3) )
      & ssList(sK55) ) ),
    introduced(choice_axiom,[]) ).

fof(f347,plain,
    ( ? [X3] :
        ( ( ( nil = sK55
            & nil = X3 )
          | ? [X4] :
              ( memberP(X3,X4)
              & cons(X4,nil) = sK55
              & ssItem(X4) ) )
        & ! [X5] :
            ( ! [X6] :
                ( ! [X7] :
                    ( ? [X8] :
                        ( ~ leq(X5,X8)
                        & lt(X5,X8)
                        & memberP(X7,X8)
                        & memberP(X6,X8)
                        & ssItem(X8) )
                    | app(app(X6,cons(X5,nil)),X7) != sK53
                    | ~ ssList(X7) )
                | ~ ssList(X6) )
            | ~ ssItem(X5) )
        & nil != sK53
        & sK53 = sK55
        & sK54 = X3
        & ssList(X3) )
   => ( ( ( nil = sK55
          & nil = sK56 )
        | ? [X4] :
            ( memberP(sK56,X4)
            & cons(X4,nil) = sK55
            & ssItem(X4) ) )
      & ! [X5] :
          ( ! [X6] :
              ( ! [X7] :
                  ( ? [X8] :
                      ( ~ leq(X5,X8)
                      & lt(X5,X8)
                      & memberP(X7,X8)
                      & memberP(X6,X8)
                      & ssItem(X8) )
                  | app(app(X6,cons(X5,nil)),X7) != sK53
                  | ~ ssList(X7) )
              | ~ ssList(X6) )
          | ~ ssItem(X5) )
      & nil != sK53
      & sK53 = sK55
      & sK54 = sK56
      & ssList(sK56) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f349,plain,
    ! [X5,X6,X7] :
      ( ? [X8] :
          ( ~ leq(X5,X8)
          & lt(X5,X8)
          & memberP(X7,X8)
          & memberP(X6,X8)
          & ssItem(X8) )
     => ( ~ leq(X5,sK58(X5,X6,X7))
        & lt(X5,sK58(X5,X6,X7))
        & memberP(X7,sK58(X5,X6,X7))
        & memberP(X6,sK58(X5,X6,X7))
        & ssItem(sK58(X5,X6,X7)) ) ),
    introduced(choice_axiom,[]) ).

fof(f350,plain,
    ( ( ( nil = sK55
        & nil = sK56 )
      | ( memberP(sK56,sK57)
        & sK55 = cons(sK57,nil)
        & ssItem(sK57) ) )
    & ! [X5] :
        ( ! [X6] :
            ( ! [X7] :
                ( ( ~ leq(X5,sK58(X5,X6,X7))
                  & lt(X5,sK58(X5,X6,X7))
                  & memberP(X7,sK58(X5,X6,X7))
                  & memberP(X6,sK58(X5,X6,X7))
                  & ssItem(sK58(X5,X6,X7)) )
                | app(app(X6,cons(X5,nil)),X7) != sK53
                | ~ ssList(X7) )
            | ~ ssList(X6) )
        | ~ ssItem(X5) )
    & nil != sK53
    & 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(f443,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f457,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f473,plain,
    ! [X0] :
      ( ~ memberP(nil,X0)
      | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f536,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f202]) ).

fof(f550,plain,
    ssList(sK53),
    inference(cnf_transformation,[],[f350]) ).

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

fof(f556,plain,
    nil != sK53,
    inference(cnf_transformation,[],[f350]) ).

fof(f557,plain,
    ! [X6,X7,X5] :
      ( ssItem(sK58(X5,X6,X7))
      | app(app(X6,cons(X5,nil)),X7) != sK53
      | ~ ssList(X7)
      | ~ ssList(X6)
      | ~ ssItem(X5) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f559,plain,
    ! [X6,X7,X5] :
      ( memberP(X7,sK58(X5,X6,X7))
      | app(app(X6,cons(X5,nil)),X7) != sK53
      | ~ ssList(X7)
      | ~ ssList(X6)
      | ~ ssItem(X5) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f565,plain,
    ( nil = sK55
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f566,plain,
    ( nil = sK55
    | sK55 = cons(sK57,nil) ),
    inference(cnf_transformation,[],[f350]) ).

fof(f570,plain,
    ! [X6,X7,X5] :
      ( memberP(X7,sK58(X5,X6,X7))
      | app(app(X6,cons(X5,nil)),X7) != sK55
      | ~ ssList(X7)
      | ~ ssList(X6)
      | ~ ssItem(X5) ),
    inference(definition_unfolding,[],[f559,f555]) ).

fof(f572,plain,
    ! [X6,X7,X5] :
      ( ssItem(sK58(X5,X6,X7))
      | app(app(X6,cons(X5,nil)),X7) != sK55
      | ~ ssList(X7)
      | ~ ssList(X6)
      | ~ ssItem(X5) ),
    inference(definition_unfolding,[],[f557,f555]) ).

fof(f573,plain,
    nil != sK55,
    inference(definition_unfolding,[],[f556,f555]) ).

fof(f575,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f550,f555]) ).

cnf(c_141,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f443]) ).

cnf(c_155,plain,
    ( ~ ssList(X0)
    | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f457]) ).

cnf(c_171,plain,
    ( ~ memberP(nil,X0)
    | ~ ssItem(X0) ),
    inference(cnf_transformation,[],[f473]) ).

cnf(c_232,plain,
    ( ~ ssList(X0)
    | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f536]) ).

cnf(c_247,negated_conjecture,
    ( cons(sK57,nil) = sK55
    | nil = sK55 ),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_248,negated_conjecture,
    ( nil = sK55
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f565]) ).

cnf(c_254,negated_conjecture,
    ( app(app(X0,cons(X1,nil)),X2) != sK55
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(X2,sK58(X1,X0,X2)) ),
    inference(cnf_transformation,[],[f570]) ).

cnf(c_256,negated_conjecture,
    ( app(app(X0,cons(X1,nil)),X2) != sK55
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ssItem(sK58(X1,X0,X2)) ),
    inference(cnf_transformation,[],[f572]) ).

cnf(c_257,negated_conjecture,
    nil != sK55,
    inference(cnf_transformation,[],[f573]) ).

cnf(c_261,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f575]) ).

cnf(c_374,negated_conjecture,
    ssItem(sK57),
    inference(global_subsumption_just,[status(thm)],[c_248,c_257,c_248]) ).

cnf(c_390,negated_conjecture,
    cons(sK57,nil) = sK55,
    inference(global_subsumption_just,[status(thm)],[c_247,c_257,c_247]) ).

cnf(c_9007,plain,
    cons(sK57,nil) = sP0_iProver_def,
    definition ).

cnf(c_9008,negated_conjecture,
    sP0_iProver_def = sK55,
    inference(demodulation,[status(thm)],[c_390,c_9007]) ).

cnf(c_9010,negated_conjecture,
    ssItem(sK57),
    inference(demodulation,[status(thm)],[c_374]) ).

cnf(c_9011,negated_conjecture,
    ssList(sK55),
    inference(demodulation,[status(thm)],[c_261]) ).

cnf(c_9014,negated_conjecture,
    ( app(app(X0,cons(X1,nil)),X2) != sK55
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ssItem(sK58(X1,X0,X2)) ),
    inference(demodulation,[status(thm)],[c_256]) ).

cnf(c_9016,negated_conjecture,
    ( app(app(X0,cons(X1,nil)),X2) != sK55
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(X2,sK58(X1,X0,X2)) ),
    inference(demodulation,[status(thm)],[c_254]) ).

cnf(c_11922,plain,
    ssList(sP0_iProver_def),
    inference(light_normalisation,[status(thm)],[c_9011,c_9008]) ).

cnf(c_11924,plain,
    ( app(app(X0,cons(X1,nil)),X2) != sP0_iProver_def
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | ssItem(sK58(X1,X0,X2)) ),
    inference(light_normalisation,[status(thm)],[c_9014,c_9008]) ).

cnf(c_11941,plain,
    ( app(app(X0,cons(X1,nil)),X2) != sP0_iProver_def
    | ~ ssItem(X1)
    | ~ ssList(X0)
    | ~ ssList(X2)
    | memberP(X2,sK58(X1,X0,X2)) ),
    inference(light_normalisation,[status(thm)],[c_9016,c_9008]) ).

cnf(c_11976,plain,
    ( app(app(X0,sP0_iProver_def),X1) != sP0_iProver_def
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssItem(sK57)
    | memberP(X1,sK58(sK57,X0,X1)) ),
    inference(superposition,[status(thm)],[c_9007,c_11941]) ).

cnf(c_11978,plain,
    ( app(app(X0,sP0_iProver_def),X1) != sP0_iProver_def
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssItem(sK57)
    | ssItem(sK58(sK57,X0,X1)) ),
    inference(superposition,[status(thm)],[c_9007,c_11924]) ).

cnf(c_11979,plain,
    ( app(app(X0,sP0_iProver_def),X1) != sP0_iProver_def
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ssItem(sK58(sK57,X0,X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11978,c_9010]) ).

cnf(c_11989,plain,
    ( app(app(X0,sP0_iProver_def),X1) != sP0_iProver_def
    | ~ ssList(X0)
    | ~ ssList(X1)
    | memberP(X1,sK58(sK57,X0,X1)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_11976,c_9010]) ).

cnf(c_12419,plain,
    app(nil,sP0_iProver_def) = sP0_iProver_def,
    inference(superposition,[status(thm)],[c_11922,c_155]) ).

cnf(c_12479,plain,
    ( app(sP0_iProver_def,X0) != sP0_iProver_def
    | ~ ssList(X0)
    | ~ ssList(nil)
    | memberP(X0,sK58(sK57,nil,X0)) ),
    inference(superposition,[status(thm)],[c_12419,c_11989]) ).

cnf(c_12481,plain,
    ( app(sP0_iProver_def,X0) != sP0_iProver_def
    | ~ ssList(X0)
    | ~ ssList(nil)
    | ssItem(sK58(sK57,nil,X0)) ),
    inference(superposition,[status(thm)],[c_12419,c_11979]) ).

cnf(c_12484,plain,
    ( app(sP0_iProver_def,X0) != sP0_iProver_def
    | ~ ssList(X0)
    | ssItem(sK58(sK57,nil,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12481,c_141]) ).

cnf(c_12492,plain,
    ( app(sP0_iProver_def,X0) != sP0_iProver_def
    | ~ ssList(X0)
    | memberP(X0,sK58(sK57,nil,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_12479,c_141]) ).

cnf(c_12571,plain,
    app(sP0_iProver_def,nil) = sP0_iProver_def,
    inference(superposition,[status(thm)],[c_11922,c_232]) ).

cnf(c_12671,plain,
    ( ~ ssList(nil)
    | memberP(nil,sK58(sK57,nil,nil)) ),
    inference(superposition,[status(thm)],[c_12571,c_12492]) ).

cnf(c_12673,plain,
    ( ~ ssList(nil)
    | ssItem(sK58(sK57,nil,nil)) ),
    inference(superposition,[status(thm)],[c_12571,c_12484]) ).

cnf(c_12674,plain,
    ssItem(sK58(sK57,nil,nil)),
    inference(forward_subsumption_resolution,[status(thm)],[c_12673,c_141]) ).

cnf(c_12675,plain,
    memberP(nil,sK58(sK57,nil,nil)),
    inference(forward_subsumption_resolution,[status(thm)],[c_12671,c_141]) ).

cnf(c_12679,plain,
    ~ ssItem(sK58(sK57,nil,nil)),
    inference(superposition,[status(thm)],[c_12675,c_171]) ).

cnf(c_12680,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_12679,c_12674]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWC252+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n018.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 23:37:01 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  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
% 4.32/1.17  % SZS status Started for theBenchmark.p
% 4.32/1.17  % SZS status Theorem for theBenchmark.p
% 4.32/1.17  
% 4.32/1.17  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.32/1.17  
% 4.32/1.17  ------  iProver source info
% 4.32/1.17  
% 4.32/1.17  git: date: 2024-05-02 19:28:25 +0000
% 4.32/1.17  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.32/1.17  git: non_committed_changes: false
% 4.32/1.17  
% 4.32/1.17  ------ Parsing...
% 4.32/1.17  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.32/1.17  
% 4.32/1.17  ------ 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 
% 4.32/1.17  
% 4.32/1.17  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.32/1.17  
% 4.32/1.17  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.32/1.17  ------ Proving...
% 4.32/1.17  ------ Problem Properties 
% 4.32/1.17  
% 4.32/1.17  
% 4.32/1.17  clauses                                 192
% 4.32/1.17  conjectures                             11
% 4.32/1.17  EPR                                     55
% 4.32/1.17  Horn                                    124
% 4.32/1.17  unary                                   23
% 4.32/1.17  binary                                  40
% 4.32/1.17  lits                                    650
% 4.32/1.17  lits eq                                 86
% 4.32/1.17  fd_pure                                 0
% 4.32/1.17  fd_pseudo                               0
% 4.32/1.17  fd_cond                                 21
% 4.32/1.17  fd_pseudo_cond                          14
% 4.32/1.17  AC symbols                              0
% 4.32/1.17  
% 4.32/1.17  ------ Schedule dynamic 5 is on 
% 4.32/1.17  
% 4.32/1.17  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.32/1.17  
% 4.32/1.17  
% 4.32/1.17  ------ 
% 4.32/1.17  Current options:
% 4.32/1.17  ------ 
% 4.32/1.17  
% 4.32/1.17  
% 4.32/1.17  
% 4.32/1.17  
% 4.32/1.17  ------ Proving...
% 4.32/1.17  
% 4.32/1.17  
% 4.32/1.17  % SZS status Theorem for theBenchmark.p
% 4.32/1.17  
% 4.32/1.17  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.32/1.17  
% 4.32/1.17  
%------------------------------------------------------------------------------