TSTP Solution File: SWC016+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWC016+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n009.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 : Thu Aug 31 20:40:19 EDT 2023

% Result   : Theorem 1.43s 1.14s
% Output   : CNFRefutation 1.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   45 (   7 unt;   0 def)
%            Number of atoms       :  365 ( 104 equ)
%            Maximal formula atoms :   40 (   8 avg)
%            Number of connectives :  483 ( 163   ~; 145   |; 155   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   74 (   0 sgn;  30   !;  38   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( ( ? [X5] :
                            ( frontsegP(X0,X5)
                            & frontsegP(X1,X5)
                            & neq(X5,nil)
                            & ssList(X5) )
                        | ~ neq(X1,nil) )
                      & ( nil = X0
                        | nil != X1 ) )
                    | ( neq(X3,nil)
                      & ! [X4] :
                          ( ssList(X4)
                         => ( ~ frontsegP(X2,X4)
                            | ~ frontsegP(X3,X4)
                            | ~ neq(X4,nil) ) ) )
                    | ( nil = X3
                      & nil != X2 )
                    | 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)
                   => ( ( ( ? [X5] :
                              ( frontsegP(X0,X5)
                              & frontsegP(X1,X5)
                              & neq(X5,nil)
                              & ssList(X5) )
                          | ~ neq(X1,nil) )
                        & ( nil = X0
                          | nil != X1 ) )
                      | ( neq(X3,nil)
                        & ! [X4] :
                            ( ssList(X4)
                           => ( ~ frontsegP(X2,X4)
                              | ~ frontsegP(X3,X4)
                              | ~ neq(X4,nil) ) ) )
                      | ( nil = X3
                        & nil != X2 )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

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

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

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

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

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

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

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

fof(f348,plain,
    ( ? [X5] :
        ( frontsegP(sK55,X5)
        & frontsegP(sK56,X5)
        & neq(X5,nil)
        & ssList(X5) )
   => ( frontsegP(sK55,sK57)
      & frontsegP(sK56,sK57)
      & neq(sK57,nil)
      & ssList(sK57) ) ),
    introduced(choice_axiom,[]) ).

fof(f349,plain,
    ( ( ( ! [X4] :
            ( ~ frontsegP(sK53,X4)
            | ~ frontsegP(sK54,X4)
            | ~ neq(X4,nil)
            | ~ ssList(X4) )
        & neq(sK54,nil) )
      | ( nil != sK53
        & nil = sK54 ) )
    & ( ~ neq(sK56,nil)
      | ( frontsegP(sK55,sK57)
        & frontsegP(sK56,sK57)
        & neq(sK57,nil)
        & ssList(sK57) ) )
    & ( nil != sK56
      | nil = sK55 )
    & 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(f555,plain,
    ( nil != sK56
    | nil = sK55 ),
    inference(cnf_transformation,[],[f349]) ).

fof(f556,plain,
    ( ~ neq(sK56,nil)
    | ssList(sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f557,plain,
    ( ~ neq(sK56,nil)
    | neq(sK57,nil) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f558,plain,
    ( ~ neq(sK56,nil)
    | frontsegP(sK56,sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f559,plain,
    ( ~ neq(sK56,nil)
    | frontsegP(sK55,sK57) ),
    inference(cnf_transformation,[],[f349]) ).

fof(f560,plain,
    ( neq(sK54,nil)
    | nil = sK54 ),
    inference(cnf_transformation,[],[f349]) ).

fof(f561,plain,
    ( neq(sK54,nil)
    | nil != sK53 ),
    inference(cnf_transformation,[],[f349]) ).

fof(f562,plain,
    ! [X4] :
      ( ~ frontsegP(sK53,X4)
      | ~ frontsegP(sK54,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4)
      | nil = sK54 ),
    inference(cnf_transformation,[],[f349]) ).

fof(f563,plain,
    ! [X4] :
      ( ~ frontsegP(sK53,X4)
      | ~ frontsegP(sK54,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4)
      | nil != sK53 ),
    inference(cnf_transformation,[],[f349]) ).

fof(f564,plain,
    ! [X4] :
      ( ~ frontsegP(sK55,X4)
      | ~ frontsegP(sK56,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4)
      | nil != sK55 ),
    inference(definition_unfolding,[],[f563,f554,f553,f554]) ).

fof(f565,plain,
    ! [X4] :
      ( ~ frontsegP(sK55,X4)
      | ~ frontsegP(sK56,X4)
      | ~ neq(X4,nil)
      | ~ ssList(X4)
      | nil = sK56 ),
    inference(definition_unfolding,[],[f562,f554,f553,f553]) ).

fof(f566,plain,
    ( neq(sK56,nil)
    | nil != sK55 ),
    inference(definition_unfolding,[],[f561,f553,f554]) ).

fof(f567,plain,
    ( neq(sK56,nil)
    | nil = sK56 ),
    inference(definition_unfolding,[],[f560,f553,f553]) ).

cnf(c_246,negated_conjecture,
    ( nil != sK55
    | ~ neq(X0,nil)
    | ~ frontsegP(sK55,X0)
    | ~ frontsegP(sK56,X0)
    | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f564]) ).

cnf(c_247,negated_conjecture,
    ( ~ neq(X0,nil)
    | ~ frontsegP(sK55,X0)
    | ~ frontsegP(sK56,X0)
    | ~ ssList(X0)
    | nil = sK56 ),
    inference(cnf_transformation,[],[f565]) ).

cnf(c_248,negated_conjecture,
    ( nil != sK55
    | neq(sK56,nil) ),
    inference(cnf_transformation,[],[f566]) ).

cnf(c_249,negated_conjecture,
    ( nil = sK56
    | neq(sK56,nil) ),
    inference(cnf_transformation,[],[f567]) ).

cnf(c_250,negated_conjecture,
    ( ~ neq(sK56,nil)
    | frontsegP(sK55,sK57) ),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_251,negated_conjecture,
    ( ~ neq(sK56,nil)
    | frontsegP(sK56,sK57) ),
    inference(cnf_transformation,[],[f558]) ).

cnf(c_252,negated_conjecture,
    ( ~ neq(sK56,nil)
    | neq(sK57,nil) ),
    inference(cnf_transformation,[],[f557]) ).

cnf(c_253,negated_conjecture,
    ( ~ neq(sK56,nil)
    | ssList(sK57) ),
    inference(cnf_transformation,[],[f556]) ).

cnf(c_254,negated_conjecture,
    ( nil != sK56
    | nil = sK55 ),
    inference(cnf_transformation,[],[f555]) ).

cnf(c_367,negated_conjecture,
    ssList(sK57),
    inference(global_subsumption_just,[status(thm)],[c_253,c_253,c_249,c_248,c_254]) ).

cnf(c_375,negated_conjecture,
    neq(sK57,nil),
    inference(global_subsumption_just,[status(thm)],[c_252,c_252,c_249,c_248,c_254]) ).

cnf(c_377,negated_conjecture,
    frontsegP(sK56,sK57),
    inference(global_subsumption_just,[status(thm)],[c_251,c_251,c_249,c_248,c_254]) ).

cnf(c_379,negated_conjecture,
    frontsegP(sK55,sK57),
    inference(global_subsumption_just,[status(thm)],[c_250,c_250,c_249,c_248,c_254]) ).

cnf(c_397,plain,
    ( ~ ssList(X0)
    | ~ frontsegP(sK56,X0)
    | ~ frontsegP(sK55,X0)
    | ~ neq(X0,nil) ),
    inference(global_subsumption_just,[status(thm)],[c_247,c_254,c_247,c_246]) ).

cnf(c_398,negated_conjecture,
    ( ~ neq(X0,nil)
    | ~ frontsegP(sK55,X0)
    | ~ frontsegP(sK56,X0)
    | ~ ssList(X0) ),
    inference(renaming,[status(thm)],[c_397]) ).

cnf(c_399,negated_conjecture,
    ( ~ neq(X0,nil)
    | ~ frontsegP(sK55,X0)
    | ~ frontsegP(sK56,X0)
    | ~ ssList(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_246,c_398]) ).

cnf(c_3300,plain,
    ( X0 != sK57
    | nil != nil
    | ~ frontsegP(sK55,X0)
    | ~ frontsegP(sK56,X0)
    | ~ ssList(X0) ),
    inference(resolution_lifted,[status(thm)],[c_399,c_375]) ).

cnf(c_3301,plain,
    ( ~ frontsegP(sK55,sK57)
    | ~ frontsegP(sK56,sK57)
    | ~ ssList(sK57) ),
    inference(unflattening,[status(thm)],[c_3300]) ).

cnf(c_3302,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_3301,c_379,c_377,c_367]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWC016+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13  % Command  : run_iprover %s %d THM
% 0.13/0.34  % Computer : n009.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 : Mon Aug 28 15:50:35 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.46  Running first-order theorem proving
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.43/1.14  % SZS status Started for theBenchmark.p
% 1.43/1.14  % SZS status Theorem for theBenchmark.p
% 1.43/1.14  
% 1.43/1.14  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.43/1.14  
% 1.43/1.14  ------  iProver source info
% 1.43/1.14  
% 1.43/1.14  git: date: 2023-05-31 18:12:56 +0000
% 1.43/1.14  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.43/1.14  git: non_committed_changes: false
% 1.43/1.14  git: last_make_outside_of_git: false
% 1.43/1.14  
% 1.43/1.14  ------ Parsing...
% 1.43/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.43/1.14  
% 1.43/1.14  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s
% 1.43/1.14  
% 1.43/1.14  % SZS status Theorem for theBenchmark.p
% 1.43/1.14  
% 1.43/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.43/1.14  
% 1.43/1.14  
%------------------------------------------------------------------------------