TSTP Solution File: SWC355+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWC355+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n010.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 03:12:08 EDT 2024

% Result   : Theorem 3.87s 0.98s
% Output   : CNFRefutation 3.87s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f604)

% Comments : 
%------------------------------------------------------------------------------
fof(f7,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).

fof(f16,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ssList(cons(X1,X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).

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

fof(f28,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(nil,X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

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

fof(f103,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( segmentP(X0,X1)
          <=> ? [X2] :
                ( ? [X3] :
                    ( app(app(X2,X1),X3) = X0
                    & ssList(X3) )
                & ssList(X2) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f119,plain,
    ! [X0] :
      ( ! [X1] :
          ( ssList(cons(X1,X0))
          | ~ ssItem(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f134,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f28]) ).

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

fof(f253,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X2] :
                  ( ? [X3] :
                      ( app(app(X2,X1),X3) = X0
                      & ssList(X3) )
                  & ssList(X2) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(nnf_transformation,[],[f103]) ).

fof(f254,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ? [X4] :
                  ( ? [X5] :
                      ( app(app(X4,X1),X5) = X0
                      & ssList(X5) )
                  & ssList(X4) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(rectify,[],[f253]) ).

fof(f255,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( ? [X5] :
              ( app(app(X4,X1),X5) = X0
              & ssList(X5) )
          & ssList(X4) )
     => ( ? [X5] :
            ( app(app(sK13(X0,X1),X1),X5) = X0
            & ssList(X5) )
        & ssList(sK13(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f256,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( app(app(sK13(X0,X1),X1),X5) = X0
          & ssList(X5) )
     => ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
        & ssList(sK14(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f257,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( segmentP(X0,X1)
              | ! [X2] :
                  ( ! [X3] :
                      ( app(app(X2,X1),X3) != X0
                      | ~ ssList(X3) )
                  | ~ ssList(X2) ) )
            & ( ( app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
                & ssList(sK14(X0,X1))
                & ssList(sK13(X0,X1)) )
              | ~ segmentP(X0,X1) ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f254,f256,f255]) ).

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

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

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

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

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

fof(f348,plain,
    ( ( ( ~ neq(sK56,nil)
        & neq(sK54,nil) )
      | ( ~ segmentP(sK54,sK53)
        & sK56 = app(sK55,cons(sK57,nil))
        & ssItem(sK57)
        & 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(f370,plain,
    ! [X2,X3,X0,X1] :
      ( segmentP(X0,X1)
      | app(app(X2,X1),X3) != X0
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f257]) ).

fof(f440,plain,
    ! [X0,X1] :
      ( ssList(cons(X1,X0))
      | ~ ssItem(X1)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f119]) ).

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

fof(f455,plain,
    ! [X0] :
      ( app(nil,X0) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f134]) ).

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

fof(f549,plain,
    ssList(sK54),
    inference(cnf_transformation,[],[f348]) ).

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

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

fof(f559,plain,
    ( ~ neq(sK56,nil)
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f560,plain,
    ( ~ neq(sK56,nil)
    | sK56 = app(sK55,cons(sK57,nil)) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f561,plain,
    ( ~ neq(sK56,nil)
    | ~ segmentP(sK54,sK53) ),
    inference(cnf_transformation,[],[f348]) ).

fof(f562,plain,
    ( ~ neq(sK56,nil)
    | ~ segmentP(sK56,sK55) ),
    inference(definition_unfolding,[],[f561,f552,f553]) ).

fof(f568,plain,
    ssList(sK56),
    inference(definition_unfolding,[],[f549,f552]) ).

fof(f569,plain,
    ssList(sK55),
    inference(definition_unfolding,[],[f548,f553]) ).

fof(f575,plain,
    ! [X2,X3,X1] :
      ( segmentP(app(app(X2,X1),X3),X1)
      | ~ ssList(X3)
      | ~ ssList(X2)
      | ~ ssList(X1)
      | ~ ssList(app(app(X2,X1),X3)) ),
    inference(equality_resolution,[],[f370]) ).

cnf(c_67,plain,
    ( ~ ssList(app(app(X0,X1),X2))
    | ~ ssList(X0)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | segmentP(app(app(X0,X1),X2),X1) ),
    inference(cnf_transformation,[],[f575]) ).

cnf(c_140,plain,
    ( ~ ssItem(X0)
    | ~ ssList(X1)
    | ssList(cons(X0,X1)) ),
    inference(cnf_transformation,[],[f440]) ).

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

cnf(c_155,plain,
    ( ~ ssList(X0)
    | app(nil,X0) = X0 ),
    inference(cnf_transformation,[],[f455]) ).

cnf(c_246,negated_conjecture,
    ( ~ neq(sK56,nil)
    | ~ segmentP(sK56,sK55) ),
    inference(cnf_transformation,[],[f562]) ).

cnf(c_247,negated_conjecture,
    ( ~ neq(sK56,nil)
    | app(sK55,cons(sK57,nil)) = sK56 ),
    inference(cnf_transformation,[],[f560]) ).

cnf(c_248,negated_conjecture,
    ( ~ neq(sK56,nil)
    | ssItem(sK57) ),
    inference(cnf_transformation,[],[f559]) ).

cnf(c_252,negated_conjecture,
    neq(sK56,nil),
    inference(cnf_transformation,[],[f604]) ).

cnf(c_255,negated_conjecture,
    ssList(sK56),
    inference(cnf_transformation,[],[f568]) ).

cnf(c_256,negated_conjecture,
    ssList(sK55),
    inference(cnf_transformation,[],[f569]) ).

cnf(c_385,negated_conjecture,
    app(sK55,cons(sK57,nil)) = sK56,
    inference(global_subsumption_just,[status(thm)],[c_247,c_252,c_247]) ).

cnf(c_11635,plain,
    app(nil,sK55) = sK55,
    inference(superposition,[status(thm)],[c_256,c_155]) ).

cnf(c_11899,plain,
    ( ~ ssList(app(app(nil,sK55),X0))
    | ~ ssList(X0)
    | ~ ssList(nil)
    | ~ ssList(sK55)
    | segmentP(app(sK55,X0),sK55) ),
    inference(superposition,[status(thm)],[c_11635,c_67]) ).

cnf(c_12770,plain,
    ( ~ ssList(app(app(nil,sK55),X0))
    | ~ ssList(X0)
    | segmentP(app(sK55,X0),sK55) ),
    inference(global_subsumption_just,[status(thm)],[c_11899,c_256,c_141,c_11899]) ).

cnf(c_12776,plain,
    ( ~ ssList(app(sK55,X0))
    | ~ ssList(X0)
    | segmentP(app(sK55,X0),sK55) ),
    inference(light_normalisation,[status(thm)],[c_12770,c_11635]) ).

cnf(c_12783,plain,
    ( ~ ssList(app(sK55,cons(sK57,nil)))
    | ~ ssList(cons(sK57,nil))
    | segmentP(sK56,sK55) ),
    inference(superposition,[status(thm)],[c_385,c_12776]) ).

cnf(c_15918,plain,
    ( ~ ssList(cons(sK57,nil))
    | ~ ssList(app(sK55,cons(sK57,nil))) ),
    inference(global_subsumption_just,[status(thm)],[c_12783,c_252,c_246,c_12783]) ).

cnf(c_15919,plain,
    ( ~ ssList(app(sK55,cons(sK57,nil)))
    | ~ ssList(cons(sK57,nil)) ),
    inference(renaming,[status(thm)],[c_15918]) ).

cnf(c_15922,plain,
    ( ~ ssList(cons(sK57,nil))
    | ~ ssList(sK56) ),
    inference(light_normalisation,[status(thm)],[c_15919,c_385]) ).

cnf(c_15925,plain,
    ~ ssList(cons(sK57,nil)),
    inference(forward_subsumption_resolution,[status(thm)],[c_15922,c_255]) ).

cnf(c_15926,plain,
    ( ~ ssItem(sK57)
    | ~ ssList(nil) ),
    inference(superposition,[status(thm)],[c_140,c_15925]) ).

cnf(c_15927,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_15926,c_248,c_252,c_141]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SWC355+1 : TPTP v8.1.2. Released v2.4.0.
% 0.02/0.11  % Command  : run_iprover %s %d THM
% 0.08/0.30  % Computer : n010.cluster.edu
% 0.08/0.30  % Model    : x86_64 x86_64
% 0.08/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30  % Memory   : 8042.1875MB
% 0.08/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30  % CPULimit : 300
% 0.08/0.30  % WCLimit  : 300
% 0.08/0.30  % DateTime : Thu May  2 23:14:34 EDT 2024
% 0.08/0.30  % CPUTime  : 
% 0.14/0.38  Running first-order theorem proving
% 0.14/0.38  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
% 3.87/0.98  % SZS status Started for theBenchmark.p
% 3.87/0.98  % SZS status Theorem for theBenchmark.p
% 3.87/0.98  
% 3.87/0.98  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.87/0.98  
% 3.87/0.98  ------  iProver source info
% 3.87/0.98  
% 3.87/0.98  git: date: 2024-05-02 19:28:25 +0000
% 3.87/0.98  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.87/0.98  git: non_committed_changes: false
% 3.87/0.98  
% 3.87/0.98  ------ Parsing...
% 3.87/0.98  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.87/0.98  
% 3.87/0.98  ------ 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 
% 3.87/0.98  
% 3.87/0.98  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.87/0.98  
% 3.87/0.98  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.87/0.98  ------ Proving...
% 3.87/0.98  ------ Problem Properties 
% 3.87/0.98  
% 3.87/0.98  
% 3.87/0.98  clauses                                 186
% 3.87/0.98  conjectures                             5
% 3.87/0.98  EPR                                     54
% 3.87/0.98  Horn                                    118
% 3.87/0.98  unary                                   22
% 3.87/0.98  binary                                  40
% 3.87/0.98  lits                                    624
% 3.87/0.98  lits eq                                 80
% 3.87/0.98  fd_pure                                 0
% 3.87/0.98  fd_pseudo                               0
% 3.87/0.98  fd_cond                                 21
% 3.87/0.98  fd_pseudo_cond                          14
% 3.87/0.98  AC symbols                              0
% 3.87/0.98  
% 3.87/0.98  ------ Input Options Time Limit: Unbounded
% 3.87/0.98  
% 3.87/0.98  
% 3.87/0.98  ------ 
% 3.87/0.98  Current options:
% 3.87/0.98  ------ 
% 3.87/0.98  
% 3.87/0.98  
% 3.87/0.98  
% 3.87/0.98  
% 3.87/0.98  ------ Proving...
% 3.87/0.98  
% 3.87/0.98  
% 3.87/0.98  % SZS status Theorem for theBenchmark.p
% 3.87/0.98  
% 3.87/0.98  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.87/0.98  
% 3.87/1.00  
%------------------------------------------------------------------------------