TSTP Solution File: SWV403+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWV403+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n025.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 03:14:20 EDT 2024

% Result   : Theorem 4.20s 1.09s
% Output   : CNFRefutation 4.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   89 (  22 unt;   0 def)
%            Number of atoms       :  231 (  65 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  224 (  82   ~;  92   |;  38   &)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :  256 (   7 sgn 127   !;  34   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | less_than(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).

fof(f3,axiom,
    ! [X0] : less_than(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
    <=> ( ~ less_than(X1,X0)
        & less_than(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).

fof(f11,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
    <=> ( ( X3 = X4
          & X1 = X2 )
        | pair_in_list(X0,X2,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).

fof(f14,axiom,
    ! [X0,X1,X2] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

fof(f17,axiom,
    ! [X0,X1,X2,X3] :
      ( strictly_less_than(X3,X2)
     => update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).

fof(f18,axiom,
    ! [X0,X1,X2,X3] :
      ( less_than(X2,X3)
     => update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).

fof(f19,conjecture,
    ! [X0] :
      ( ! [X1,X2,X3] :
          ( ( strictly_less_than(X2,X3)
            & pair_in_list(X0,X1,X2) )
         => pair_in_list(update_slb(X0,X3),X1,X3) )
     => ! [X4,X5,X6,X7,X8] :
          ( ( strictly_less_than(X5,X6)
            & pair_in_list(insert_slb(X0,pair(X7,X8)),X4,X5) )
         => pair_in_list(update_slb(insert_slb(X0,pair(X7,X8)),X6),X4,X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_co) ).

fof(f20,negated_conjecture,
    ~ ! [X0] :
        ( ! [X1,X2,X3] :
            ( ( strictly_less_than(X2,X3)
              & pair_in_list(X0,X1,X2) )
           => pair_in_list(update_slb(X0,X3),X1,X3) )
       => ! [X4,X5,X6,X7,X8] :
            ( ( strictly_less_than(X5,X6)
              & pair_in_list(insert_slb(X0,pair(X7,X8)),X4,X5) )
           => pair_in_list(update_slb(insert_slb(X0,pair(X7,X8)),X6),X4,X6) ) ),
    inference(negated_conjecture,[],[f19]) ).

fof(f27,plain,
    ! [X0,X1,X2,X3] :
      ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
      | ~ strictly_less_than(X3,X2) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f28,plain,
    ! [X0,X1,X2,X3] :
      ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
      | ~ less_than(X2,X3) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f29,plain,
    ? [X0] :
      ( ? [X4,X5,X6,X7,X8] :
          ( ~ pair_in_list(update_slb(insert_slb(X0,pair(X7,X8)),X6),X4,X6)
          & strictly_less_than(X5,X6)
          & pair_in_list(insert_slb(X0,pair(X7,X8)),X4,X5) )
      & ! [X1,X2,X3] :
          ( pair_in_list(update_slb(X0,X3),X1,X3)
          | ~ strictly_less_than(X2,X3)
          | ~ pair_in_list(X0,X1,X2) ) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f30,plain,
    ? [X0] :
      ( ? [X4,X5,X6,X7,X8] :
          ( ~ pair_in_list(update_slb(insert_slb(X0,pair(X7,X8)),X6),X4,X6)
          & strictly_less_than(X5,X6)
          & pair_in_list(insert_slb(X0,pair(X7,X8)),X4,X5) )
      & ! [X1,X2,X3] :
          ( pair_in_list(update_slb(X0,X3),X1,X3)
          | ~ strictly_less_than(X2,X3)
          | ~ pair_in_list(X0,X1,X2) ) ),
    inference(flattening,[],[f29]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( strictly_less_than(X0,X1)
        | less_than(X1,X0)
        | ~ less_than(X0,X1) )
      & ( ( ~ less_than(X1,X0)
          & less_than(X0,X1) )
        | ~ strictly_less_than(X0,X1) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( strictly_less_than(X0,X1)
        | less_than(X1,X0)
        | ~ less_than(X0,X1) )
      & ( ( ~ less_than(X1,X0)
          & less_than(X0,X1) )
        | ~ strictly_less_than(X0,X1) ) ),
    inference(flattening,[],[f31]) ).

fof(f35,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
        | ( ( X3 != X4
            | X1 != X2 )
          & ~ pair_in_list(X0,X2,X4) ) )
      & ( ( X3 = X4
          & X1 = X2 )
        | pair_in_list(X0,X2,X4)
        | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f36,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
        | ( ( X3 != X4
            | X1 != X2 )
          & ~ pair_in_list(X0,X2,X4) ) )
      & ( ( X3 = X4
          & X1 = X2 )
        | pair_in_list(X0,X2,X4)
        | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
    inference(flattening,[],[f35]) ).

fof(f37,plain,
    ? [X0] :
      ( ? [X1,X2,X3,X4,X5] :
          ( ~ pair_in_list(update_slb(insert_slb(X0,pair(X4,X5)),X3),X1,X3)
          & strictly_less_than(X2,X3)
          & pair_in_list(insert_slb(X0,pair(X4,X5)),X1,X2) )
      & ! [X6,X7,X8] :
          ( pair_in_list(update_slb(X0,X8),X6,X8)
          | ~ strictly_less_than(X7,X8)
          | ~ pair_in_list(X0,X6,X7) ) ),
    inference(rectify,[],[f30]) ).

fof(f38,plain,
    ( ? [X0] :
        ( ? [X1,X2,X3,X4,X5] :
            ( ~ pair_in_list(update_slb(insert_slb(X0,pair(X4,X5)),X3),X1,X3)
            & strictly_less_than(X2,X3)
            & pair_in_list(insert_slb(X0,pair(X4,X5)),X1,X2) )
        & ! [X6,X7,X8] :
            ( pair_in_list(update_slb(X0,X8),X6,X8)
            | ~ strictly_less_than(X7,X8)
            | ~ pair_in_list(X0,X6,X7) ) )
   => ( ? [X5,X4,X3,X2,X1] :
          ( ~ pair_in_list(update_slb(insert_slb(sK0,pair(X4,X5)),X3),X1,X3)
          & strictly_less_than(X2,X3)
          & pair_in_list(insert_slb(sK0,pair(X4,X5)),X1,X2) )
      & ! [X8,X7,X6] :
          ( pair_in_list(update_slb(sK0,X8),X6,X8)
          | ~ strictly_less_than(X7,X8)
          | ~ pair_in_list(sK0,X6,X7) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,plain,
    ( ? [X5,X4,X3,X2,X1] :
        ( ~ pair_in_list(update_slb(insert_slb(sK0,pair(X4,X5)),X3),X1,X3)
        & strictly_less_than(X2,X3)
        & pair_in_list(insert_slb(sK0,pair(X4,X5)),X1,X2) )
   => ( ~ pair_in_list(update_slb(insert_slb(sK0,pair(sK4,sK5)),sK3),sK1,sK3)
      & strictly_less_than(sK2,sK3)
      & pair_in_list(insert_slb(sK0,pair(sK4,sK5)),sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f40,plain,
    ( ~ pair_in_list(update_slb(insert_slb(sK0,pair(sK4,sK5)),sK3),sK1,sK3)
    & strictly_less_than(sK2,sK3)
    & pair_in_list(insert_slb(sK0,pair(sK4,sK5)),sK1,sK2)
    & ! [X6,X7,X8] :
        ( pair_in_list(update_slb(sK0,X8),X6,X8)
        | ~ strictly_less_than(X7,X8)
        | ~ pair_in_list(sK0,X6,X7) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f37,f39,f38]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | less_than(X0,X1) ),
    inference(cnf_transformation,[],[f2]) ).

fof(f43,plain,
    ! [X0] : less_than(X0,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ~ less_than(X1,X0)
      | ~ strictly_less_than(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f55,plain,
    ! [X2,X3,X0,X1,X4] :
      ( X1 = X2
      | pair_in_list(X0,X2,X4)
      | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f56,plain,
    ! [X2,X3,X0,X1,X4] :
      ( X3 = X4
      | pair_in_list(X0,X2,X4)
      | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f57,plain,
    ! [X2,X3,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
      | ~ pair_in_list(X0,X2,X4) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f58,plain,
    ! [X2,X3,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
      | X3 != X4
      | X1 != X2 ),
    inference(cnf_transformation,[],[f36]) ).

fof(f61,plain,
    ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
    inference(cnf_transformation,[],[f14]) ).

fof(f64,plain,
    ! [X2,X3,X0,X1] :
      ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
      | ~ strictly_less_than(X3,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f65,plain,
    ! [X2,X3,X0,X1] :
      ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
      | ~ less_than(X2,X3) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f66,plain,
    ! [X8,X6,X7] :
      ( pair_in_list(update_slb(sK0,X8),X6,X8)
      | ~ strictly_less_than(X7,X8)
      | ~ pair_in_list(sK0,X6,X7) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f67,plain,
    pair_in_list(insert_slb(sK0,pair(sK4,sK5)),sK1,sK2),
    inference(cnf_transformation,[],[f40]) ).

fof(f68,plain,
    strictly_less_than(sK2,sK3),
    inference(cnf_transformation,[],[f40]) ).

fof(f69,plain,
    ~ pair_in_list(update_slb(insert_slb(sK0,pair(sK4,sK5)),sK3),sK1,sK3),
    inference(cnf_transformation,[],[f40]) ).

fof(f71,plain,
    ! [X2,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X4)),X2,X4)
      | X1 != X2 ),
    inference(equality_resolution,[],[f58]) ).

fof(f72,plain,
    ! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
    inference(equality_resolution,[],[f71]) ).

cnf(c_50,plain,
    ( less_than(X0,X1)
    | less_than(X1,X0) ),
    inference(cnf_transformation,[],[f42]) ).

cnf(c_51,plain,
    less_than(X0,X0),
    inference(cnf_transformation,[],[f43]) ).

cnf(c_52,plain,
    ( ~ less_than(X0,X1)
    | less_than(X1,X0)
    | strictly_less_than(X0,X1) ),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_53,plain,
    ( ~ less_than(X0,X1)
    | ~ strictly_less_than(X1,X0) ),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_63,plain,
    pair_in_list(insert_slb(X0,pair(X1,X2)),X1,X2),
    inference(cnf_transformation,[],[f72]) ).

cnf(c_64,plain,
    ( ~ pair_in_list(X0,X1,X2)
    | pair_in_list(insert_slb(X0,pair(X3,X4)),X1,X2) ),
    inference(cnf_transformation,[],[f57]) ).

cnf(c_65,plain,
    ( ~ pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4)
    | X2 = X4
    | pair_in_list(X0,X3,X4) ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_66,plain,
    ( ~ pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4)
    | X1 = X3
    | pair_in_list(X0,X3,X4) ),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_69,plain,
    lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
    inference(cnf_transformation,[],[f61]) ).

cnf(c_72,plain,
    ( ~ strictly_less_than(X0,X1)
    | insert_slb(update_slb(X2,X1),pair(X3,X1)) = update_slb(insert_slb(X2,pair(X3,X0)),X1) ),
    inference(cnf_transformation,[],[f64]) ).

cnf(c_73,plain,
    ( ~ less_than(X0,X1)
    | insert_slb(update_slb(X2,X0),pair(X3,X1)) = update_slb(insert_slb(X2,pair(X3,X1)),X0) ),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_74,negated_conjecture,
    ~ pair_in_list(update_slb(insert_slb(sK0,pair(sK4,sK5)),sK3),sK1,sK3),
    inference(cnf_transformation,[],[f69]) ).

cnf(c_75,negated_conjecture,
    strictly_less_than(sK2,sK3),
    inference(cnf_transformation,[],[f68]) ).

cnf(c_76,negated_conjecture,
    pair_in_list(insert_slb(sK0,pair(sK4,sK5)),sK1,sK2),
    inference(cnf_transformation,[],[f67]) ).

cnf(c_77,negated_conjecture,
    ( ~ pair_in_list(sK0,X0,X1)
    | ~ strictly_less_than(X1,X2)
    | pair_in_list(update_slb(sK0,X2),X0,X2) ),
    inference(cnf_transformation,[],[f66]) ).

cnf(c_94,plain,
    ( less_than(X1,X0)
    | strictly_less_than(X0,X1) ),
    inference(global_subsumption_just,[status(thm)],[c_52,c_50,c_52]) ).

cnf(c_95,plain,
    ( less_than(X0,X1)
    | strictly_less_than(X1,X0) ),
    inference(renaming,[status(thm)],[c_94]) ).

cnf(c_108,plain,
    ( strictly_less_than(X1,X0)
    | insert_slb(update_slb(X2,X0),pair(X3,X1)) = update_slb(insert_slb(X2,pair(X3,X1)),X0) ),
    inference(prop_impl_just,[status(thm)],[c_73,c_95]) ).

cnf(c_109,plain,
    ( insert_slb(update_slb(X0,X1),pair(X2,X3)) = update_slb(insert_slb(X0,pair(X2,X3)),X1)
    | strictly_less_than(X3,X1) ),
    inference(renaming,[status(thm)],[c_108]) ).

cnf(c_287,plain,
    ( ~ strictly_less_than(X1,X0)
    | ~ less_than(X0,X1) ),
    inference(prop_impl_just,[status(thm)],[c_53]) ).

cnf(c_288,plain,
    ( ~ less_than(X0,X1)
    | ~ strictly_less_than(X1,X0) ),
    inference(renaming,[status(thm)],[c_287]) ).

cnf(c_303,plain,
    ( strictly_less_than(X3,X1)
    | insert_slb(update_slb(X0,X1),pair(X2,X3)) = update_slb(insert_slb(X0,pair(X2,X3)),X1) ),
    inference(prop_impl_just,[status(thm)],[c_109]) ).

cnf(c_304,plain,
    ( insert_slb(update_slb(X0,X1),pair(X2,X3)) = update_slb(insert_slb(X0,pair(X2,X3)),X1)
    | strictly_less_than(X3,X1) ),
    inference(renaming,[status(thm)],[c_303]) ).

cnf(c_474,plain,
    ( X0 != X1
    | X1 != X2
    | ~ strictly_less_than(X2,X0) ),
    inference(resolution_lifted,[status(thm)],[c_288,c_51]) ).

cnf(c_475,plain,
    ~ strictly_less_than(X0,X0),
    inference(unflattening,[status(thm)],[c_474]) ).

cnf(c_905,plain,
    ( sK5 = sK2
    | pair_in_list(sK0,sK1,sK2) ),
    inference(superposition,[status(thm)],[c_76,c_65]) ).

cnf(c_910,plain,
    ( ~ strictly_less_than(sK2,X0)
    | sK5 = sK2
    | pair_in_list(update_slb(sK0,X0),sK1,X0) ),
    inference(superposition,[status(thm)],[c_905,c_77]) ).

cnf(c_920,plain,
    ( sK4 = sK1
    | pair_in_list(sK0,sK1,sK2) ),
    inference(superposition,[status(thm)],[c_76,c_66]) ).

cnf(c_925,plain,
    ( ~ strictly_less_than(sK2,X0)
    | sK4 = sK1
    | pair_in_list(update_slb(sK0,X0),sK1,X0) ),
    inference(superposition,[status(thm)],[c_920,c_77]) ).

cnf(c_933,plain,
    ( insert_slb(update_slb(X0,X1),pair(X2,X3)) = update_slb(insert_slb(X0,pair(X2,X3)),X1)
    | insert_slb(update_slb(X4,X1),pair(X5,X1)) = update_slb(insert_slb(X4,pair(X5,X3)),X1) ),
    inference(superposition,[status(thm)],[c_304,c_72]) ).

cnf(c_934,plain,
    insert_slb(update_slb(X0,sK3),pair(X1,sK3)) = update_slb(insert_slb(X0,pair(X1,sK2)),sK3),
    inference(superposition,[status(thm)],[c_75,c_72]) ).

cnf(c_1063,plain,
    ( ~ pair_in_list(insert_slb(update_slb(sK0,sK3),pair(sK4,sK3)),sK1,sK3)
    | insert_slb(update_slb(X0,sK3),pair(X1,sK5)) = update_slb(insert_slb(X0,pair(X1,sK5)),sK3) ),
    inference(superposition,[status(thm)],[c_933,c_74]) ).

cnf(c_1243,plain,
    ( ~ pair_in_list(update_slb(sK0,sK3),sK1,sK3)
    | insert_slb(update_slb(X0,sK3),pair(X1,sK5)) = update_slb(insert_slb(X0,pair(X1,sK5)),sK3) ),
    inference(superposition,[status(thm)],[c_64,c_1063]) ).

cnf(c_1358,plain,
    ( ~ strictly_less_than(sK2,sK3)
    | insert_slb(update_slb(X0,sK3),pair(X1,sK5)) = update_slb(insert_slb(X0,pair(X1,sK5)),sK3)
    | sK4 = sK1 ),
    inference(superposition,[status(thm)],[c_925,c_1243]) ).

cnf(c_1359,plain,
    ( ~ strictly_less_than(sK2,sK3)
    | insert_slb(update_slb(X0,sK3),pair(X1,sK5)) = update_slb(insert_slb(X0,pair(X1,sK5)),sK3)
    | sK5 = sK2 ),
    inference(superposition,[status(thm)],[c_910,c_1243]) ).

cnf(c_1361,plain,
    ( insert_slb(update_slb(X0,sK3),pair(X1,sK5)) = update_slb(insert_slb(X0,pair(X1,sK5)),sK3)
    | sK5 = sK2 ),
    inference(global_subsumption_just,[status(thm)],[c_1359,c_75,c_1359]) ).

cnf(c_1367,plain,
    ( insert_slb(update_slb(X0,sK3),pair(X1,sK5)) = update_slb(insert_slb(X0,pair(X1,sK5)),sK3)
    | sK4 = sK1 ),
    inference(global_subsumption_just,[status(thm)],[c_1358,c_75,c_1358]) ).

cnf(c_1418,plain,
    ( ~ pair_in_list(insert_slb(update_slb(sK0,sK3),pair(sK4,sK5)),sK1,sK3)
    | sK5 = sK2 ),
    inference(superposition,[status(thm)],[c_1361,c_74]) ).

cnf(c_1424,plain,
    ( ~ pair_in_list(update_slb(sK0,sK3),sK1,sK3)
    | sK5 = sK2 ),
    inference(superposition,[status(thm)],[c_64,c_1418]) ).

cnf(c_1430,plain,
    ( ~ strictly_less_than(sK2,sK3)
    | sK5 = sK2 ),
    inference(superposition,[status(thm)],[c_910,c_1424]) ).

cnf(c_1431,plain,
    sK5 = sK2,
    inference(global_subsumption_just,[status(thm)],[c_1430,c_75,c_1430]) ).

cnf(c_1441,plain,
    insert_slb(update_slb(X0,sK3),pair(X1,sK3)) = update_slb(insert_slb(X0,pair(X1,sK5)),sK3),
    inference(superposition,[status(thm)],[c_1431,c_934]) ).

cnf(c_1501,plain,
    ( insert_slb(update_slb(X0,sK3),pair(X1,sK5)) = insert_slb(update_slb(X0,sK3),pair(X1,sK3))
    | sK4 = sK1 ),
    inference(demodulation,[status(thm)],[c_1367,c_1441]) ).

cnf(c_1508,plain,
    ( lookup_slb(insert_slb(update_slb(X0,sK3),pair(X1,sK5)),X1) = sK3
    | sK4 = sK1 ),
    inference(superposition,[status(thm)],[c_1501,c_69]) ).

cnf(c_1533,plain,
    ( sK4 = sK1
    | sK5 = sK3 ),
    inference(demodulation,[status(thm)],[c_1508,c_69]) ).

cnf(c_1702,plain,
    ( sK4 = sK1
    | strictly_less_than(sK2,sK5) ),
    inference(superposition,[status(thm)],[c_1533,c_75]) ).

cnf(c_1706,plain,
    ( sK4 = sK1
    | strictly_less_than(sK5,sK5) ),
    inference(light_normalisation,[status(thm)],[c_1702,c_1431]) ).

cnf(c_1798,plain,
    sK4 = sK1,
    inference(superposition,[status(thm)],[c_1706,c_475]) ).

cnf(c_1802,plain,
    ~ pair_in_list(update_slb(insert_slb(sK0,pair(sK1,sK5)),sK3),sK1,sK3),
    inference(superposition,[status(thm)],[c_1798,c_74]) ).

cnf(c_1804,plain,
    ~ pair_in_list(insert_slb(update_slb(sK0,sK3),pair(sK1,sK3)),sK1,sK3),
    inference(demodulation,[status(thm)],[c_1802,c_1441]) ).

cnf(c_1808,plain,
    $false,
    inference(superposition,[status(thm)],[c_63,c_1804]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : SWV403+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.10  % Command  : run_iprover %s %d THM
% 0.10/0.31  % Computer : n025.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Fri May  3 00:24:58 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.16/0.41  Running first-order theorem proving
% 0.16/0.41  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
% 4.20/1.09  % SZS status Started for theBenchmark.p
% 4.20/1.09  % SZS status Theorem for theBenchmark.p
% 4.20/1.09  
% 4.20/1.09  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.20/1.09  
% 4.20/1.09  ------  iProver source info
% 4.20/1.09  
% 4.20/1.09  git: date: 2024-05-02 19:28:25 +0000
% 4.20/1.09  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.20/1.09  git: non_committed_changes: false
% 4.20/1.09  
% 4.20/1.09  ------ Parsing...
% 4.20/1.09  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.20/1.09  
% 4.20/1.09  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 3 0s  sf_e  pe_s  pe_e 
% 4.20/1.09  
% 4.20/1.09  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.20/1.09  
% 4.20/1.09  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.20/1.09  ------ Proving...
% 4.20/1.09  ------ Problem Properties 
% 4.20/1.09  
% 4.20/1.09  
% 4.20/1.09  clauses                                 25
% 4.20/1.09  conjectures                             4
% 4.20/1.09  EPR                                     7
% 4.20/1.09  Horn                                    18
% 4.20/1.09  unary                                   13
% 4.20/1.09  binary                                  5
% 4.20/1.09  lits                                    44
% 4.20/1.09  lits eq                                 13
% 4.20/1.09  fd_pure                                 0
% 4.20/1.09  fd_pseudo                               0
% 4.20/1.09  fd_cond                                 0
% 4.20/1.09  fd_pseudo_cond                          5
% 4.20/1.09  AC symbols                              0
% 4.20/1.09  
% 4.20/1.09  ------ Input Options Time Limit: Unbounded
% 4.20/1.09  
% 4.20/1.09  
% 4.20/1.09  ------ 
% 4.20/1.09  Current options:
% 4.20/1.09  ------ 
% 4.20/1.09  
% 4.20/1.09  
% 4.20/1.09  
% 4.20/1.09  
% 4.20/1.09  ------ Proving...
% 4.20/1.09  
% 4.20/1.09  
% 4.20/1.09  % SZS status Theorem for theBenchmark.p
% 4.20/1.09  
% 4.20/1.09  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.20/1.09  
% 4.20/1.09  
%------------------------------------------------------------------------------