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Vampire-SAT---5.0.1.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SWC274+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Sep 29 01:05:21 PM UTC 2026

% Result   : Theorem 6.73s 1.25s
% Output   : Refutation 6.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   91 (  21 unt;   7 def)
%            Number of atoms       :  355 (  40 equ)
%            Maximal formula atoms :   27 (   3 avg)
%            Number of connectives :  433 ( 169   ~; 184   |;  41   &)
%                                         (  15 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :   15 (  13 usr;   8 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-2 aty)
%            Number of variables   :  110 (   0 sgn  88   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f11,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( totalorderedP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => leq(X1,X2) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax11) ).

fof(f12,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( strictorderedP(X0)
      <=> ! [X1] :
            ( ssItem(X1)
           => ! [X2] :
                ( ssItem(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ssList(X5)
                           => ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
                             => lt(X1,X2) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax12) ).

fof(f93,axiom,
    ! [X0] :
      ( ssItem(X0)
     => ! [X1] :
          ( ssItem(X1)
         => ( lt(X0,X1)
          <=> ( X0 != X1
              & leq(X0,X1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax93) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ~ ssList(X3)
                  | X1 != X3
                  | X0 != X2
                  | ! [X4] :
                      ( ssList(X4)
                     => ! [X5] :
                          ( ~ ssList(X5)
                          | app(app(X4,X2),X5) != X3
                          | ~ strictorderedP(X2)
                          | ? [X6] :
                              ( ssItem(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(X7,cons(X6,nil)) = X4
                                  & ? [X8] :
                                      ( ssItem(X8)
                                      & ? [X9] :
                                          ( ssList(X9)
                                          & app(cons(X8,nil),X9) = X2
                                          & lt(X6,X8) ) ) ) )
                          | ? [X10] :
                              ( ssItem(X10)
                              & ? [X11] :
                                  ( ssList(X11)
                                  & app(cons(X10,nil),X11) = X5
                                  & ? [X12] :
                                      ( ssItem(X12)
                                      & ? [X13] :
                                          ( ssList(X13)
                                          & app(X13,cons(X12,nil)) = X2
                                          & lt(X12,X10) ) ) ) ) ) )
                  | totalorderedP(X0)
                  | ( nil != X3
                    & nil = X2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ~ ssList(X3)
                    | X1 != X3
                    | X0 != X2
                    | ! [X4] :
                        ( ssList(X4)
                       => ! [X5] :
                            ( ~ ssList(X5)
                            | app(app(X4,X2),X5) != X3
                            | ~ strictorderedP(X2)
                            | ? [X6] :
                                ( ssItem(X6)
                                & ? [X7] :
                                    ( ssList(X7)
                                    & app(X7,cons(X6,nil)) = X4
                                    & ? [X8] :
                                        ( ssItem(X8)
                                        & ? [X9] :
                                            ( ssList(X9)
                                            & app(cons(X8,nil),X9) = X2
                                            & lt(X6,X8) ) ) ) )
                            | ? [X10] :
                                ( ssItem(X10)
                                & ? [X11] :
                                    ( ssList(X11)
                                    & app(cons(X10,nil),X11) = X5
                                    & ? [X12] :
                                        ( ssItem(X12)
                                        & ? [X13] :
                                            ( ssList(X13)
                                            & app(X13,cons(X12,nil)) = X2
                                            & lt(X12,X10) ) ) ) ) ) )
                    | totalorderedP(X0)
                    | ( nil != X3
                      & nil = X2 ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f110,plain,
    ! [X0] :
      ( ( totalorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f111,plain,
    ! [X0] :
      ( ( totalorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( leq(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f110]) ).

fof(f112,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f113,plain,
    ! [X0] :
      ( ( strictorderedP(X0)
      <=> ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( ! [X5] :
                            ( lt(X1,X2)
                            | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
                            | ~ ssList(X5) )
                        | ~ ssList(X4) )
                    | ~ ssList(X3) )
                | ~ ssItem(X2) )
            | ~ ssItem(X1) ) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f112]) ).

fof(f216,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( lt(X0,X1)
          <=> ( X0 != X1
              & leq(X0,X1) ) )
          | ~ ssItem(X1) )
      | ~ ssItem(X0) ),
    inference(ennf_transformation,[],[f93]) ).

fof(f221,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ssList(X3)
                  & X1 = X3
                  & X0 = X2
                  & ? [X4] :
                      ( ? [X5] :
                          ( ssList(X5)
                          & app(app(X4,X2),X5) = X3
                          & strictorderedP(X2)
                          & ! [X6] :
                              ( ~ ssItem(X6)
                              | ! [X7] :
                                  ( ~ ssList(X7)
                                  | app(X7,cons(X6,nil)) != X4
                                  | ! [X8] :
                                      ( ~ ssItem(X8)
                                      | ! [X9] :
                                          ( ~ ssList(X9)
                                          | app(cons(X8,nil),X9) != X2
                                          | ~ lt(X6,X8) ) ) ) )
                          & ! [X10] :
                              ( ~ ssItem(X10)
                              | ! [X11] :
                                  ( ~ ssList(X11)
                                  | app(cons(X10,nil),X11) != X5
                                  | ! [X12] :
                                      ( ~ ssItem(X12)
                                      | ! [X13] :
                                          ( ~ ssList(X13)
                                          | app(X13,cons(X12,nil)) != X2
                                          | ~ lt(X12,X10) ) ) ) ) )
                      & ssList(X4) )
                  & ~ totalorderedP(X0)
                  & ( nil = X3
                    | nil != X2 ) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f272,plain,
    ! [X0] :
      ( ssList(sK28(X0))
      | ~ ssList(X0)
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f273,plain,
    ! [X0] :
      ( totalorderedP(X0)
      | app(app(sK26(X0),cons(sK24(X0),sK27(X0))),cons(sK25(X0),sK28(X0))) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f274,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | ~ leq(sK24(X0),sK25(X0))
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f275,plain,
    ! [X0] :
      ( ssList(sK27(X0))
      | ~ ssList(X0)
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f276,plain,
    ! [X0] :
      ( ssList(sK26(X0))
      | ~ ssList(X0)
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f277,plain,
    ! [X0] :
      ( ssItem(sK25(X0))
      | ~ ssList(X0)
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f278,plain,
    ! [X0] :
      ( ssItem(sK24(X0))
      | ~ ssList(X0)
      | totalorderedP(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f279,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ ssList(X0)
      | ~ ssItem(X1)
      | ~ ssItem(X2)
      | ~ ssList(X3)
      | ~ ssList(X4)
      | ~ ssList(X5)
      | app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
      | lt(X1,X2)
      | ~ strictorderedP(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f405,plain,
    ! [X0,X1] :
      ( ~ ssItem(X0)
      | ~ ssItem(X1)
      | leq(X0,X1)
      | ~ lt(X0,X1) ),
    inference(cnf_transformation,[],[f216]) ).

fof(f412,plain,
    strictorderedP(sK49),
    inference(cnf_transformation,[],[f221]) ).

fof(f417,plain,
    ~ totalorderedP(sK47),
    inference(cnf_transformation,[],[f221]) ).

fof(f418,plain,
    sK47 = sK49,
    inference(cnf_transformation,[],[f221]) ).

fof(f421,plain,
    ssList(sK49),
    inference(cnf_transformation,[],[f221]) ).

fof(f426,plain,
    ~ totalorderedP(sK49),
    inference(definition_unfolding,[],[f417,f418]) ).

fof(f437,plain,
    ! [X2,X3,X1,X4,X5] :
      ( ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5)))
      | ~ ssItem(X1)
      | ~ ssItem(X2)
      | ~ ssList(X3)
      | ~ ssList(X4)
      | ~ ssList(X5)
      | lt(X1,X2)
      | ~ strictorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5))) ),
    inference(equality_resolution,[],[f279]) ).

fof(f472,plain,
    ! [X0] :
      ( leq(sK24(X0),sK25(X0))
      | ~ ssList(X0)
      | totalorderedP(X0) ),
    inference(consistent_polarity_flipping,[],[f274]) ).

fof(f475,plain,
    ! [X2,X3,X1,X4,X5] :
      ( ~ strictorderedP(app(app(X3,cons(X1,X4)),cons(X2,X5)))
      | ~ ssItem(X1)
      | ~ ssItem(X2)
      | ~ ssList(X3)
      | ~ ssList(X4)
      | ~ ssList(X5)
      | ~ lt(X1,X2)
      | ~ ssList(app(app(X3,cons(X1,X4)),cons(X2,X5))) ),
    inference(consistent_polarity_flipping,[],[f437]) ).

fof(f515,plain,
    ! [X0,X1] :
      ( lt(X0,X1)
      | ~ ssItem(X1)
      | ~ leq(X0,X1)
      | ~ ssItem(X0) ),
    inference(consistent_polarity_flipping,[],[f405]) ).

fof(f1972,plain,
    ( sK49 = app(app(sK26(sK49),cons(sK24(sK49),sK27(sK49))),cons(sK25(sK49),sK28(sK49)))
    | ~ ssList(sK49) ),
    inference(resolution,[],[f273,f426]) ).

fof(f1977,plain,
    sK49 = app(app(sK26(sK49),cons(sK24(sK49),sK27(sK49))),cons(sK25(sK49),sK28(sK49))),
    inference(forward_subsumption_resolution,[],[f1972,f421]) ).

fof(f4259,plain,
    ( ~ strictorderedP(sK49)
    | ~ ssItem(sK24(sK49))
    | ~ ssItem(sK25(sK49))
    | ~ ssList(sK26(sK49))
    | ~ ssList(sK27(sK49))
    | ~ ssList(sK28(sK49))
    | ~ lt(sK24(sK49),sK25(sK49))
    | ~ ssList(sK49) ),
    inference(superposition,[],[f475,f1977]) ).

fof(f4322,definition,
    ( spl53_324
  <=> ssList(sK28(sK49)) ),
    introduced(definition,[new_symbols(definition,[spl53_324])],[avatar_definition]) ).

fof(f4324,plain,
    ( ~ ssList(sK28(sK49))
    | spl53_324 ),
    inference(avatar_component_clause,[],[f4322]) ).

fof(f4326,definition,
    ( spl53_325
  <=> ssItem(sK25(sK49)) ),
    introduced(definition,[new_symbols(definition,[spl53_325])],[avatar_definition]) ).

fof(f4327,plain,
    ( ssItem(sK25(sK49))
    | ~ spl53_325 ),
    inference(avatar_component_clause,[],[f4326]) ).

fof(f4328,plain,
    ( ~ ssItem(sK25(sK49))
    | spl53_325 ),
    inference(avatar_component_clause,[],[f4326]) ).

fof(f4355,plain,
    ( ~ ssItem(sK24(sK49))
    | ~ ssItem(sK25(sK49))
    | ~ ssList(sK26(sK49))
    | ~ ssList(sK27(sK49))
    | ~ ssList(sK28(sK49))
    | ~ lt(sK24(sK49),sK25(sK49))
    | ~ ssList(sK49) ),
    inference(forward_subsumption_resolution,[],[f4259,f412]) ).

fof(f4369,definition,
    ( spl53_334
  <=> ssList(sK26(sK49)) ),
    introduced(definition,[new_symbols(definition,[spl53_334])],[avatar_definition]) ).

fof(f4371,plain,
    ( ~ ssList(sK26(sK49))
    | spl53_334 ),
    inference(avatar_component_clause,[],[f4369]) ).

fof(f4377,plain,
    ( ~ ssItem(sK24(sK49))
    | ~ ssItem(sK25(sK49))
    | ~ ssList(sK26(sK49))
    | ~ ssList(sK27(sK49))
    | ~ ssList(sK28(sK49))
    | ~ lt(sK24(sK49),sK25(sK49)) ),
    inference(forward_subsumption_resolution,[],[f4355,f421]) ).

fof(f4379,definition,
    ( spl53_336
  <=> leq(sK24(sK49),sK25(sK49)) ),
    introduced(definition,[new_symbols(definition,[spl53_336])],[avatar_definition]) ).

fof(f4380,plain,
    ( ~ leq(sK24(sK49),sK25(sK49))
    | spl53_336 ),
    inference(avatar_component_clause,[],[f4379]) ).

fof(f4387,definition,
    ( spl53_338
  <=> ssList(sK27(sK49)) ),
    introduced(definition,[new_symbols(definition,[spl53_338])],[avatar_definition]) ).

fof(f4389,plain,
    ( ~ ssList(sK27(sK49))
    | spl53_338 ),
    inference(avatar_component_clause,[],[f4387]) ).

fof(f4391,definition,
    ( spl53_339
  <=> ssItem(sK24(sK49)) ),
    introduced(definition,[new_symbols(definition,[spl53_339])],[avatar_definition]) ).

fof(f4392,plain,
    ( ssItem(sK24(sK49))
    | ~ spl53_339 ),
    inference(avatar_component_clause,[],[f4391]) ).

fof(f4393,plain,
    ( ~ ssItem(sK24(sK49))
    | spl53_339 ),
    inference(avatar_component_clause,[],[f4391]) ).

fof(f4409,definition,
    ( spl53_343
  <=> lt(sK24(sK49),sK25(sK49)) ),
    introduced(definition,[new_symbols(definition,[spl53_343])],[avatar_definition]) ).

fof(f4411,plain,
    ( ~ lt(sK24(sK49),sK25(sK49))
    | spl53_343 ),
    inference(avatar_component_clause,[],[f4409]) ).

fof(f4417,plain,
    ( ~ spl53_343
    | ~ spl53_324
    | ~ spl53_338
    | ~ spl53_334
    | ~ spl53_325
    | ~ spl53_339 ),
    inference(avatar_split_clause,[],[f4377,f4391,f4326,f4369,f4387,f4322,f4409]) ).

fof(f4568,plain,
    ( ~ ssList(sK49)
    | totalorderedP(sK49)
    | spl53_334 ),
    inference(resolution,[],[f4371,f276]) ).

fof(f4569,plain,
    ( totalorderedP(sK49)
    | spl53_334 ),
    inference(forward_subsumption_resolution,[],[f4568,f421]) ).

fof(f4570,plain,
    ( $false
    | spl53_334 ),
    inference(forward_subsumption_resolution,[],[f4569,f426]) ).

fof(f4571,plain,
    spl53_334,
    inference(avatar_contradiction_clause,[],[f4570]) ).

fof(f4683,plain,
    ( ~ ssList(sK49)
    | totalorderedP(sK49)
    | spl53_324 ),
    inference(resolution,[],[f4324,f272]) ).

fof(f4684,plain,
    ( totalorderedP(sK49)
    | spl53_324 ),
    inference(forward_subsumption_resolution,[],[f4683,f421]) ).

fof(f4685,plain,
    ( $false
    | spl53_324 ),
    inference(forward_subsumption_resolution,[],[f4684,f426]) ).

fof(f4686,plain,
    spl53_324,
    inference(avatar_contradiction_clause,[],[f4685]) ).

fof(f4834,plain,
    ( ~ ssList(sK49)
    | totalorderedP(sK49)
    | spl53_325 ),
    inference(resolution,[],[f4328,f277]) ).

fof(f4835,plain,
    ( totalorderedP(sK49)
    | spl53_325 ),
    inference(forward_subsumption_resolution,[],[f4834,f421]) ).

fof(f4836,plain,
    ( $false
    | spl53_325 ),
    inference(forward_subsumption_resolution,[],[f4835,f426]) ).

fof(f4837,plain,
    spl53_325,
    inference(avatar_contradiction_clause,[],[f4836]) ).

fof(f5237,plain,
    ( ~ ssList(sK49)
    | totalorderedP(sK49)
    | spl53_339 ),
    inference(resolution,[],[f4393,f278]) ).

fof(f5238,plain,
    ( totalorderedP(sK49)
    | spl53_339 ),
    inference(forward_subsumption_resolution,[],[f5237,f421]) ).

fof(f5239,plain,
    ( $false
    | spl53_339 ),
    inference(forward_subsumption_resolution,[],[f5238,f426]) ).

fof(f5240,plain,
    spl53_339,
    inference(avatar_contradiction_clause,[],[f5239]) ).

fof(f5241,plain,
    ( ~ ssList(sK49)
    | totalorderedP(sK49)
    | spl53_338 ),
    inference(resolution,[],[f4389,f275]) ).

fof(f5242,plain,
    ( totalorderedP(sK49)
    | spl53_338 ),
    inference(forward_subsumption_resolution,[],[f5241,f421]) ).

fof(f5243,plain,
    ( $false
    | spl53_338 ),
    inference(forward_subsumption_resolution,[],[f5242,f426]) ).

fof(f5244,plain,
    spl53_338,
    inference(avatar_contradiction_clause,[],[f5243]) ).

fof(f36316,plain,
    ( ~ ssItem(sK25(sK49))
    | ~ leq(sK24(sK49),sK25(sK49))
    | ~ ssItem(sK24(sK49))
    | spl53_343 ),
    inference(resolution,[],[f4411,f515]) ).

fof(f36317,plain,
    ( ~ leq(sK24(sK49),sK25(sK49))
    | ~ ssItem(sK24(sK49))
    | ~ spl53_325
    | spl53_343 ),
    inference(forward_subsumption_resolution,[],[f36316,f4327]) ).

fof(f36326,plain,
    ( ~ leq(sK24(sK49),sK25(sK49))
    | ~ spl53_325
    | ~ spl53_339
    | spl53_343 ),
    inference(forward_subsumption_resolution,[],[f36317,f4392]) ).

fof(f36327,plain,
    ( ~ spl53_336
    | ~ spl53_325
    | ~ spl53_339
    | spl53_343 ),
    inference(avatar_split_clause,[],[f36326,f4409,f4391,f4326,f4379]) ).

fof(f36328,plain,
    ( ~ ssList(sK49)
    | totalorderedP(sK49)
    | spl53_336 ),
    inference(resolution,[],[f4380,f472]) ).

fof(f36329,plain,
    ( totalorderedP(sK49)
    | spl53_336 ),
    inference(forward_subsumption_resolution,[],[f36328,f421]) ).

fof(f36330,plain,
    ( $false
    | spl53_336 ),
    inference(forward_subsumption_resolution,[],[f36329,f426]) ).

fof(f36331,plain,
    spl53_336,
    inference(avatar_contradiction_clause,[],[f36330]) ).

cnf(s423,plain,
    ( ~ spl53_324
    | ~ spl53_325
    | ~ spl53_334
    | ~ spl53_338
    | ~ spl53_339
    | ~ spl53_343 ),
    inference(sat_conversion,[],[f4417]) ).

cnf(s442,plain,
    spl53_334,
    inference(sat_conversion,[],[f4571]) ).

cnf(s452,plain,
    spl53_324,
    inference(sat_conversion,[],[f4686]) ).

cnf(s462,plain,
    spl53_325,
    inference(sat_conversion,[],[f4837]) ).

cnf(s485,plain,
    spl53_339,
    inference(sat_conversion,[],[f5240]) ).

cnf(s486,plain,
    spl53_338,
    inference(sat_conversion,[],[f5244]) ).

cnf(s4263,plain,
    ( ~ spl53_325
    | ~ spl53_336
    | ~ spl53_339
    | spl53_343 ),
    inference(sat_conversion,[],[f36327]) ).

cnf(s4264,plain,
    spl53_336,
    inference(sat_conversion,[],[f36331]) ).

cnf(s4265,plain,
    ( ~ spl53_325
    | ~ spl53_339
    | spl53_343 ),
    inference(rat,[],[s4263,s4264]) ).

cnf(s4291,plain,
    spl53_343,
    inference(rat,[],[s4265,s485,s462]) ).

cnf(s4292,plain,
    $false,
    inference(rat,[],[s423,s4291,s485,s486,s442,s462,s452]) ).

fof(f36332,plain,
    $false,
    inference(avatar_sat_refutation,[],[s4292]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC274+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20  % Computer : n017.cluster.edu
% 0.08/0.20  % Model    : x86_64 x86_64
% 0.08/0.20  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20  % Memory   : 8046.5625MB
% 0.08/0.20  % OS       : Linux 6.8.0-71-generic
% 0.08/0.20  % CPULimit : 300
% 0.08/0.20  % WCLimit  : 300
% 0.08/0.20  % DateTime : Mon Sep 28 08:44:21 UTC 2026
% 0.08/0.21  % CPUTime  : 
% 0.08/0.21  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.24  Running first-order model finding
% 0.08/0.24  Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.73/1.25  % (3404967)Will run a generic schedule for satisfiability detection.
% 6.73/1.25  % (3404976)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2458102967:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.73/1.25  % (3404973)% WARNING: option uhcvi not known.
% 6.73/1.25  % (3404972)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2320704922_2999 on theBenchmark for (2999ds/0Mi)
% 6.73/1.25  % (3404973)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2626470119:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.73/1.25  % (3404974)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1499708133:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.73/1.25  % (3404975)dis+10_1_sil=32000:sp=arity:random_seed=3929126598:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.73/1.25  % (3404977)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1399032722:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.73/1.25  % (3404978)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3416436418:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.73/1.25  % TRYING [1]
% 6.73/1.25  % TRYING [2]
% 6.73/1.25  % TRYING [3]
% 6.73/1.25  % (3404976)Instruction limit reached! 
% 6.73/1.25  % (3404976)------------------------------
% 6.73/1.25  % (3404976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3404976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3404976)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3404976)Termination reason: Instruction limit
% 6.73/1.25  % (3404976)Termination phase: Saturation
% 6.73/1.25  % (3404976)Time elapsed: 0.039 s
% 6.73/1.25  % (3404976)Peak memory usage: 13 MB
% 6.73/1.25  % (3404976)Instructions burned: 117 (million)
% 6.73/1.25  % TRYING [4]
% 6.73/1.25  % (3404986)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2840607832:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.73/1.25  % TRYING [1]
% 6.73/1.25  % TRYING [2]
% 6.73/1.25  % TRYING [3]
% 6.73/1.25  % (3404975)Instruction limit reached! 
% 6.73/1.25  % (3404975)------------------------------
% 6.73/1.25  % (3404975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3404975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3404975)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3404975)Termination reason: Instruction limit
% 6.73/1.25  % (3404975)Termination phase: Saturation
% 6.73/1.25  % (3404975)Time elapsed: 0.062 s
% 6.73/1.25  % (3404975)Peak memory usage: 13 MB
% 6.73/1.25  % (3404975)Instructions burned: 104 (million)
% 6.73/1.25  % TRYING [4]
% 6.73/1.25  % (3404977)Instruction limit reached! 
% 6.73/1.25  % (3404977)------------------------------
% 6.73/1.25  % (3404977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3404977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3404977)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3404977)Termination reason: Instruction limit
% 6.73/1.25  % (3404977)Termination phase: Saturation
% 6.73/1.25  % (3404977)Time elapsed: 0.075 s
% 6.73/1.25  % (3404977)Peak memory usage: 14 MB
% 6.73/1.25  % (3404977)Instructions burned: 131 (million)
% 6.73/1.25  % (3404988)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3312774907:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.73/1.25  % TRYING [5]
% 6.73/1.25  % TRYING [5]
% 6.73/1.25  % (3404989)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1189263706:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 6.73/1.25  % (3404978)Instruction limit reached! 
% 6.73/1.25  % (3404978)------------------------------
% 6.73/1.25  % (3404978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3404978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3404978)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3404978)Termination reason: Instruction limit
% 6.73/1.25  % (3404978)Termination phase: Saturation
% 6.73/1.25  % (3404978)Time elapsed: 0.103 s
% 6.73/1.25  % (3404978)Peak memory usage: 15 MB
% 6.73/1.25  % (3404978)Instructions burned: 159 (million)
% 6.73/1.25  % (3404992)ott-21_1_sil=16000:fs=off:random_seed=653247273:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.73/1.25  % (3404988)Instruction limit reached! 
% 6.73/1.25  % (3404988)------------------------------
% 6.73/1.25  % (3404988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3404988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3404988)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3404988)Termination reason: Instruction limit
% 6.73/1.25  % (3404988)Termination phase: Saturation
% 6.73/1.25  % (3404988)Time elapsed: 0.076 s
% 6.73/1.25  % (3404988)Peak memory usage: 13 MB
% 6.73/1.25  % (3404988)Instructions burned: 137 (million)
% 6.73/1.25  % (3404994)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2687322063:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 6.73/1.25  % TRYING [6]
% 6.73/1.25  % (3404986)Instruction limit reached! 
% 6.73/1.25  % (3404986)------------------------------
% 6.73/1.25  % (3404986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3404986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3404986)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3404986)Termination reason: Instruction limit
% 6.73/1.25  % (3404986)Termination phase: Finite model building constraint generation
% 6.73/1.25  % (3404986)Time elapsed: 0.162 s
% 6.73/1.25  % (3404986)Peak memory usage: 28 MB
% 6.73/1.25  % (3404986)Instructions burned: 717 (million)
% 6.73/1.25  % TRYING [6]
% 6.73/1.25  % (3404992)Instruction limit reached! 
% 6.73/1.25  % (3404992)------------------------------
% 6.73/1.25  % (3404992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3404992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3404992)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3404992)Termination reason: Instruction limit
% 6.73/1.25  % (3404992)Termination phase: Saturation
% 6.73/1.25  % (3404992)Time elapsed: 0.090 s
% 6.73/1.25  % (3404992)Peak memory usage: 13 MB
% 6.73/1.25  % (3404992)Instructions burned: 181 (million)
% 6.73/1.25  % (3404996)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4186155717:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 6.73/1.25  % TRYING [1]
% 6.73/1.25  % TRYING [2]
% 6.73/1.25  % TRYING [3]
% 6.73/1.25  % (3404997)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3868959091:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 6.73/1.25  % TRYING [4]
% 6.73/1.25  % TRYING [5]
% 6.73/1.25  % (3404996)Instruction limit reached! 
% 6.73/1.25  % (3404996)------------------------------
% 6.73/1.25  % (3404996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3404996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3404996)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3404996)Termination reason: Instruction limit
% 6.73/1.25  % (3404996)Termination phase: Finite model building SAT solving
% 6.73/1.25  % (3404996)Time elapsed: 0.185 s
% 6.73/1.25  % (3404996)Peak memory usage: 23 MB
% 6.73/1.25  % (3404996)Instructions burned: 869 (million)
% 6.73/1.25  % (3405000)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3981998223:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 6.73/1.25  % (3404989)Instruction limit reached! 
% 6.73/1.25  % (3404989)------------------------------
% 6.73/1.25  % (3404989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3404989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3404989)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3404989)Termination reason: Instruction limit
% 6.73/1.25  % (3404989)Termination phase: Saturation
% 6.73/1.25  % (3404989)Time elapsed: 0.362 s
% 6.73/1.25  % (3404989)Peak memory usage: 24 MB
% 6.73/1.25  % (3404989)Instructions burned: 686 (million)
% 6.73/1.25  % TRYING [14]
% 6.73/1.25  % (3405002)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1378945976:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2995 on theBenchmark for (2995ds/692Mi)
% 6.73/1.25  % TRYING [7]
% 6.73/1.25  % (3404994)Instruction limit reached! 
% 6.73/1.25  % (3404994)------------------------------
% 6.73/1.25  % (3404994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3404994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3404994)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3404994)Termination reason: Instruction limit
% 6.73/1.25  % (3404994)Termination phase: Saturation
% 6.73/1.25  % (3404994)Time elapsed: 0.328 s
% 6.73/1.25  % (3404994)Peak memory usage: 15 MB
% 6.73/1.25  % (3404994)Instructions burned: 478 (million)
% 6.73/1.25  % (3405004)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=920945011:i=879:kws=inv_precedence:fsr=off_2994 on theBenchmark for (2994ds/879Mi)
% 6.73/1.25  % (3405000)Instruction limit reached! 
% 6.73/1.25  % (3405000)------------------------------
% 6.73/1.25  % (3405000)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3405000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3405000)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3405000)Termination reason: Instruction limit
% 6.73/1.25  % (3405000)Termination phase: Finite model building constraint generation
% 6.73/1.25  % (3405000)Time elapsed: 0.178 s
% 6.73/1.25  % (3405000)Peak memory usage: 71 MB
% 6.73/1.25  % (3405000)Instructions burned: 894 (million)
% 6.73/1.25  % (3405006)fmb+10_1_sil=64000:random_seed=3049091558:i=22061:nm=2:gsp=on_2993 on theBenchmark for (2993ds/22061Mi)
% 6.73/1.25  % TRYING [1]
% 6.73/1.25  % TRYING [2]
% 6.73/1.25  % TRYING [3]
% 6.73/1.25  % TRYING [4]
% 6.73/1.25  % TRYING [5]
% 6.73/1.25  % (3405002)Instruction limit reached! 
% 6.73/1.25  % (3405002)------------------------------
% 6.73/1.25  % (3405002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3405002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3405002)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3405002)Termination reason: Instruction limit
% 6.73/1.25  % (3405002)Termination phase: Saturation
% 6.73/1.25  % (3405002)Time elapsed: 0.376 s
% 6.73/1.25  % (3405002)Peak memory usage: 24 MB
% 6.73/1.25  % (3405002)Instructions burned: 695 (million)
% 6.73/1.25  % (3405008)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=4111288869:i=9515:nm=5_2991 on theBenchmark for (2991ds/9515Mi)
% 6.73/1.25  % TRYING [6]
% 6.73/1.25  % (3404997)Instruction limit reached! 
% 6.73/1.25  % (3404997)------------------------------
% 6.73/1.25  % (3404997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3404997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3404997)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3404997)Termination reason: Instruction limit
% 6.73/1.25  % (3404997)Termination phase: Saturation
% 6.73/1.25  % (3404997)Time elapsed: 0.655 s
% 6.73/1.25  % (3404997)Peak memory usage: 27 MB
% 6.73/1.25  % (3404997)Instructions burned: 1179 (million)
% 6.73/1.25  % TRYING [20]
% 6.73/1.25  % (3405010)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3880649124:fmbsr=1.7:i=920_2990 on theBenchmark for (2990ds/920Mi)
% 6.73/1.25  % TRYING [8]
% 6.73/1.25  % (3404973) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3404967-3404973"...
% 6.73/1.25  % (3404973)...printing done.
% 6.73/1.25  % (3404973)Refutation found. Thanks to Tanya!
% 6.73/1.25  % SZS status Theorem for theBenchmark
% 6.73/1.25  % SZS output start Proof for theBenchmark
% See solution above
% 6.73/1.25  % (3404973)------------------------------
% 6.73/1.25  % (3404973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.73/1.25  % (3404973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.73/1.25  % (3404973)CaDiCaL version: 2.1.3
% 6.73/1.25  % (3404973)Termination reason: Refutation
% 6.73/1.25  % (3404973)Time elapsed: 0.952 s
% 6.73/1.25  % (3404973)Peak memory usage: 30 MB
% 6.73/1.25  % (3404973)Instructions burned: 1771 (million)
% 6.73/1.25  % (3404967)Success in time 1.002 s
% 6.73/1.25  % Vampire exiting
%------------------------------------------------------------------------------