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

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SWC108+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT

% Computer : n010.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 01:04:42 PM UTC 2026

% Result   : Theorem 1.23s 0.66s
% Output   : Refutation 1.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  119 (  15 unt;   8 def)
%            Number of atoms       :  372 (  55 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  435 ( 182   ~; 193   |;  30   &)
%                                         (  12 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   9 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   63 (   0 sgn  53   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ( rearsegP(X0,X1)
          <=> ? [X2] :
                ( ssList(X2)
                & app(X2,X1) = X0 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax6) ).

fof(f17,axiom,
    ssList(nil),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).

fof(f52,axiom,
    ! [X0] :
      ( ssList(X0)
     => ( rearsegP(nil,X0)
      <=> nil = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax52) ).

fof(f55,axiom,
    ! [X0] :
      ( ssList(X0)
     => segmentP(X0,X0) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).

fof(f56,axiom,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( segmentP(X0,X1)
                   => segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).

fof(f84,axiom,
    ! [X0] :
      ( ssList(X0)
     => app(X0,nil) = X0 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( X1 != X3
                    | X0 != X2
                    | ( ( nil != X1
                        | nil = X0 )
                      & ( ~ neq(X1,nil)
                        | ( neq(X0,nil)
                          & segmentP(X1,X0) ) ) )
                    | ( ( nil != X3
                        | nil != X2 )
                      & ( ~ neq(X2,nil)
                        | ~ rearsegP(X3,X2) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( X1 != X3
                      | X0 != X2
                      | ( ( nil != X1
                          | nil = X0 )
                        & ( ~ neq(X1,nil)
                          | ( neq(X0,nil)
                            & segmentP(X1,X0) ) ) )
                      | ( ( nil != X3
                          | nil != X2 )
                        & ( ~ neq(X2,nil)
                          | ~ rearsegP(X3,X2) ) ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f96]) ).

fof(f102,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( rearsegP(X0,X1)
          <=> ? [X2] :
                ( ssList(X2)
                & app(X2,X1) = X0 ) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f167,plain,
    ! [X0] :
      ( ( rearsegP(nil,X0)
      <=> nil = X0 )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f172,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f173,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( segmentP(app(app(X2,X0),X3),X1)
                  | ~ segmentP(X0,X1)
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f174,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( segmentP(app(app(X2,X0),X3),X1)
                  | ~ segmentP(X0,X1)
                  | ~ ssList(X3) )
              | ~ ssList(X2) )
          | ~ ssList(X1) )
      | ~ ssList(X0) ),
    inference(flattening,[],[f173]) ).

fof(f201,plain,
    ! [X0] :
      ( app(X0,nil) = X0
      | ~ ssList(X0) ),
    inference(ennf_transformation,[],[f84]) ).

fof(f221,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & X0 = X2
                  & ( ( nil = X1
                      & nil != X0 )
                    | ( neq(X1,nil)
                      & ( ~ neq(X0,nil)
                        | ~ segmentP(X1,X0) ) ) )
                  & ( ( nil = X3
                      & nil = X2 )
                    | ( neq(X2,nil)
                      & rearsegP(X3,X2) ) )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f97]) ).

fof(f222,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( X1 = X3
                  & X0 = X2
                  & ( ( nil = X1
                      & nil != X0 )
                    | ( neq(X1,nil)
                      & ( ~ neq(X0,nil)
                        | ~ segmentP(X1,X0) ) ) )
                  & ( ( nil = X3
                      & nil = X2 )
                    | ( neq(X2,nil)
                      & rearsegP(X3,X2) ) )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f221]) ).

fof(f238,plain,
    ! [X0,X1] :
      ( ~ rearsegP(X0,X1)
      | ~ ssList(X1)
      | app(sK6(X0,X1),X1) = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f239,plain,
    ! [X0,X1] :
      ( ssList(sK6(X0,X1))
      | ~ ssList(X1)
      | ~ ssList(X0)
      | ~ rearsegP(X0,X1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f306,plain,
    ssList(nil),
    inference(cnf_transformation,[],[f17]) ).

fof(f354,plain,
    ! [X0] :
      ( ~ rearsegP(nil,X0)
      | nil = X0
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f167]) ).

fof(f357,plain,
    ! [X0] :
      ( segmentP(X0,X0)
      | ~ ssList(X0) ),
    inference(cnf_transformation,[],[f172]) ).

fof(f358,plain,
    ! [X2,X3,X0,X1] :
      ( ~ segmentP(X0,X1)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | ~ ssList(X3)
      | ~ ssList(X0)
      | segmentP(app(app(X2,X0),X3),X1) ),
    inference(cnf_transformation,[],[f174]) ).

fof(f397,plain,
    ! [X0] :
      ( ~ ssList(X0)
      | app(X0,nil) = X0 ),
    inference(cnf_transformation,[],[f201]) ).

fof(f411,plain,
    ( ~ segmentP(sK48,sK47)
    | ~ neq(sK47,nil)
    | nil = sK48 ),
    inference(cnf_transformation,[],[f222]) ).

fof(f412,plain,
    ( ~ segmentP(sK48,sK47)
    | ~ neq(sK47,nil)
    | nil != sK47 ),
    inference(cnf_transformation,[],[f222]) ).

fof(f413,plain,
    ( neq(sK48,nil)
    | nil != sK47 ),
    inference(cnf_transformation,[],[f222]) ).

fof(f415,plain,
    ( neq(sK49,nil)
    | nil = sK49 ),
    inference(cnf_transformation,[],[f222]) ).

fof(f416,plain,
    ( neq(sK49,nil)
    | nil = sK50 ),
    inference(cnf_transformation,[],[f222]) ).

fof(f417,plain,
    ( rearsegP(sK50,sK49)
    | nil = sK49 ),
    inference(cnf_transformation,[],[f222]) ).

fof(f418,plain,
    ( rearsegP(sK50,sK49)
    | nil = sK50 ),
    inference(cnf_transformation,[],[f222]) ).

fof(f419,plain,
    ssList(sK50),
    inference(cnf_transformation,[],[f222]) ).

fof(f420,plain,
    sK47 = sK49,
    inference(cnf_transformation,[],[f222]) ).

fof(f421,plain,
    sK48 = sK50,
    inference(cnf_transformation,[],[f222]) ).

fof(f422,plain,
    ssList(sK49),
    inference(cnf_transformation,[],[f222]) ).

fof(f428,plain,
    ( neq(sK50,nil)
    | nil != sK49 ),
    inference(definition_unfolding,[],[f413,f421,f420]) ).

fof(f429,plain,
    ( ~ segmentP(sK50,sK49)
    | ~ neq(sK49,nil)
    | nil != sK49 ),
    inference(definition_unfolding,[],[f412,f421,f420,f420,f420]) ).

fof(f430,plain,
    ( ~ segmentP(sK50,sK49)
    | ~ neq(sK49,nil)
    | nil = sK50 ),
    inference(definition_unfolding,[],[f411,f421,f420,f420,f421]) ).

fof(f464,definition,
    ( spl51_1
  <=> nil = sK50 ),
    introduced(definition,[new_symbols(definition,[spl51_1])],[avatar_definition]) ).

fof(f466,plain,
    ( nil = sK50
    | ~ spl51_1 ),
    inference(avatar_component_clause,[],[f464]) ).

fof(f468,definition,
    ( spl51_2
  <=> neq(sK49,nil) ),
    introduced(definition,[new_symbols(definition,[spl51_2])],[avatar_definition]) ).

fof(f470,plain,
    ( ~ neq(sK49,nil)
    | spl51_2 ),
    inference(avatar_component_clause,[],[f468]) ).

fof(f472,definition,
    ( spl51_3
  <=> segmentP(sK50,sK49) ),
    introduced(definition,[new_symbols(definition,[spl51_3])],[avatar_definition]) ).

fof(f474,plain,
    ( ~ segmentP(sK50,sK49)
    | spl51_3 ),
    inference(avatar_component_clause,[],[f472]) ).

fof(f475,plain,
    ( spl51_1
    | ~ spl51_2
    | ~ spl51_3 ),
    inference(avatar_split_clause,[],[f430,f472,f468,f464]) ).

fof(f477,definition,
    ( spl51_4
  <=> nil = sK49 ),
    introduced(definition,[new_symbols(definition,[spl51_4])],[avatar_definition]) ).

fof(f478,plain,
    ( nil = sK49
    | ~ spl51_4 ),
    inference(avatar_component_clause,[],[f477]) ).

fof(f479,plain,
    ( nil != sK49
    | spl51_4 ),
    inference(avatar_component_clause,[],[f477]) ).

fof(f480,plain,
    ( ~ spl51_4
    | ~ spl51_2
    | ~ spl51_3 ),
    inference(avatar_split_clause,[],[f429,f472,f468,f477]) ).

fof(f482,definition,
    ( spl51_5
  <=> neq(sK50,nil) ),
    introduced(definition,[new_symbols(definition,[spl51_5])],[avatar_definition]) ).

fof(f484,plain,
    ( neq(sK50,nil)
    | ~ spl51_5 ),
    inference(avatar_component_clause,[],[f482]) ).

fof(f485,plain,
    ( ~ spl51_4
    | spl51_5 ),
    inference(avatar_split_clause,[],[f428,f482,f477]) ).

fof(f487,plain,
    ( spl51_4
    | spl51_2 ),
    inference(avatar_split_clause,[],[f415,f468,f477]) ).

fof(f488,plain,
    ( spl51_1
    | spl51_2 ),
    inference(avatar_split_clause,[],[f416,f468,f464]) ).

fof(f490,definition,
    ( spl51_6
  <=> rearsegP(sK50,sK49) ),
    introduced(definition,[new_symbols(definition,[spl51_6])],[avatar_definition]) ).

fof(f492,plain,
    ( rearsegP(sK50,sK49)
    | ~ spl51_6 ),
    inference(avatar_component_clause,[],[f490]) ).

fof(f493,plain,
    ( spl51_4
    | spl51_6 ),
    inference(avatar_split_clause,[],[f417,f490,f477]) ).

fof(f494,plain,
    ( spl51_1
    | spl51_6 ),
    inference(avatar_split_clause,[],[f418,f490,f464]) ).

fof(f500,definition,
    ( spl51_8
  <=> ssList(nil) ),
    introduced(definition,[new_symbols(definition,[spl51_8])],[avatar_definition]) ).

fof(f501,plain,
    ( ssList(nil)
    | ~ spl51_8 ),
    inference(avatar_component_clause,[],[f500]) ).

fof(f502,plain,
    ( ~ ssList(nil)
    | spl51_8 ),
    inference(avatar_component_clause,[],[f500]) ).

fof(f528,plain,
    ( rearsegP(nil,sK49)
    | ~ spl51_1
    | ~ spl51_6 ),
    inference(forward_demodulation,[],[f492,f466]) ).

fof(f529,plain,
    ( nil = sK49
    | ~ ssList(sK49)
    | ~ spl51_1
    | ~ spl51_6 ),
    inference(resolution,[],[f354,f528]) ).

fof(f535,plain,
    ( ~ ssList(sK49)
    | ~ spl51_1
    | spl51_4
    | ~ spl51_6 ),
    inference(forward_subsumption_resolution,[],[f529,f479]) ).

fof(f536,plain,
    ( $false
    | ~ spl51_1
    | spl51_4
    | ~ spl51_6 ),
    inference(forward_subsumption_resolution,[],[f535,f422]) ).

fof(f537,plain,
    ( ~ spl51_1
    | spl51_4
    | ~ spl51_6 ),
    inference(avatar_contradiction_clause,[],[f536]) ).

fof(f538,plain,
    ( $false
    | spl51_8 ),
    inference(forward_subsumption_resolution,[],[f306,f502]) ).

fof(f539,plain,
    spl51_8,
    inference(avatar_contradiction_clause,[],[f538]) ).

fof(f584,plain,
    ( ~ ssList(sK49)
    | sK50 = app(sK6(sK50,sK49),sK49)
    | ~ ssList(sK50)
    | ~ spl51_6 ),
    inference(resolution,[],[f238,f492]) ).

fof(f589,plain,
    ( sK50 = app(sK6(sK50,sK49),sK49)
    | ~ ssList(sK50)
    | ~ spl51_6 ),
    inference(forward_subsumption_resolution,[],[f584,f422]) ).

fof(f592,plain,
    ( sK50 = app(sK6(sK50,sK49),sK49)
    | ~ spl51_6 ),
    inference(forward_subsumption_resolution,[],[f589,f419]) ).

fof(f644,definition,
    ( spl51_20
  <=> ssList(sK6(sK50,sK49)) ),
    introduced(definition,[new_symbols(definition,[spl51_20])],[avatar_definition]) ).

fof(f645,plain,
    ( ssList(sK6(sK50,sK49))
    | ~ spl51_20 ),
    inference(avatar_component_clause,[],[f644]) ).

fof(f646,plain,
    ( ~ ssList(sK6(sK50,sK49))
    | spl51_20 ),
    inference(avatar_component_clause,[],[f644]) ).

fof(f651,plain,
    ( ~ ssList(sK49)
    | ~ ssList(sK50)
    | ~ rearsegP(sK50,sK49)
    | spl51_20 ),
    inference(resolution,[],[f646,f239]) ).

fof(f652,plain,
    ( ~ ssList(sK50)
    | ~ rearsegP(sK50,sK49)
    | spl51_20 ),
    inference(forward_subsumption_resolution,[],[f651,f422]) ).

fof(f653,plain,
    ( ~ rearsegP(sK50,sK49)
    | spl51_20 ),
    inference(forward_subsumption_resolution,[],[f652,f419]) ).

fof(f654,plain,
    ( $false
    | ~ spl51_6
    | spl51_20 ),
    inference(forward_subsumption_resolution,[],[f653,f492]) ).

fof(f655,plain,
    ( ~ spl51_6
    | spl51_20 ),
    inference(avatar_contradiction_clause,[],[f654]) ).

fof(f1167,plain,
    sK50 = app(sK50,nil),
    inference(resolution,[],[f397,f419]) ).

fof(f1391,plain,
    ! [X2,X0,X1] :
      ( ~ ssList(X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | ~ ssList(X0)
      | segmentP(app(app(X1,X0),X2),X0)
      | ~ ssList(X0) ),
    inference(resolution,[],[f358,f357]) ).

fof(f1396,plain,
    ! [X2,X0,X1] :
      ( segmentP(app(app(X1,X0),X2),X0)
      | ~ ssList(X1)
      | ~ ssList(X2)
      | ~ ssList(X0) ),
    inference(duplicate_literal_removal,[],[f1391]) ).

fof(f2848,plain,
    ( ! [X0] :
        ( segmentP(app(sK50,X0),sK49)
        | ~ ssList(sK6(sK50,sK49))
        | ~ ssList(X0)
        | ~ ssList(sK49) )
    | ~ spl51_6 ),
    inference(superposition,[],[f1396,f592]) ).

fof(f2855,plain,
    ! [X0] :
      ( segmentP(app(sK50,X0),nil)
      | ~ ssList(sK50)
      | ~ ssList(X0)
      | ~ ssList(nil) ),
    inference(superposition,[],[f1396,f1167]) ).

fof(f2863,plain,
    ! [X0] :
      ( segmentP(app(sK50,X0),nil)
      | ~ ssList(X0)
      | ~ ssList(nil) ),
    inference(forward_subsumption_resolution,[],[f2855,f419]) ).

fof(f2870,plain,
    ( ! [X0] :
        ( segmentP(app(sK50,X0),sK49)
        | ~ ssList(X0)
        | ~ ssList(sK49) )
    | ~ spl51_6
    | ~ spl51_20 ),
    inference(forward_subsumption_resolution,[],[f2848,f645]) ).

fof(f2894,plain,
    ( ! [X0] :
        ( segmentP(app(sK50,X0),nil)
        | ~ ssList(X0) )
    | ~ spl51_8 ),
    inference(forward_subsumption_resolution,[],[f2863,f501]) ).

fof(f2901,plain,
    ( ! [X0] :
        ( segmentP(app(sK50,X0),sK49)
        | ~ ssList(X0) )
    | ~ spl51_6
    | ~ spl51_20 ),
    inference(forward_subsumption_resolution,[],[f2870,f422]) ).

fof(f3375,plain,
    ( segmentP(sK50,nil)
    | ~ ssList(nil)
    | ~ spl51_8 ),
    inference(superposition,[],[f2894,f1167]) ).

fof(f3376,plain,
    ( segmentP(sK50,nil)
    | ~ spl51_8 ),
    inference(forward_subsumption_resolution,[],[f3375,f501]) ).

fof(f4226,plain,
    ( segmentP(sK50,sK49)
    | ~ ssList(nil)
    | ~ spl51_6
    | ~ spl51_20 ),
    inference(superposition,[],[f2901,f1167]) ).

fof(f4227,plain,
    ( ~ ssList(nil)
    | spl51_3
    | ~ spl51_6
    | ~ spl51_20 ),
    inference(forward_subsumption_resolution,[],[f4226,f474]) ).

fof(f4232,plain,
    ( $false
    | spl51_3
    | ~ spl51_6
    | ~ spl51_8
    | ~ spl51_20 ),
    inference(forward_subsumption_resolution,[],[f4227,f501]) ).

fof(f4233,plain,
    ( spl51_3
    | ~ spl51_6
    | ~ spl51_8
    | ~ spl51_20 ),
    inference(avatar_contradiction_clause,[],[f4232]) ).

fof(f4362,plain,
    ( neq(nil,nil)
    | ~ spl51_1
    | ~ spl51_5 ),
    inference(superposition,[],[f484,f466]) ).

fof(f4425,plain,
    ( ~ segmentP(sK50,nil)
    | spl51_3
    | ~ spl51_4 ),
    inference(superposition,[],[f474,f478]) ).

fof(f4471,plain,
    ( $false
    | spl51_3
    | ~ spl51_4
    | ~ spl51_8 ),
    inference(forward_subsumption_resolution,[],[f4425,f3376]) ).

fof(f4472,plain,
    ( spl51_3
    | ~ spl51_4
    | ~ spl51_8 ),
    inference(avatar_contradiction_clause,[],[f4471]) ).

fof(f4475,plain,
    ( ~ neq(nil,nil)
    | spl51_2
    | ~ spl51_4 ),
    inference(forward_demodulation,[],[f470,f478]) ).

fof(f4655,plain,
    ( $false
    | ~ spl51_1
    | spl51_2
    | ~ spl51_4
    | ~ spl51_5 ),
    inference(forward_subsumption_resolution,[],[f4362,f4475]) ).

fof(f4656,plain,
    ( ~ spl51_1
    | spl51_2
    | ~ spl51_4
    | ~ spl51_5 ),
    inference(avatar_contradiction_clause,[],[f4655]) ).

cnf(s1,plain,
    ( spl51_1
    | ~ spl51_2
    | ~ spl51_3 ),
    inference(sat_conversion,[],[f475]) ).

cnf(s2,plain,
    ( ~ spl51_2
    | ~ spl51_3
    | ~ spl51_4 ),
    inference(sat_conversion,[],[f480]) ).

cnf(s3,plain,
    ( ~ spl51_4
    | spl51_5 ),
    inference(sat_conversion,[],[f485]) ).

cnf(s5,plain,
    ( spl51_2
    | spl51_4 ),
    inference(sat_conversion,[],[f487]) ).

cnf(s6,plain,
    ( spl51_1
    | spl51_2 ),
    inference(sat_conversion,[],[f488]) ).

cnf(s7,plain,
    ( spl51_4
    | spl51_6 ),
    inference(sat_conversion,[],[f493]) ).

cnf(s8,plain,
    ( spl51_1
    | spl51_6 ),
    inference(sat_conversion,[],[f494]) ).

cnf(s15,plain,
    ( ~ spl51_1
    | spl51_4
    | ~ spl51_6 ),
    inference(sat_conversion,[],[f537]) ).

cnf(s16,plain,
    spl51_8,
    inference(sat_conversion,[],[f539]) ).

cnf(s21,plain,
    ( ~ spl51_6
    | spl51_20 ),
    inference(sat_conversion,[],[f655]) ).

cnf(s187,plain,
    ( spl51_3
    | ~ spl51_6
    | ~ spl51_8
    | ~ spl51_20 ),
    inference(sat_conversion,[],[f4233]) ).

cnf(s227,plain,
    ( spl51_3
    | ~ spl51_4
    | ~ spl51_8 ),
    inference(sat_conversion,[],[f4472]) ).

cnf(s229,plain,
    ( ~ spl51_1
    | spl51_2
    | ~ spl51_4
    | ~ spl51_5 ),
    inference(sat_conversion,[],[f4656]) ).

cnf(s255,plain,
    spl51_1,
    inference(rat,[],[s187,s21,s1,s6,s8,s16]) ).

cnf(s257,plain,
    spl51_2,
    inference(rat,[],[s229,s3,s5,s255]) ).

cnf(s258,plain,
    spl51_4,
    inference(rat,[],[s7,s15,s255]) ).

cnf(s259,plain,
    spl51_3,
    inference(rat,[],[s227,s16,s258]) ).

cnf(s261,plain,
    $false,
    inference(rat,[],[s2,s257,s258,s259]) ).

fof(f4657,plain,
    $false,
    inference(avatar_sat_refutation,[],[s261]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWC108+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39  % Computer : n010.cluster.edu
% 0.12/0.39  % Model    : x86_64 x86_64
% 0.12/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39  % Memory   : 8046.5625MB
% 0.12/0.39  % OS       : Linux 6.8.0-71-generic
% 0.12/0.39  % CPULimit : 300
% 0.12/0.39  % WCLimit  : 300
% 0.12/0.39  % DateTime : Mon Sep 28 07:54:48 UTC 2026
% 0.12/0.40  % CPUTime  : 
% 0.12/0.40  Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43  Running first-order model finding
% 0.12/0.43  Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.23/0.66  % (1753718)Will run a generic schedule for satisfiability detection.
% 1.23/0.66  % (1753728)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3694971409:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.23/0.66  % (1753724)% WARNING: option uhcvi not known.
% 1.23/0.66  % (1753723)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2842836426_2999 on theBenchmark for (2999ds/0Mi)
% 1.23/0.66  % (1753724)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3676317906:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.23/0.66  % (1753727)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3174226533:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.23/0.66  % (1753725)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=989508917:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.23/0.66  % (1753726)dis+10_1_sil=32000:sp=arity:random_seed=954923025:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.23/0.66  % (1753729)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3353252884:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.23/0.66  % TRYING [1]
% 1.23/0.66  % TRYING [2]
% 1.23/0.66  % TRYING [3]
% 1.23/0.66  % (1753728)Instruction limit reached! 
% 1.23/0.66  % (1753728)------------------------------
% 1.23/0.66  % (1753728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.66  % (1753728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.66  % (1753728)CaDiCaL version: 2.1.3
% 1.23/0.66  % (1753728)Termination reason: Instruction limit
% 1.23/0.66  % (1753728)Termination phase: Saturation
% 1.23/0.66  % (1753728)Time elapsed: 0.042 s
% 1.23/0.66  % (1753728)Peak memory usage: 14 MB
% 1.23/0.66  % (1753728)Instructions burned: 134 (million)
% 1.23/0.66  % TRYING [4]
% 1.23/0.66  % (1753737)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3185576360:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.23/0.66  % TRYING [1]
% 1.23/0.66  % TRYING [2]
% 1.23/0.66  % TRYING [3]
% 1.23/0.66  % (1753726)Instruction limit reached! 
% 1.23/0.66  % (1753726)------------------------------
% 1.23/0.66  % (1753726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.66  % (1753726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.66  % (1753726)CaDiCaL version: 2.1.3
% 1.23/0.66  % (1753726)Termination reason: Instruction limit
% 1.23/0.66  % (1753726)Termination phase: Saturation
% 1.23/0.66  % (1753726)Time elapsed: 0.060 s
% 1.23/0.66  % (1753726)Peak memory usage: 13 MB
% 1.23/0.66  % (1753726)Instructions burned: 103 (million)
% 1.23/0.66  % TRYING [4]
% 1.23/0.66  % (1753727)Instruction limit reached! 
% 1.23/0.66  % (1753727)------------------------------
% 1.23/0.66  % (1753727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.66  % (1753727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.66  % (1753727)CaDiCaL version: 2.1.3
% 1.23/0.66  % (1753727)Termination reason: Instruction limit
% 1.23/0.66  % (1753727)Termination phase: Saturation
% 1.23/0.66  % (1753727)Time elapsed: 0.071 s
% 1.23/0.66  % (1753727)Peak memory usage: 13 MB
% 1.23/0.66  % (1753727)Instructions burned: 117 (million)
% 1.23/0.66  % (1753739)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1310539910:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.23/0.66  % (1753740)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=1803190824:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.23/0.66  % TRYING [5]
% 1.23/0.66  % TRYING [5]
% 1.23/0.66  % (1753729)Instruction limit reached! 
% 1.23/0.66  % (1753729)------------------------------
% 1.23/0.66  % (1753729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.66  % (1753729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.66  % (1753729)CaDiCaL version: 2.1.3
% 1.23/0.66  % (1753729)Termination reason: Instruction limit
% 1.23/0.66  % (1753729)Termination phase: Saturation
% 1.23/0.66  % (1753729)Time elapsed: 0.094 s
% 1.23/0.66  % (1753729)Peak memory usage: 15 MB
% 1.23/0.66  % (1753729)Instructions burned: 160 (million)
% 1.23/0.66  % (1753743)ott-21_1_sil=16000:fs=off:random_seed=1265859363:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.23/0.66  % (1753739)Instruction limit reached! 
% 1.23/0.66  % (1753739)------------------------------
% 1.23/0.66  % (1753739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.66  % (1753739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.66  % (1753739)CaDiCaL version: 2.1.3
% 1.23/0.66  % (1753739)Termination reason: Instruction limit
% 1.23/0.66  % (1753739)Termination phase: Saturation
% 1.23/0.66  % (1753739)Time elapsed: 0.070 s
% 1.23/0.66  % (1753739)Peak memory usage: 13 MB
% 1.23/0.66  % (1753739)Instructions burned: 131 (million)
% 1.23/0.66  % (1753745)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1930502444:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.23/0.66  % (1753740) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1753718-1753740"...
% 1.23/0.66  % (1753740)...printing done.
% 1.23/0.66  % (1753740)Refutation found. Thanks to Tanya!
% 1.23/0.66  % SZS status Theorem for theBenchmark
% 1.23/0.66  % SZS output start Proof for theBenchmark
% See solution above
% 1.23/0.66  % (1753740)------------------------------
% 1.23/0.66  % (1753740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.23/0.66  % (1753740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.23/0.66  % (1753740)CaDiCaL version: 2.1.3
% 1.23/0.66  % (1753740)Termination reason: Refutation
% 1.23/0.66  % (1753740)Time elapsed: 0.090 s
% 1.23/0.66  % (1753740)Peak memory usage: 15 MB
% 1.23/0.66  % (1753740)Instructions burned: 141 (million)
% 1.23/0.66  % (1753718)Success in time 0.224 s
% 1.23/0.66  % Vampire exiting
%------------------------------------------------------------------------------