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

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SET595+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n019.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 12:44:03 PM UTC 2026

% Result   : Theorem 4.29s 1.07s
% Output   : Refutation 4.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   16
% Syntax   : Number of formulae    :  122 (  13 unt;   9 def)
%            Number of atoms       :  306 (   4 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  309 ( 125   ~; 139   |;  27   &)
%                                         (  14 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   8 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :  128 (   0 sgn 121   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( equal_set(X0,X1)
    <=> ( subset(X0,X1)
        & subset(X1,X0) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( member(X0,power_set(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
    <=> ( member(X0,X1)
        | member(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',union) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( member(X0,difference(X2,X1))
    <=> ( member(X0,X2)
        & ~ member(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( member(X0,sum(X1))
    <=> ? [X2] :
          ( member(X2,X1)
          & member(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',sum) ).

fof(f12,conjecture,
    ! [X0,X1] :
      ( subset(X0,X1)
     => equal_set(union(difference(X1,X0),X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI27) ).

fof(f13,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(X0,X1)
       => equal_set(union(difference(X1,X0),X0),X1) ),
    inference(negated_conjecture,[status(cth)],[f12]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(flattening,[],[f16]) ).

fof(f19,plain,
    ? [X0,X1] :
      ( ~ equal_set(union(difference(X1,X0),X0),X1)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f20]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( member(X0,power_set(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ member(X0,power_set(X1)) ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X1)
          & ~ member(X0,X2) ) )
      & ( member(X0,X1)
        | member(X0,X2)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,union(X1,X2))
        | ( ~ member(X0,X1)
          & ~ member(X0,X2) ) )
      & ( member(X0,X1)
        | member(X0,X2)
        | ~ member(X0,union(X1,X2)) ) ),
    inference(flattening,[],[f26]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | ~ member(X0,X2)
        | member(X0,X1) )
      & ( ( member(X0,X2)
          & ~ member(X0,X1) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | ~ member(X0,X2)
        | member(X0,X1) )
      & ( ( member(X0,X2)
          & ~ member(X0,X1) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(flattening,[],[f28]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X0,X2) ) )
      & ( ? [X2] :
            ( member(X2,X1)
            & member(X0,X2) )
        | ~ member(X0,sum(X1)) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X0,X2) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & member(X0,X3) )
        | ~ member(X0,sum(X1)) ) ),
    inference(rectify,[],[f33]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( member(X0,sum(X1))
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X0,X2) ) )
      & ( ( member(sK1(X0,X1),X1)
          & member(X0,sK1(X0,X1)) )
        | ~ member(X0,sum(X1)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f34]) ).

fof(f39,plain,
    ( ~ equal_set(union(difference(sK4,sK3),sK3),sK4)
    & subset(sK3,sK4) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f19]) ).

fof(f40,plain,
    ! [X3,X0,X1] :
      ( ~ member(X3,X0)
      | member(X3,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ~ member(sK0(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ member(X0,power_set(X1))
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | member(X0,power_set(X1)) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,union(X1,X2))
      | member(X0,X2)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(X2,X1))
      | member(X0,X2) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f55,plain,
    ! [X2,X0,X1] :
      ( member(X0,difference(X2,X1))
      | ~ member(X0,X2)
      | member(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( member(X0,sK1(X0,X1))
      | ~ member(X0,sum(X1)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X1)
      | ~ member(X0,sum(X1)) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f63,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | member(X0,sum(X1))
      | ~ member(X0,X2) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f67,plain,
    subset(sK3,sK4),
    inference(cnf_transformation,[],[f39]) ).

fof(f68,plain,
    ~ equal_set(union(difference(sK4,sK3),sK3),sK4),
    inference(cnf_transformation,[],[f39]) ).

fof(f72,definition,
    sF5 = difference(sK4,sK3),
    introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).

fof(f73,plain,
    difference(sK4,sK3) = sF5,
    inference(reorient_equations,[],[f72]) ).

fof(f74,definition,
    sF6 = union(sF5,sK3),
    introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).

fof(f75,plain,
    union(sF5,sK3) = sF6,
    inference(reorient_equations,[],[f74]) ).

fof(f76,plain,
    ~ equal_set(sF6,sK4),
    inference(definition_folding,[],[f68,f75,f73]) ).

fof(f77,plain,
    member(sK3,power_set(sK4)),
    inference(resolution,[],[f45,f67]) ).

fof(f81,plain,
    ! [X2,X0,X1] :
      ( ~ member(sK0(X0,union(X1,X2)),X2)
      | subset(X0,union(X1,X2)) ),
    inference(resolution,[],[f50,f42]) ).

fof(f83,plain,
    ! [X2,X0,X1] :
      ( ~ member(sK0(X0,union(X1,X2)),X1)
      | subset(X0,union(X1,X2)) ),
    inference(resolution,[],[f51,f42]) ).

fof(f86,plain,
    ! [X0] :
      ( ~ member(X0,sF5)
      | member(X0,sK4) ),
    inference(superposition,[],[f54,f73]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | equal_set(X0,X1)
      | member(sK0(X1,X0),X1) ),
    inference(resolution,[],[f43,f41]) ).

fof(f106,plain,
    ! [X2,X0,X1] :
      ( ~ subset(sK1(X0,X1),X2)
      | member(X0,X2)
      | ~ member(X0,sum(X1)) ),
    inference(resolution,[],[f61,f40]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( subset(sK1(X0,power_set(X1)),X1)
      | ~ member(X0,sum(power_set(X1))) ),
    inference(resolution,[],[f62,f44]) ).

fof(f146,plain,
    ! [X0] :
      ( member(X0,sum(power_set(sK4)))
      | ~ member(X0,sK3) ),
    inference(resolution,[],[f63,f77]) ).

fof(f190,plain,
    ! [X0] :
      ( ~ member(X0,sF6)
      | member(X0,sK3)
      | member(X0,sF5) ),
    inference(superposition,[],[f49,f75]) ).

fof(f198,plain,
    ! [X0] :
      ( ~ member(X0,sK4)
      | member(X0,sF5)
      | member(X0,sK3) ),
    inference(superposition,[],[f55,f73]) ).

fof(f327,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | member(sK0(X1,X0),X1)
      | member(sK0(X0,X1),X0) ),
    inference(resolution,[],[f95,f41]) ).

fof(f369,plain,
    ! [X0] :
      ( ~ member(sK0(X0,sF6),sK3)
      | subset(X0,sF6) ),
    inference(superposition,[],[f81,f75]) ).

fof(f393,plain,
    ! [X0] :
      ( ~ member(sK0(X0,sF6),sF5)
      | subset(X0,sF6) ),
    inference(superposition,[],[f83,f75]) ).

fof(f402,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ member(X0,sum(power_set(X1)))
      | ~ member(X0,sum(power_set(X1))) ),
    inference(resolution,[],[f106,f109]) ).

fof(f404,plain,
    ! [X0,X1] :
      ( ~ member(X0,sum(power_set(X1)))
      | member(X0,X1) ),
    inference(duplicate_literal_removal,[],[f402]) ).

fof(f2096,plain,
    ! [X0] :
      ( ~ member(X0,sK3)
      | member(X0,sK4) ),
    inference(resolution,[],[f404,f146]) ).

fof(f3941,plain,
    ( member(sK0(sK4,sF6),sK4)
    | member(sK0(sF6,sK4),sF6) ),
    inference(resolution,[],[f327,f76]) ).

fof(f3943,definition,
    ( spl7_31
  <=> member(sK0(sF6,sK4),sF6) ),
    introduced(definition,[new_symbols(definition,[spl7_31])],[avatar_definition]) ).

fof(f3944,plain,
    ( ~ member(sK0(sF6,sK4),sF6)
    | spl7_31 ),
    inference(avatar_component_clause,[],[f3943]) ).

fof(f3945,plain,
    ( member(sK0(sF6,sK4),sF6)
    | ~ spl7_31 ),
    inference(avatar_component_clause,[],[f3943]) ).

fof(f3947,definition,
    ( spl7_32
  <=> member(sK0(sK4,sF6),sK4) ),
    introduced(definition,[new_symbols(definition,[spl7_32])],[avatar_definition]) ).

fof(f3948,plain,
    ( ~ member(sK0(sK4,sF6),sK4)
    | spl7_32 ),
    inference(avatar_component_clause,[],[f3947]) ).

fof(f3949,plain,
    ( member(sK0(sK4,sF6),sK4)
    | ~ spl7_32 ),
    inference(avatar_component_clause,[],[f3947]) ).

fof(f3950,plain,
    ( spl7_31
    | spl7_32 ),
    inference(avatar_split_clause,[],[f3941,f3947,f3943]) ).

fof(f3951,plain,
    ( member(sK0(sF6,sK4),sK3)
    | member(sK0(sF6,sK4),sF5)
    | ~ spl7_31 ),
    inference(resolution,[],[f3945,f190]) ).

fof(f3967,definition,
    ( spl7_33
  <=> member(sK0(sF6,sK4),sF5) ),
    introduced(definition,[new_symbols(definition,[spl7_33])],[avatar_definition]) ).

fof(f3969,plain,
    ( member(sK0(sF6,sK4),sF5)
    | ~ spl7_33 ),
    inference(avatar_component_clause,[],[f3967]) ).

fof(f3971,definition,
    ( spl7_34
  <=> member(sK0(sF6,sK4),sK3) ),
    introduced(definition,[new_symbols(definition,[spl7_34])],[avatar_definition]) ).

fof(f3973,plain,
    ( member(sK0(sF6,sK4),sK3)
    | ~ spl7_34 ),
    inference(avatar_component_clause,[],[f3971]) ).

fof(f3974,plain,
    ( spl7_33
    | spl7_34
    | ~ spl7_31 ),
    inference(avatar_split_clause,[],[f3951,f3943,f3971,f3967]) ).

fof(f4045,definition,
    ( spl7_36
  <=> subset(sK4,sF6) ),
    introduced(definition,[new_symbols(definition,[spl7_36])],[avatar_definition]) ).

fof(f4046,plain,
    ( subset(sK4,sF6)
    | ~ spl7_36 ),
    inference(avatar_component_clause,[],[f4045]) ).

fof(f4047,plain,
    ( ~ subset(sK4,sF6)
    | spl7_36 ),
    inference(avatar_component_clause,[],[f4045]) ).

fof(f4065,plain,
    ( member(sK0(sK4,sF6),sK4)
    | spl7_36 ),
    inference(resolution,[],[f4047,f41]) ).

fof(f4069,plain,
    ( member(sK0(sK4,sF6),sF5)
    | member(sK0(sK4,sF6),sK3)
    | ~ spl7_32 ),
    inference(resolution,[],[f3949,f198]) ).

fof(f4085,definition,
    ( spl7_37
  <=> member(sK0(sK4,sF6),sK3) ),
    introduced(definition,[new_symbols(definition,[spl7_37])],[avatar_definition]) ).

fof(f4087,plain,
    ( member(sK0(sK4,sF6),sK3)
    | ~ spl7_37 ),
    inference(avatar_component_clause,[],[f4085]) ).

fof(f4089,definition,
    ( spl7_38
  <=> member(sK0(sK4,sF6),sF5) ),
    introduced(definition,[new_symbols(definition,[spl7_38])],[avatar_definition]) ).

fof(f4091,plain,
    ( member(sK0(sK4,sF6),sF5)
    | ~ spl7_38 ),
    inference(avatar_component_clause,[],[f4089]) ).

fof(f4092,plain,
    ( spl7_37
    | spl7_38
    | ~ spl7_32 ),
    inference(avatar_split_clause,[],[f4069,f3947,f4089,f4085]) ).

fof(f4097,plain,
    ( $false
    | spl7_32
    | spl7_36 ),
    inference(forward_subsumption_resolution,[],[f4065,f3948]) ).

fof(f4098,plain,
    ( spl7_32
    | spl7_36 ),
    inference(avatar_contradiction_clause,[],[f4097]) ).

fof(f4122,plain,
    ( ~ subset(sF6,sK4)
    | equal_set(sF6,sK4)
    | ~ spl7_36 ),
    inference(resolution,[],[f4046,f43]) ).

fof(f4124,plain,
    ( ~ subset(sF6,sK4)
    | ~ spl7_36 ),
    inference(forward_subsumption_resolution,[],[f4122,f76]) ).

fof(f4140,plain,
    ( member(sK0(sF6,sK4),sF6)
    | ~ spl7_36 ),
    inference(resolution,[],[f4124,f41]) ).

fof(f4223,plain,
    ( member(sK0(sF6,sK4),sK4)
    | ~ spl7_33 ),
    inference(resolution,[],[f3969,f86]) ).

fof(f4259,plain,
    ( subset(sF6,sK4)
    | ~ spl7_33 ),
    inference(resolution,[],[f4223,f42]) ).

fof(f4276,plain,
    ( $false
    | ~ spl7_33
    | ~ spl7_36 ),
    inference(forward_subsumption_resolution,[],[f4259,f4124]) ).

fof(f4277,plain,
    ( ~ spl7_33
    | ~ spl7_36 ),
    inference(avatar_contradiction_clause,[],[f4276]) ).

fof(f4311,plain,
    ( member(sK0(sF6,sK4),sK4)
    | ~ spl7_34 ),
    inference(resolution,[],[f3973,f2096]) ).

fof(f4345,plain,
    ( subset(sF6,sK4)
    | ~ spl7_34 ),
    inference(resolution,[],[f4311,f42]) ).

fof(f4362,plain,
    ( $false
    | ~ spl7_34
    | ~ spl7_36 ),
    inference(forward_subsumption_resolution,[],[f4345,f4124]) ).

fof(f4363,plain,
    ( ~ spl7_34
    | ~ spl7_36 ),
    inference(avatar_contradiction_clause,[],[f4362]) ).

fof(f4366,plain,
    ( $false
    | spl7_31
    | ~ spl7_36 ),
    inference(forward_subsumption_resolution,[],[f4140,f3944]) ).

fof(f4367,plain,
    ( spl7_31
    | ~ spl7_36 ),
    inference(avatar_contradiction_clause,[],[f4366]) ).

fof(f4549,plain,
    ( subset(sK4,sF6)
    | ~ spl7_37 ),
    inference(resolution,[],[f4087,f369]) ).

fof(f4567,plain,
    ( $false
    | spl7_36
    | ~ spl7_37 ),
    inference(forward_subsumption_resolution,[],[f4549,f4047]) ).

fof(f4568,plain,
    ( spl7_36
    | ~ spl7_37 ),
    inference(avatar_contradiction_clause,[],[f4567]) ).

fof(f4807,plain,
    ( subset(sK4,sF6)
    | ~ spl7_38 ),
    inference(resolution,[],[f4091,f393]) ).

fof(f4827,plain,
    ( $false
    | spl7_36
    | ~ spl7_38 ),
    inference(forward_subsumption_resolution,[],[f4807,f4047]) ).

fof(f4828,plain,
    ( spl7_36
    | ~ spl7_38 ),
    inference(avatar_contradiction_clause,[],[f4827]) ).

cnf(s22,plain,
    ( spl7_31
    | spl7_32 ),
    inference(sat_conversion,[],[f3950]) ).

cnf(s23,plain,
    ( ~ spl7_31
    | spl7_33
    | spl7_34 ),
    inference(sat_conversion,[],[f3974]) ).

cnf(s25,plain,
    ( ~ spl7_32
    | spl7_37
    | spl7_38 ),
    inference(sat_conversion,[],[f4092]) ).

cnf(s27,plain,
    ( spl7_32
    | spl7_36 ),
    inference(sat_conversion,[],[f4098]) ).

cnf(s29,plain,
    ( ~ spl7_33
    | ~ spl7_36 ),
    inference(sat_conversion,[],[f4277]) ).

cnf(s30,plain,
    ( ~ spl7_34
    | ~ spl7_36 ),
    inference(sat_conversion,[],[f4363]) ).

cnf(s32,plain,
    ( spl7_31
    | ~ spl7_36 ),
    inference(sat_conversion,[],[f4367]) ).

cnf(s34,plain,
    ( spl7_36
    | ~ spl7_37 ),
    inference(sat_conversion,[],[f4568]) ).

cnf(s35,plain,
    ( spl7_36
    | ~ spl7_38 ),
    inference(sat_conversion,[],[f4828]) ).

cnf(s36,plain,
    spl7_31,
    inference(rat,[],[s25,s34,s35,s22,s32]) ).

cnf(s37,plain,
    ( spl7_36
    | ~ spl7_32 ),
    inference(rat,[],[s25,s34,s35]) ).

cnf(s38,plain,
    ~ spl7_36,
    inference(rat,[],[s23,s29,s30,s36]) ).

cnf(s41,plain,
    spl7_32,
    inference(rat,[],[s27,s38]) ).

cnf(s42,plain,
    $false,
    inference(rat,[],[s37,s41,s38]) ).

fof(f4829,plain,
    $false,
    inference(avatar_sat_refutation,[],[s42]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SET595+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.37  % Computer : n019.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8046.5625MB
% 0.14/0.37  % OS       : Linux 6.8.0-71-generic
% 0.14/0.38  % CPULimit : 300
% 0.14/0.38  % WCLimit  : 300
% 0.14/0.38  % DateTime : Mon Sep 28 02:17:04 UTC 2026
% 0.14/0.38  % CPUTime  : 
% 0.14/0.38  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.41  Running first-order model finding
% 0.14/0.41  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
% 4.29/1.07  % (3596004)Will run a generic schedule for satisfiability detection.
% 4.29/1.07  % (3596011)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=731815724:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.29/1.07  % (3596010)% WARNING: option uhcvi not known.
% 4.29/1.07  % (3596009)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1483640897_2999 on theBenchmark for (2999ds/0Mi)
% 4.29/1.07  % (3596010)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4095632394:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.29/1.07  % (3596012)dis+10_1_sil=32000:sp=arity:random_seed=4239493230:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.29/1.07  % (3596013)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2113175603:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.29/1.07  % (3596014)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4124210887:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.29/1.07  % (3596015)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1540916824:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.29/1.07  % TRYING [1]
% 4.29/1.07  % TRYING [2]
% 4.29/1.07  % TRYING [3]
% 4.29/1.07  % TRYING [4]
% 4.29/1.07  % TRYING [5]
% 4.29/1.07  % TRYING [6]
% 4.29/1.07  % TRYING [7]
% 4.29/1.07  % (3596012)Instruction limit reached! 
% 4.29/1.07  % (3596012)------------------------------
% 4.29/1.07  % (3596012)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.07  % (3596012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.07  % (3596012)CaDiCaL version: 2.1.3
% 4.29/1.07  % (3596012)Termination reason: Instruction limit
% 4.29/1.07  % (3596012)Termination phase: Saturation
% 4.29/1.07  % (3596012)Time elapsed: 0.063 s
% 4.29/1.07  % (3596012)Peak memory usage: 12 MB
% 4.29/1.07  % (3596012)Instructions burned: 104 (million)
% 4.29/1.07  % (3596013)Instruction limit reached! 
% 4.29/1.07  % (3596013)------------------------------
% 4.29/1.07  % (3596013)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.07  % (3596013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.07  % (3596013)CaDiCaL version: 2.1.3
% 4.29/1.07  % (3596013)Termination reason: Instruction limit
% 4.29/1.07  % (3596013)Termination phase: Saturation
% 4.29/1.07  % (3596013)Time elapsed: 0.067 s
% 4.29/1.07  % (3596013)Peak memory usage: 12 MB
% 4.29/1.07  % (3596013)Instructions burned: 116 (million)
% 4.29/1.07  % (3596023)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3710991505:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 4.29/1.07  % (3596014)Instruction limit reached! 
% 4.29/1.07  % (3596014)------------------------------
% 4.29/1.07  % (3596014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.07  % (3596014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.07  % (3596014)CaDiCaL version: 2.1.3
% 4.29/1.07  % (3596014)Termination reason: Instruction limit
% 4.29/1.07  % (3596014)Termination phase: Saturation
% 4.29/1.07  % (3596014)Time elapsed: 0.083 s
% 4.29/1.07  % (3596014)Peak memory usage: 14 MB
% 4.29/1.07  % (3596014)Instructions burned: 132 (million)
% 4.29/1.07  % TRYING [1]
% 4.29/1.07  % TRYING [2]
% 4.29/1.07  % TRYING [3]
% 4.29/1.07  % (3596024)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1778190724:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 4.29/1.07  % TRYING [4]
% 4.29/1.07  % TRYING [5]
% 4.29/1.07  % (3596015)Instruction limit reached! 
% 4.29/1.07  % (3596015)------------------------------
% 4.29/1.07  % (3596015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.07  % (3596015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.07  % (3596015)CaDiCaL version: 2.1.3
% 4.29/1.07  % (3596015)Termination reason: Instruction limit
% 4.29/1.07  % (3596015)Termination phase: Saturation
% 4.29/1.07  % (3596015)Time elapsed: 0.096 s
% 4.29/1.07  % (3596015)Peak memory usage: 14 MB
% 4.29/1.07  % (3596015)Instructions burned: 160 (million)
% 4.29/1.07  % (3596026)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=2492980520:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 4.29/1.07  % TRYING [6]
% 4.29/1.07  % (3596028)ott-21_1_sil=16000:fs=off:random_seed=786920894:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 4.29/1.07  % TRYING [8]
% 4.29/1.07  % TRYING [7]
% 4.29/1.07  % (3596024)Instruction limit reached! 
% 4.29/1.07  % (3596024)------------------------------
% 4.29/1.07  % (3596024)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.07  % (3596024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.07  % (3596024)CaDiCaL version: 2.1.3
% 4.29/1.07  % (3596024)Termination reason: Instruction limit
% 4.29/1.07  % (3596024)Termination phase: Saturation
% 4.29/1.07  % (3596024)Time elapsed: 0.085 s
% 4.29/1.07  % (3596024)Peak memory usage: 14 MB
% 4.29/1.07  % (3596024)Instructions burned: 131 (million)
% 4.29/1.07  % (3596031)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=322684981:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 4.29/1.07  % (3596028)Instruction limit reached! 
% 4.29/1.07  % (3596028)------------------------------
% 4.29/1.07  % (3596028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.07  % (3596028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.07  % (3596028)CaDiCaL version: 2.1.3
% 4.29/1.07  % (3596028)Termination reason: Instruction limit
% 4.29/1.07  % (3596028)Termination phase: Saturation
% 4.29/1.07  % (3596028)Time elapsed: 0.096 s
% 4.29/1.07  % (3596028)Peak memory usage: 13 MB
% 4.29/1.07  % (3596028)Instructions burned: 180 (million)
% 4.29/1.07  % (3596033)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1749408757:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 4.29/1.07  % TRYING [1]
% 4.29/1.07  % TRYING [2]
% 4.29/1.07  % TRYING [3]
% 4.29/1.07  % TRYING [4]
% 4.29/1.07  % TRYING [5]
% 4.29/1.07  % TRYING [6]
% 4.29/1.07  % TRYING [7]
% 4.29/1.07  % TRYING [8]
% 4.29/1.07  % TRYING [9]
% 4.29/1.07  % TRYING [8]
% 4.29/1.07  % (3596023)Instruction limit reached! 
% 4.29/1.07  % (3596023)------------------------------
% 4.29/1.07  % (3596023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.07  % (3596023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.07  % (3596023)CaDiCaL version: 2.1.3
% 4.29/1.07  % (3596023)Termination reason: Instruction limit
% 4.29/1.07  % (3596023)Termination phase: Finite model building SAT solving
% 4.29/1.07  % (3596023)Time elapsed: 0.346 s
% 4.29/1.07  % (3596023)Peak memory usage: 20 MB
% 4.29/1.07  % (3596023)Instructions burned: 715 (million)
% 4.29/1.07  % (3596035)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3572575311:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 4.29/1.07  % (3596026)Instruction limit reached! 
% 4.29/1.07  % (3596026)------------------------------
% 4.29/1.07  % (3596026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.07  % (3596026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.07  % (3596026)CaDiCaL version: 2.1.3
% 4.29/1.07  % (3596026)Termination reason: Instruction limit
% 4.29/1.07  % (3596026)Termination phase: Saturation
% 4.29/1.07  % (3596026)Time elapsed: 0.376 s
% 4.29/1.07  % (3596026)Peak memory usage: 18 MB
% 4.29/1.07  % (3596026)Instructions burned: 686 (million)
% 4.29/1.07  % (3596031)Instruction limit reached! 
% 4.29/1.07  % (3596031)------------------------------
% 4.29/1.07  % (3596031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.07  % (3596031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.07  % (3596031)CaDiCaL version: 2.1.3
% 4.29/1.07  % (3596031)Termination reason: Instruction limit
% 4.29/1.07  % (3596031)Termination phase: Saturation
% 4.29/1.07  % (3596031)Time elapsed: 0.299 s
% 4.29/1.07  % (3596031)Peak memory usage: 14 MB
% 4.29/1.07  % (3596031)Instructions burned: 479 (million)
% 4.29/1.07  % (3596037)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=352233137:i=889:ins=1_2994 on theBenchmark for (2994ds/889Mi)
% 4.29/1.07  % (3596038)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=2788160921:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 4.29/1.07  % TRYING [14]
% 4.29/1.07  % (3596033)Instruction limit reached! 
% 4.29/1.07  % (3596033)------------------------------
% 4.29/1.07  % (3596033)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.07  % (3596033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.07  % (3596033)CaDiCaL version: 2.1.3
% 4.29/1.07  % (3596033)Termination reason: Instruction limit
% 4.29/1.07  % (3596033)Termination phase: Finite model building SAT solving
% 4.29/1.07  % (3596033)Time elapsed: 0.338 s
% 4.29/1.07  % (3596033)Peak memory usage: 17 MB
% 4.29/1.07  % (3596033)Instructions burned: 865 (million)
% 4.29/1.07  % (3596041)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3131603495:i=879:kws=inv_precedence:fsr=off_2993 on theBenchmark for (2993ds/879Mi)
% 4.29/1.07  % (3596035) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3596004-3596035"...
% 4.29/1.07  % (3596035)...printing done.
% 4.29/1.07  % (3596035)Refutation found. Thanks to Tanya!
% 4.29/1.07  % SZS status Theorem for theBenchmark
% 4.29/1.07  % SZS output start Proof for theBenchmark
% See solution above
% 4.29/1.08  % (3596035)------------------------------
% 4.29/1.08  % (3596035)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.29/1.08  % (3596035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.29/1.08  % (3596035)CaDiCaL version: 2.1.3
% 4.29/1.08  % (3596035)Termination reason: Refutation
% 4.29/1.08  % (3596035)Time elapsed: 0.159 s
% 4.29/1.08  % (3596035)Peak memory usage: 15 MB
% 4.29/1.08  % (3596035)Instructions burned: 257 (million)
% 4.29/1.08  % (3596004)Success in time 0.656 s
% 4.29/1.08  % Vampire exiting
%------------------------------------------------------------------------------