TSTP Solution File: SEU188+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU188+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 18:27:14 EDT 2022

% Result   : Theorem 1.25s 0.52s
% Output   : Refutation 1.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   81 (  12 unt;   0 def)
%            Number of atoms       :  234 (  55 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  252 (  99   ~; 103   |;  27   &)
%                                         (   8 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   4 con; 0-2 aty)
%            Number of variables   :  100 (  78   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f244,plain,
    $false,
    inference(avatar_sat_refutation,[],[f154,f182,f188,f193,f243]) ).

fof(f243,plain,
    ~ spl16_4,
    inference(avatar_contradiction_clause,[],[f242]) ).

fof(f242,plain,
    ( $false
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f241,f202]) ).

fof(f202,plain,
    ( empty(sF14)
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f199,f163]) ).

fof(f163,plain,
    ( empty(sK4)
    | ~ spl16_4 ),
    inference(avatar_component_clause,[],[f162]) ).

fof(f162,plain,
    ( spl16_4
  <=> empty(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).

fof(f199,plain,
    ( empty(sF14)
    | ~ empty(sK4) ),
    inference(superposition,[],[f111,f143]) ).

fof(f143,plain,
    relation_rng(sK4) = sF14,
    introduced(function_definition,[]) ).

fof(f111,plain,
    ! [X0] :
      ( empty(relation_rng(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ~ empty(X0)
      | ( empty(relation_rng(X0))
        & relation(relation_rng(X0)) ) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0] :
      ( empty(X0)
     => ( empty(relation_rng(X0))
        & relation(relation_rng(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).

fof(f241,plain,
    ~ empty(sF14),
    inference(resolution,[],[f239,f103]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ empty(X1) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(rectify,[],[f48]) ).

fof(f48,plain,
    ! [X1,X0] :
      ( ~ empty(X0)
      | ~ in(X1,X0) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X1,X0] :
      ~ ( in(X1,X0)
        & empty(X0) ),
    inference(rectify,[],[f34]) ).

fof(f34,axiom,
    ! [X1,X0] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f239,plain,
    in(sK13(sK4),sF14),
    inference(subsumption_resolution,[],[f238,f107]) ).

fof(f107,plain,
    empty_set != sK4,
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ( empty_set != sK4
    & ( empty_set = relation_rng(sK4)
      | empty_set = relation_dom(sK4) )
    & relation(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f52,f70]) ).

fof(f70,plain,
    ( ? [X0] :
        ( empty_set != X0
        & ( relation_rng(X0) = empty_set
          | relation_dom(X0) = empty_set )
        & relation(X0) )
   => ( empty_set != sK4
      & ( empty_set = relation_rng(sK4)
        | empty_set = relation_dom(sK4) )
      & relation(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f52,plain,
    ? [X0] :
      ( empty_set != X0
      & ( relation_rng(X0) = empty_set
        | relation_dom(X0) = empty_set )
      & relation(X0) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ? [X0] :
      ( empty_set != X0
      & ( relation_rng(X0) = empty_set
        | relation_dom(X0) = empty_set )
      & relation(X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,negated_conjecture,
    ~ ! [X0] :
        ( relation(X0)
       => ( ( relation_rng(X0) = empty_set
            | relation_dom(X0) = empty_set )
         => empty_set = X0 ) ),
    inference(negated_conjecture,[],[f31]) ).

fof(f31,conjecture,
    ! [X0] :
      ( relation(X0)
     => ( ( relation_rng(X0) = empty_set
          | relation_dom(X0) = empty_set )
       => empty_set = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).

fof(f238,plain,
    ( empty_set = sK4
    | in(sK13(sK4),sF14) ),
    inference(subsumption_resolution,[],[f237,f105]) ).

fof(f105,plain,
    relation(sK4),
    inference(cnf_transformation,[],[f71]) ).

fof(f237,plain,
    ( in(sK13(sK4),sF14)
    | ~ relation(sK4)
    | empty_set = sK4 ),
    inference(superposition,[],[f233,f143]) ).

fof(f233,plain,
    ! [X1] :
      ( in(sK13(X1),relation_rng(X1))
      | empty_set = X1
      | ~ relation(X1) ),
    inference(duplicate_literal_removal,[],[f228]) ).

fof(f228,plain,
    ! [X1] :
      ( ~ relation(X1)
      | in(sK13(X1),relation_rng(X1))
      | empty_set = X1
      | ~ relation(X1) ),
    inference(resolution,[],[f138,f139]) ).

fof(f139,plain,
    ! [X2,X3,X0] :
      ( ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
      | in(X2,relation_rng(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f130]) ).

fof(f130,plain,
    ! [X2,X3,X0,X1] :
      ( in(X2,X1)
      | ~ in(unordered_pair(unordered_pair(X3,X2),singleton(X3)),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f115,f126]) ).

fof(f126,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).

fof(f115,plain,
    ! [X2,X3,X0,X1] :
      ( in(X2,X1)
      | ~ in(ordered_pair(X3,X2),X0)
      | relation_rng(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( in(ordered_pair(sK6(X0,X2),X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 )
          & ( relation_rng(X0) = X1
            | ( ( ! [X6] : ~ in(ordered_pair(X6,sK7(X0,X1)),X0)
                | ~ in(sK7(X0,X1),X1) )
              & ( in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0)
                | in(sK7(X0,X1),X1) ) ) ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f75,f78,f77,f76]) ).

fof(f76,plain,
    ! [X0,X2] :
      ( ? [X4] : in(ordered_pair(X4,X2),X0)
     => in(ordered_pair(sK6(X0,X2),X2),X0) ),
    introduced(choice_axiom,[]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
            | ~ in(X5,X1) )
          & ( ? [X7] : in(ordered_pair(X7,X5),X0)
            | in(X5,X1) ) )
     => ( ( ! [X6] : ~ in(ordered_pair(X6,sK7(X0,X1)),X0)
          | ~ in(sK7(X0,X1),X1) )
        & ( ? [X7] : in(ordered_pair(X7,sK7(X0,X1)),X0)
          | in(sK7(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ? [X7] : in(ordered_pair(X7,sK7(X0,X1)),X0)
     => in(ordered_pair(sK8(X0,X1),sK7(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( ? [X4] : in(ordered_pair(X4,X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 )
          & ( relation_rng(X0) = X1
            | ? [X5] :
                ( ( ! [X6] : ~ in(ordered_pair(X6,X5),X0)
                  | ~ in(X5,X1) )
                & ( ? [X7] : in(ordered_pair(X7,X5),X0)
                  | in(X5,X1) ) ) ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) ) )
            | relation_rng(X0) != X1 )
          & ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X3,X2),X0)
                  | in(X2,X1) ) ) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) )
        <=> relation_rng(X0) = X1 )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X3,X2),X0) )
        <=> relation_rng(X0) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).

fof(f138,plain,
    ! [X0] :
      ( in(unordered_pair(unordered_pair(sK12(X0),sK13(X0)),singleton(sK12(X0))),X0)
      | empty_set = X0
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f121,f126]) ).

fof(f121,plain,
    ! [X0] :
      ( ~ relation(X0)
      | empty_set = X0
      | in(ordered_pair(sK12(X0),sK13(X0)),X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ~ relation(X0)
      | empty_set = X0
      | in(ordered_pair(sK12(X0),sK13(X0)),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f41,f87]) ).

fof(f87,plain,
    ! [X0] :
      ( ? [X1,X2] : in(ordered_pair(X1,X2),X0)
     => in(ordered_pair(sK12(X0),sK13(X0)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ! [X0] :
      ( ~ relation(X0)
      | empty_set = X0
      | ? [X1,X2] : in(ordered_pair(X1,X2),X0) ),
    inference(flattening,[],[f40]) ).

fof(f40,plain,
    ! [X0] :
      ( empty_set = X0
      | ? [X1,X2] : in(ordered_pair(X1,X2),X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0] :
      ( relation(X0)
     => ( ! [X2,X1] : ~ in(ordered_pair(X1,X2),X0)
       => empty_set = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_relat_1) ).

fof(f193,plain,
    ( ~ spl16_1
    | spl16_5 ),
    inference(avatar_contradiction_clause,[],[f192]) ).

fof(f192,plain,
    ( $false
    | ~ spl16_1
    | spl16_5 ),
    inference(subsumption_resolution,[],[f191,f125]) ).

fof(f125,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f191,plain,
    ( ~ empty(empty_set)
    | ~ spl16_1
    | spl16_5 ),
    inference(forward_demodulation,[],[f185,f149]) ).

fof(f149,plain,
    ( empty_set = sF15
    | ~ spl16_1 ),
    inference(avatar_component_clause,[],[f147]) ).

fof(f147,plain,
    ( spl16_1
  <=> empty_set = sF15 ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).

fof(f185,plain,
    ( ~ empty(sF15)
    | spl16_5 ),
    inference(avatar_component_clause,[],[f184]) ).

fof(f184,plain,
    ( spl16_5
  <=> empty(sF15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).

fof(f188,plain,
    ( ~ spl16_5
    | spl16_4 ),
    inference(avatar_split_clause,[],[f174,f162,f184]) ).

fof(f174,plain,
    ( empty(sK4)
    | ~ empty(sF15) ),
    inference(subsumption_resolution,[],[f173,f105]) ).

fof(f173,plain,
    ( ~ empty(sF15)
    | ~ relation(sK4)
    | empty(sK4) ),
    inference(superposition,[],[f89,f144]) ).

fof(f144,plain,
    sF15 = relation_dom(sK4),
    introduced(function_definition,[]) ).

fof(f89,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0] :
      ( ~ relation(X0)
      | empty(X0)
      | ~ empty(relation_dom(X0)) ),
    inference(flattening,[],[f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | empty(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( ( ~ empty(X0)
        & relation(X0) )
     => ~ empty(relation_dom(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).

fof(f182,plain,
    ( spl16_4
    | ~ spl16_2 ),
    inference(avatar_split_clause,[],[f179,f151,f162]) ).

fof(f151,plain,
    ( spl16_2
  <=> empty_set = sF14 ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).

fof(f179,plain,
    ( empty(sK4)
    | ~ spl16_2 ),
    inference(subsumption_resolution,[],[f178,f105]) ).

fof(f178,plain,
    ( ~ relation(sK4)
    | empty(sK4)
    | ~ spl16_2 ),
    inference(subsumption_resolution,[],[f177,f125]) ).

fof(f177,plain,
    ( ~ empty(empty_set)
    | ~ relation(sK4)
    | empty(sK4)
    | ~ spl16_2 ),
    inference(superposition,[],[f104,f155]) ).

fof(f155,plain,
    ( empty_set = relation_rng(sK4)
    | ~ spl16_2 ),
    inference(forward_demodulation,[],[f143,f153]) ).

fof(f153,plain,
    ( empty_set = sF14
    | ~ spl16_2 ),
    inference(avatar_component_clause,[],[f151]) ).

fof(f104,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | empty(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( empty(X0)
      | ~ relation(X0)
      | ~ empty(relation_rng(X0)) ),
    inference(flattening,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] :
      ( ( relation(X0)
        & ~ empty(X0) )
     => ~ empty(relation_rng(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).

fof(f154,plain,
    ( spl16_1
    | spl16_2 ),
    inference(avatar_split_clause,[],[f145,f151,f147]) ).

fof(f145,plain,
    ( empty_set = sF14
    | empty_set = sF15 ),
    inference(definition_folding,[],[f106,f144,f143]) ).

fof(f106,plain,
    ( empty_set = relation_rng(sK4)
    | empty_set = relation_dom(sK4) ),
    inference(cnf_transformation,[],[f71]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU188+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n019.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 14:51:05 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.19/0.50  % (24816)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (24827)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.50  % (24800)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.50  % (24800)First to succeed.
% 0.19/0.51  % (24808)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.51  % (24806)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.25/0.52  % (24801)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 1.25/0.52  % (24816)Instruction limit reached!
% 1.25/0.52  % (24816)------------------------------
% 1.25/0.52  % (24816)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.52  % (24816)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.52  % (24816)Termination reason: Unknown
% 1.25/0.52  % (24816)Termination phase: Saturation
% 1.25/0.52  
% 1.25/0.52  % (24816)Memory used [KB]: 5884
% 1.25/0.52  % (24816)Time elapsed: 0.004 s
% 1.25/0.52  % (24816)Instructions burned: 3 (million)
% 1.25/0.52  % (24816)------------------------------
% 1.25/0.52  % (24816)------------------------------
% 1.25/0.52  % (24800)Refutation found. Thanks to Tanya!
% 1.25/0.52  % SZS status Theorem for theBenchmark
% 1.25/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 1.25/0.52  % (24800)------------------------------
% 1.25/0.52  % (24800)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.52  % (24800)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.52  % (24800)Termination reason: Refutation
% 1.25/0.52  
% 1.25/0.52  % (24800)Memory used [KB]: 6012
% 1.25/0.52  % (24800)Time elapsed: 0.097 s
% 1.25/0.52  % (24800)Instructions burned: 5 (million)
% 1.25/0.52  % (24800)------------------------------
% 1.25/0.52  % (24800)------------------------------
% 1.25/0.52  % (24796)Success in time 0.163 s
%------------------------------------------------------------------------------