TSTP Solution File: SEU123+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU123+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n028.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 : Tue Apr 30 15:22:16 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   90 (  26 unt;   0 def)
%            Number of atoms       :  220 (  41 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  239 ( 109   ~;  95   |;  11   &)
%                                         (  18 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   21 (  19 usr;  18 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   53 (  47   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f144,plain,
    $false,
    inference(avatar_sat_refutation,[],[f46,f51,f56,f61,f66,f70,f74,f78,f84,f90,f106,f111,f119,f125,f132,f138,f142,f143]) ).

fof(f143,plain,
    ( ~ spl3_11
    | spl3_2
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f114,f108,f48,f99]) ).

fof(f99,plain,
    ( spl3_11
  <=> sK0 = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

fof(f48,plain,
    ( spl3_2
  <=> empty_set = sK0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

fof(f108,plain,
    ( spl3_13
  <=> empty_set = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_13])]) ).

fof(f114,plain,
    ( sK0 != sK2
    | spl3_2
    | ~ spl3_13 ),
    inference(superposition,[],[f50,f110]) ).

fof(f110,plain,
    ( empty_set = sK2
    | ~ spl3_13 ),
    inference(avatar_component_clause,[],[f108]) ).

fof(f50,plain,
    ( empty_set != sK0
    | spl3_2 ),
    inference(avatar_component_clause,[],[f48]) ).

fof(f142,plain,
    ( spl3_12
    | ~ spl3_17 ),
    inference(avatar_contradiction_clause,[],[f139]) ).

fof(f139,plain,
    ( $false
    | spl3_12
    | ~ spl3_17 ),
    inference(resolution,[],[f137,f105]) ).

fof(f105,plain,
    ( ~ subset(sK2,sK0)
    | spl3_12 ),
    inference(avatar_component_clause,[],[f103]) ).

fof(f103,plain,
    ( spl3_12
  <=> subset(sK2,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

fof(f137,plain,
    ( ! [X0] : subset(sK2,X0)
    | ~ spl3_17 ),
    inference(avatar_component_clause,[],[f136]) ).

fof(f136,plain,
    ( spl3_17
  <=> ! [X0] : subset(sK2,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_17])]) ).

fof(f138,plain,
    ( spl3_17
    | ~ spl3_6
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f112,f108,f68,f136]) ).

fof(f68,plain,
    ( spl3_6
  <=> ! [X0] : subset(empty_set,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).

fof(f112,plain,
    ( ! [X0] : subset(sK2,X0)
    | ~ spl3_6
    | ~ spl3_13 ),
    inference(superposition,[],[f69,f110]) ).

fof(f69,plain,
    ( ! [X0] : subset(empty_set,X0)
    | ~ spl3_6 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f132,plain,
    ( spl3_16
    | ~ spl3_1
    | ~ spl3_13 ),
    inference(avatar_split_clause,[],[f115,f108,f43,f129]) ).

fof(f129,plain,
    ( spl3_16
  <=> subset(sK0,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_16])]) ).

fof(f43,plain,
    ( spl3_1
  <=> subset(sK0,empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f115,plain,
    ( subset(sK0,sK2)
    | ~ spl3_1
    | ~ spl3_13 ),
    inference(superposition,[],[f45,f110]) ).

fof(f45,plain,
    ( subset(sK0,empty_set)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f125,plain,
    ( spl3_15
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_8
    | ~ spl3_10 ),
    inference(avatar_split_clause,[],[f97,f88,f76,f68,f63,f123]) ).

fof(f123,plain,
    ( spl3_15
  <=> ! [X0] :
        ( ~ subset(X0,sK2)
        | sK2 = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_15])]) ).

fof(f63,plain,
    ( spl3_5
  <=> empty(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f76,plain,
    ( spl3_8
  <=> ! [X0] :
        ( empty_set = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f88,plain,
    ( spl3_10
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).

fof(f97,plain,
    ( ! [X0] :
        ( ~ subset(X0,sK2)
        | sK2 = X0 )
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_8
    | ~ spl3_10 ),
    inference(forward_demodulation,[],[f96,f80]) ).

fof(f80,plain,
    ( empty_set = sK2
    | ~ spl3_5
    | ~ spl3_8 ),
    inference(resolution,[],[f77,f65]) ).

fof(f65,plain,
    ( empty(sK2)
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f63]) ).

fof(f77,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty_set = X0 )
    | ~ spl3_8 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f96,plain,
    ( ! [X0] :
        ( sK2 = X0
        | ~ subset(X0,empty_set) )
    | ~ spl3_5
    | ~ spl3_6
    | ~ spl3_8
    | ~ spl3_10 ),
    inference(forward_demodulation,[],[f92,f80]) ).

fof(f92,plain,
    ( ! [X0] :
        ( empty_set = X0
        | ~ subset(X0,empty_set) )
    | ~ spl3_6
    | ~ spl3_10 ),
    inference(resolution,[],[f89,f69]) ).

fof(f89,plain,
    ( ! [X0,X1] :
        ( ~ subset(X1,X0)
        | X0 = X1
        | ~ subset(X0,X1) )
    | ~ spl3_10 ),
    inference(avatar_component_clause,[],[f88]) ).

fof(f119,plain,
    ( spl3_14
    | ~ spl3_5
    | ~ spl3_9 ),
    inference(avatar_split_clause,[],[f86,f82,f63,f117]) ).

fof(f117,plain,
    ( spl3_14
  <=> ! [X0] :
        ( sK2 = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_14])]) ).

fof(f82,plain,
    ( spl3_9
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).

fof(f86,plain,
    ( ! [X0] :
        ( sK2 = X0
        | ~ empty(X0) )
    | ~ spl3_5
    | ~ spl3_9 ),
    inference(resolution,[],[f83,f65]) ).

fof(f83,plain,
    ( ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) )
    | ~ spl3_9 ),
    inference(avatar_component_clause,[],[f82]) ).

fof(f111,plain,
    ( spl3_13
    | ~ spl3_5
    | ~ spl3_8 ),
    inference(avatar_split_clause,[],[f80,f76,f63,f108]) ).

fof(f106,plain,
    ( spl3_11
    | ~ spl3_12
    | ~ spl3_1
    | ~ spl3_5
    | ~ spl3_8
    | ~ spl3_10 ),
    inference(avatar_split_clause,[],[f95,f88,f76,f63,f43,f103,f99]) ).

fof(f95,plain,
    ( ~ subset(sK2,sK0)
    | sK0 = sK2
    | ~ spl3_1
    | ~ spl3_5
    | ~ spl3_8
    | ~ spl3_10 ),
    inference(forward_demodulation,[],[f94,f80]) ).

fof(f94,plain,
    ( sK0 = sK2
    | ~ subset(empty_set,sK0)
    | ~ spl3_1
    | ~ spl3_5
    | ~ spl3_8
    | ~ spl3_10 ),
    inference(forward_demodulation,[],[f91,f80]) ).

fof(f91,plain,
    ( empty_set = sK0
    | ~ subset(empty_set,sK0)
    | ~ spl3_1
    | ~ spl3_10 ),
    inference(resolution,[],[f89,f45]) ).

fof(f90,plain,
    spl3_10,
    inference(avatar_split_clause,[],[f36,f88]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).

fof(f84,plain,
    spl3_9,
    inference(avatar_split_clause,[],[f37,f82]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

fof(f78,plain,
    spl3_8,
    inference(avatar_split_clause,[],[f32,f76]) ).

fof(f32,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f74,plain,
    spl3_7,
    inference(avatar_split_clause,[],[f33,f72]) ).

fof(f72,plain,
    ( spl3_7
  <=> ! [X0] : subset(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).

fof(f33,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f70,plain,
    spl3_6,
    inference(avatar_split_clause,[],[f31,f68]) ).

fof(f31,plain,
    ! [X0] : subset(empty_set,X0),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] : subset(empty_set,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).

fof(f66,plain,
    spl3_5,
    inference(avatar_split_clause,[],[f39,f63]) ).

fof(f39,plain,
    empty(sK2),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    empty(sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f5,f26]) ).

fof(f26,plain,
    ( ? [X0] : empty(X0)
   => empty(sK2) ),
    introduced(choice_axiom,[]) ).

fof(f5,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f61,plain,
    ~ spl3_4,
    inference(avatar_split_clause,[],[f38,f58]) ).

fof(f58,plain,
    ( spl3_4
  <=> empty(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f38,plain,
    ~ empty(sK1),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ~ empty(sK1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f6,f24]) ).

fof(f24,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK1) ),
    introduced(choice_axiom,[]) ).

fof(f6,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

fof(f56,plain,
    spl3_3,
    inference(avatar_split_clause,[],[f30,f53]) ).

fof(f53,plain,
    ( spl3_3
  <=> empty(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f30,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f51,plain,
    ~ spl3_2,
    inference(avatar_split_clause,[],[f29,f48]) ).

fof(f29,plain,
    empty_set != sK0,
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ( empty_set != sK0
    & subset(sK0,empty_set) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f17,f20]) ).

fof(f20,plain,
    ( ? [X0] :
        ( empty_set != X0
        & subset(X0,empty_set) )
   => ( empty_set != sK0
      & subset(sK0,empty_set) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,plain,
    ? [X0] :
      ( empty_set != X0
      & subset(X0,empty_set) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0] :
        ( subset(X0,empty_set)
       => empty_set = X0 ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0] :
      ( subset(X0,empty_set)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).

fof(f46,plain,
    spl3_1,
    inference(avatar_split_clause,[],[f28,f43]) ).

fof(f28,plain,
    subset(sK0,empty_set),
    inference(cnf_transformation,[],[f21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU123+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n028.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon Apr 29 21:14:59 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (26067)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (26072)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38  % (26070)WARNING: value z3 for option sas not known
% 0.15/0.38  % (26069)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (26068)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (26071)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (26073)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38  % (26070)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  % (26074)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38  % (26072)First to succeed.
% 0.15/0.38  Detected minimum model sizes of [1]
% 0.15/0.38  Detected maximum model sizes of [4]
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  Detected minimum model sizes of [1]
% 0.15/0.38  Detected maximum model sizes of [8]
% 0.15/0.38  TRYING [1]
% 0.15/0.38  % (26071)Also succeeded, but the first one will report.
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  % (26073)Also succeeded, but the first one will report.
% 0.15/0.38  % (26072)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (26072)------------------------------
% 0.15/0.38  % (26072)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38  % (26072)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (26072)Memory used [KB]: 783
% 0.15/0.38  % (26072)Time elapsed: 0.005 s
% 0.15/0.38  % (26072)Instructions burned: 5 (million)
% 0.15/0.38  % (26072)------------------------------
% 0.15/0.38  % (26072)------------------------------
% 0.15/0.38  % (26067)Success in time 0.019 s
%------------------------------------------------------------------------------