TSTP Solution File: SET975+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n003.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 18:26:14 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   73 (  13 unt;   0 def)
%            Number of atoms       :  156 (  34 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  146 (  63   ~;  66   |;   5   &)
%                                         (  11 <=>;   0  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   6 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-2 aty)
%            Number of variables   :   91 (  87   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f473,plain,
    $false,
    inference(avatar_sat_refutation,[],[f60,f61,f63,f124,f214,f217,f470,f472]) ).

fof(f472,plain,
    spl12_12,
    inference(avatar_contradiction_clause,[],[f471]) ).

fof(f471,plain,
    ( $false
    | spl12_12 ),
    inference(resolution,[],[f435,f65]) ).

fof(f65,plain,
    in(sK1,sF8),
    inference(superposition,[],[f38,f41]) ).

fof(f41,plain,
    singleton(sK1) = sF8,
    introduced(function_definition,[]) ).

fof(f38,plain,
    ! [X2] : in(X2,singleton(X2)),
    inference(equality_resolution,[],[f37]) ).

fof(f37,plain,
    ! [X2,X1] :
      ( in(X2,X1)
      | singleton(X2) != X1 ),
    inference(equality_resolution,[],[f26]) ).

fof(f26,plain,
    ! [X2,X0,X1] :
      ( in(X2,X1)
      | X0 != X2
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( X0 = X2
        <=> in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f435,plain,
    ( ~ in(sK1,sF8)
    | spl12_12 ),
    inference(avatar_component_clause,[],[f433]) ).

fof(f433,plain,
    ( spl12_12
  <=> in(sK1,sF8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_12])]) ).

fof(f470,plain,
    ( ~ spl12_2
    | spl12_3
    | ~ spl12_12
    | ~ spl12_1 ),
    inference(avatar_split_clause,[],[f467,f49,f433,f57,f53]) ).

fof(f53,plain,
    ( spl12_2
  <=> in(sK3,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).

fof(f57,plain,
    ( spl12_3
  <=> in(sF9,sF11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).

fof(f49,plain,
    ( spl12_1
  <=> sK2 = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).

fof(f467,plain,
    ( ~ in(sK1,sF8)
    | in(sF9,sF11)
    | ~ in(sK3,sK4)
    | ~ spl12_1 ),
    inference(superposition,[],[f457,f228]) ).

fof(f228,plain,
    ( cartesian_product2(sF8,sK4) = sF11
    | ~ spl12_1 ),
    inference(superposition,[],[f44,f227]) ).

fof(f227,plain,
    ( sF10 = sF8
    | ~ spl12_1 ),
    inference(forward_demodulation,[],[f218,f41]) ).

fof(f218,plain,
    ( sF10 = singleton(sK1)
    | ~ spl12_1 ),
    inference(superposition,[],[f43,f50]) ).

fof(f50,plain,
    ( sK2 = sK1
    | ~ spl12_1 ),
    inference(avatar_component_clause,[],[f49]) ).

fof(f43,plain,
    sF10 = singleton(sK2),
    introduced(function_definition,[]) ).

fof(f44,plain,
    cartesian_product2(sF10,sK4) = sF11,
    introduced(function_definition,[]) ).

fof(f457,plain,
    ! [X0,X1] :
      ( in(sF9,cartesian_product2(X0,X1))
      | ~ in(sK3,X1)
      | ~ in(sK1,X0) ),
    inference(forward_demodulation,[],[f456,f42]) ).

fof(f42,plain,
    sF9 = unordered_pair(sF7,sF8),
    introduced(function_definition,[]) ).

fof(f456,plain,
    ! [X0,X1] :
      ( ~ in(sK3,X1)
      | ~ in(sK1,X0)
      | in(unordered_pair(sF7,sF8),cartesian_product2(X0,X1)) ),
    inference(forward_demodulation,[],[f455,f41]) ).

fof(f455,plain,
    ! [X0,X1] :
      ( ~ in(sK3,X1)
      | in(unordered_pair(sF7,singleton(sK1)),cartesian_product2(X0,X1))
      | ~ in(sK1,X0) ),
    inference(forward_demodulation,[],[f449,f15]) ).

fof(f15,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f449,plain,
    ! [X0,X1] :
      ( in(unordered_pair(singleton(sK1),sF7),cartesian_product2(X0,X1))
      | ~ in(sK1,X0)
      | ~ in(sK3,X1) ),
    inference(superposition,[],[f62,f40]) ).

fof(f40,plain,
    sF7 = unordered_pair(sK1,sK3),
    introduced(function_definition,[]) ).

fof(f62,plain,
    ! [X2,X3,X0,X1] :
      ( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
      | ~ in(X0,X2)
      | ~ in(X1,X3) ),
    inference(forward_demodulation,[],[f34,f15]) ).

fof(f34,plain,
    ! [X2,X3,X0,X1] :
      ( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
      | ~ in(X0,X2)
      | ~ in(X1,X3) ),
    inference(definition_unfolding,[],[f22,f23]) ).

fof(f23,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

fof(f22,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(X0,X2)
      | ~ in(X1,X3)
      | in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X3,X0,X2,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X1,X3)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).

fof(f217,plain,
    ( spl12_1
    | ~ spl12_10 ),
    inference(avatar_split_clause,[],[f215,f211,f49]) ).

fof(f211,plain,
    ( spl12_10
  <=> in(sK1,sF10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).

fof(f215,plain,
    ( sK2 = sK1
    | ~ spl12_10 ),
    inference(resolution,[],[f213,f75]) ).

fof(f75,plain,
    ! [X1] :
      ( ~ in(X1,sF10)
      | sK2 = X1 ),
    inference(superposition,[],[f39,f43]) ).

fof(f39,plain,
    ! [X2,X0] :
      ( ~ in(X2,singleton(X0))
      | X0 = X2 ),
    inference(equality_resolution,[],[f25]) ).

fof(f25,plain,
    ! [X2,X0,X1] :
      ( ~ in(X2,X1)
      | X0 = X2
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f3]) ).

fof(f213,plain,
    ( in(sK1,sF10)
    | ~ spl12_10 ),
    inference(avatar_component_clause,[],[f211]) ).

fof(f214,plain,
    ( ~ spl12_3
    | spl12_10 ),
    inference(avatar_split_clause,[],[f209,f211,f57]) ).

fof(f209,plain,
    ( in(sK1,sF10)
    | ~ in(sF9,sF11) ),
    inference(superposition,[],[f206,f44]) ).

fof(f206,plain,
    ! [X0,X1] :
      ( ~ in(sF9,cartesian_product2(X0,X1))
      | in(sK1,X0) ),
    inference(forward_demodulation,[],[f205,f42]) ).

fof(f205,plain,
    ! [X0,X1] :
      ( in(sK1,X0)
      | ~ in(unordered_pair(sF7,sF8),cartesian_product2(X0,X1)) ),
    inference(forward_demodulation,[],[f193,f41]) ).

fof(f193,plain,
    ! [X0,X1] :
      ( in(sK1,X0)
      | ~ in(unordered_pair(sF7,singleton(sK1)),cartesian_product2(X0,X1)) ),
    inference(superposition,[],[f36,f40]) ).

fof(f36,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
      | in(X0,X2) ),
    inference(definition_unfolding,[],[f20,f23]) ).

fof(f20,plain,
    ! [X2,X3,X0,X1] :
      ( in(X0,X2)
      | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    inference(cnf_transformation,[],[f6]) ).

fof(f124,plain,
    ( spl12_2
    | ~ spl12_3 ),
    inference(avatar_split_clause,[],[f123,f57,f53]) ).

fof(f123,plain,
    ( ~ in(sF9,sF11)
    | in(sK3,sK4) ),
    inference(superposition,[],[f118,f44]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ~ in(sF9,cartesian_product2(X0,X1))
      | in(sK3,X1) ),
    inference(forward_demodulation,[],[f117,f42]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( in(sK3,X1)
      | ~ in(unordered_pair(sF7,sF8),cartesian_product2(X0,X1)) ),
    inference(forward_demodulation,[],[f107,f41]) ).

fof(f107,plain,
    ! [X0,X1] :
      ( in(sK3,X1)
      | ~ in(unordered_pair(sF7,singleton(sK1)),cartesian_product2(X0,X1)) ),
    inference(superposition,[],[f35,f40]) ).

fof(f35,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
      | in(X1,X3) ),
    inference(definition_unfolding,[],[f21,f23]) ).

fof(f21,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X3)
      | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    inference(cnf_transformation,[],[f6]) ).

fof(f63,plain,
    ( spl12_1
    | spl12_3 ),
    inference(avatar_split_clause,[],[f46,f57,f49]) ).

fof(f46,plain,
    ( in(sF9,sF11)
    | sK2 = sK1 ),
    inference(definition_folding,[],[f31,f44,f43,f42,f41,f40]) ).

fof(f31,plain,
    ( sK2 = sK1
    | in(unordered_pair(unordered_pair(sK1,sK3),singleton(sK1)),cartesian_product2(singleton(sK2),sK4)) ),
    inference(definition_unfolding,[],[f17,f23]) ).

fof(f17,plain,
    ( sK2 = sK1
    | in(ordered_pair(sK1,sK3),cartesian_product2(singleton(sK2),sK4)) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ? [X3,X1,X0,X2] :
      ( in(ordered_pair(X3,X0),cartesian_product2(singleton(X1),X2))
    <~> ( in(X0,X2)
        & X1 = X3 ) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ~ ! [X1,X2,X0,X3] :
        ( ( in(X0,X2)
          & X1 = X3 )
      <=> in(ordered_pair(X3,X0),cartesian_product2(singleton(X1),X2)) ),
    inference(rectify,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X1,X2,X3,X0] :
        ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
      <=> ( in(X1,X3)
          & X0 = X2 ) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X1,X2,X3,X0] :
      ( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
    <=> ( in(X1,X3)
        & X0 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t128_zfmisc_1) ).

fof(f61,plain,
    ( spl12_2
    | spl12_3 ),
    inference(avatar_split_clause,[],[f45,f57,f53]) ).

fof(f45,plain,
    ( in(sF9,sF11)
    | in(sK3,sK4) ),
    inference(definition_folding,[],[f30,f44,f43,f42,f41,f40]) ).

fof(f30,plain,
    ( in(sK3,sK4)
    | in(unordered_pair(unordered_pair(sK1,sK3),singleton(sK1)),cartesian_product2(singleton(sK2),sK4)) ),
    inference(definition_unfolding,[],[f18,f23]) ).

fof(f18,plain,
    ( in(sK3,sK4)
    | in(ordered_pair(sK1,sK3),cartesian_product2(singleton(sK2),sK4)) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f60,plain,
    ( ~ spl12_1
    | ~ spl12_2
    | ~ spl12_3 ),
    inference(avatar_split_clause,[],[f47,f57,f53,f49]) ).

fof(f47,plain,
    ( ~ in(sF9,sF11)
    | ~ in(sK3,sK4)
    | sK2 != sK1 ),
    inference(definition_folding,[],[f32,f44,f43,f42,f41,f40]) ).

fof(f32,plain,
    ( sK2 != sK1
    | ~ in(sK3,sK4)
    | ~ in(unordered_pair(unordered_pair(sK1,sK3),singleton(sK1)),cartesian_product2(singleton(sK2),sK4)) ),
    inference(definition_unfolding,[],[f16,f23]) ).

fof(f16,plain,
    ( sK2 != sK1
    | ~ in(sK3,sK4)
    | ~ in(ordered_pair(sK1,sK3),cartesian_product2(singleton(sK2),sK4)) ),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 14:33:22 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.20/0.45  % (5292)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.46  % (5289)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.47  TRYING [1]
% 0.20/0.48  TRYING [2]
% 0.20/0.48  TRYING [3]
% 0.20/0.48  TRYING [4]
% 0.20/0.49  % (5309)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.49  % (5314)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.50  % (5298)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.50  % (5310)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.50  % (5289)First to succeed.
% 0.20/0.50  % (5289)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Theorem for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (5289)------------------------------
% 0.20/0.50  % (5289)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (5289)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (5289)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (5289)Memory used [KB]: 5628
% 0.20/0.50  % (5289)Time elapsed: 0.098 s
% 0.20/0.50  % (5289)Instructions burned: 13 (million)
% 0.20/0.50  % (5289)------------------------------
% 0.20/0.50  % (5289)------------------------------
% 0.20/0.50  % (5281)Success in time 0.152 s
%------------------------------------------------------------------------------