TSTP Solution File: SET954+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET954+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 : n008.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 18:26:11 EDT 2022

% Result   : Theorem 1.73s 0.57s
% Output   : Refutation 1.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   44 (  17 unt;   0 def)
%            Number of atoms       :   90 (   5 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   83 (  37   ~;  25   |;  13   &)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   98 (  86   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f86,plain,
    $false,
    inference(avatar_sat_refutation,[],[f74,f79,f85]) ).

fof(f85,plain,
    spl6_1,
    inference(avatar_split_clause,[],[f81,f67]) ).

fof(f67,plain,
    ( spl6_1
  <=> in(sK2,sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

fof(f81,plain,
    in(sK2,sK5),
    inference(resolution,[],[f59,f49]) ).

fof(f49,plain,
    in(unordered_pair(singleton(sK4),unordered_pair(sK2,sK4)),cartesian_product2(sK3,sK5)),
    inference(forward_demodulation,[],[f47,f36]) ).

fof(f36,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(rectify,[],[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(f47,plain,
    in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK2)),cartesian_product2(sK3,sK5)),
    inference(backward_demodulation,[],[f41,f36]) ).

fof(f41,plain,
    in(unordered_pair(unordered_pair(sK4,sK2),singleton(sK4)),cartesian_product2(sK3,sK5)),
    inference(definition_unfolding,[],[f33,f34]) ).

fof(f34,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,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(f33,plain,
    in(ordered_pair(sK4,sK2),cartesian_product2(sK3,sK5)),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ( in(ordered_pair(sK4,sK2),cartesian_product2(sK3,sK5))
    & ~ in(ordered_pair(sK2,sK4),cartesian_product2(sK5,sK3)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f23,f24]) ).

fof(f24,plain,
    ( ? [X0,X1,X2,X3] :
        ( in(ordered_pair(X2,X0),cartesian_product2(X1,X3))
        & ~ in(ordered_pair(X0,X2),cartesian_product2(X3,X1)) )
   => ( in(ordered_pair(sK4,sK2),cartesian_product2(sK3,sK5))
      & ~ in(ordered_pair(sK2,sK4),cartesian_product2(sK5,sK3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ? [X0,X1,X2,X3] :
      ( in(ordered_pair(X2,X0),cartesian_product2(X1,X3))
      & ~ in(ordered_pair(X0,X2),cartesian_product2(X3,X1)) ),
    inference(rectify,[],[f15]) ).

fof(f15,plain,
    ? [X1,X3,X2,X0] :
      ( in(ordered_pair(X2,X1),cartesian_product2(X3,X0))
      & ~ in(ordered_pair(X1,X2),cartesian_product2(X0,X3)) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,plain,
    ~ ! [X3,X1,X0,X2] :
        ( in(ordered_pair(X2,X1),cartesian_product2(X3,X0))
       => in(ordered_pair(X1,X2),cartesian_product2(X0,X3)) ),
    inference(rectify,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X3,X1,X0,X2] :
        ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
       => in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X3,X1,X0,X2] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
     => in(ordered_pair(X1,X0),cartesian_product2(X3,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t107_zfmisc_1) ).

fof(f59,plain,
    ! [X6,X7,X4,X5] :
      ( ~ in(unordered_pair(singleton(X4),unordered_pair(X5,X4)),cartesian_product2(X6,X7))
      | in(X5,X7) ),
    inference(superposition,[],[f50,f36]) ).

fof(f50,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),cartesian_product2(X0,X2))
      | in(X1,X2) ),
    inference(forward_demodulation,[],[f39,f36]) ).

fof(f39,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X2)
      | ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X0,X2)) ),
    inference(definition_unfolding,[],[f28,f34]) ).

fof(f28,plain,
    ! [X2,X3,X0,X1] :
      ( in(X1,X2)
      | ~ in(ordered_pair(X3,X1),cartesian_product2(X0,X2)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X3,X1),cartesian_product2(X0,X2))
        | ~ in(X1,X2)
        | ~ in(X3,X0) )
      & ( ( in(X1,X2)
          & in(X3,X0) )
        | ~ in(ordered_pair(X3,X1),cartesian_product2(X0,X2)) ) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ! [X1,X3,X0,X2] :
      ( ( in(ordered_pair(X2,X3),cartesian_product2(X1,X0))
        | ~ in(X3,X0)
        | ~ in(X2,X1) )
      & ( ( in(X3,X0)
          & in(X2,X1) )
        | ~ in(ordered_pair(X2,X3),cartesian_product2(X1,X0)) ) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ! [X1,X3,X0,X2] :
      ( ( in(ordered_pair(X2,X3),cartesian_product2(X1,X0))
        | ~ in(X3,X0)
        | ~ in(X2,X1) )
      & ( ( in(X3,X0)
          & in(X2,X1) )
        | ~ in(ordered_pair(X2,X3),cartesian_product2(X1,X0)) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X1,X3,X0,X2] :
      ( in(ordered_pair(X2,X3),cartesian_product2(X1,X0))
    <=> ( in(X3,X0)
        & in(X2,X1) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X3,X2,X0,X1] :
      ( ( in(X0,X2)
        & in(X1,X3) )
    <=> in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).

fof(f79,plain,
    spl6_2,
    inference(avatar_split_clause,[],[f75,f71]) ).

fof(f71,plain,
    ( spl6_2
  <=> in(sK4,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

fof(f75,plain,
    in(sK4,sK3),
    inference(resolution,[],[f57,f49]) ).

fof(f57,plain,
    ! [X6,X7,X4,X5] :
      ( ~ in(unordered_pair(singleton(X4),unordered_pair(X5,X4)),cartesian_product2(X6,X7))
      | in(X4,X6) ),
    inference(superposition,[],[f46,f36]) ).

fof(f46,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),cartesian_product2(X0,X2))
      | in(X3,X0) ),
    inference(backward_demodulation,[],[f40,f36]) ).

fof(f40,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X0,X2)) ),
    inference(definition_unfolding,[],[f27,f34]) ).

fof(f27,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | ~ in(ordered_pair(X3,X1),cartesian_product2(X0,X2)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f74,plain,
    ( ~ spl6_1
    | ~ spl6_2 ),
    inference(avatar_split_clause,[],[f60,f71,f67]) ).

fof(f60,plain,
    ( ~ in(sK4,sK3)
    | ~ in(sK2,sK5) ),
    inference(resolution,[],[f45,f48]) ).

fof(f48,plain,
    ~ in(unordered_pair(singleton(sK2),unordered_pair(sK2,sK4)),cartesian_product2(sK5,sK3)),
    inference(backward_demodulation,[],[f42,f36]) ).

fof(f42,plain,
    ~ in(unordered_pair(unordered_pair(sK2,sK4),singleton(sK2)),cartesian_product2(sK5,sK3)),
    inference(definition_unfolding,[],[f32,f34]) ).

fof(f32,plain,
    ~ in(ordered_pair(sK2,sK4),cartesian_product2(sK5,sK3)),
    inference(cnf_transformation,[],[f25]) ).

fof(f45,plain,
    ! [X2,X3,X0,X1] :
      ( in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),cartesian_product2(X0,X2))
      | ~ in(X3,X0)
      | ~ in(X1,X2) ),
    inference(backward_demodulation,[],[f38,f36]) ).

fof(f38,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(X1,X2)
      | in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X0,X2))
      | ~ in(X3,X0) ),
    inference(definition_unfolding,[],[f29,f34]) ).

fof(f29,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X3,X1),cartesian_product2(X0,X2))
      | ~ in(X1,X2)
      | ~ in(X3,X0) ),
    inference(cnf_transformation,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET954+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % 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 : n008.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 14:35:40 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.53  % (24639)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)
% 0.19/0.54  TRYING [1]
% 0.19/0.54  TRYING [2]
% 0.19/0.54  TRYING [3]
% 0.19/0.55  % (24650)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.55  TRYING [1]
% 0.19/0.55  TRYING [2]
% 0.19/0.55  TRYING [3]
% 0.19/0.55  % (24647)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.56/0.55  % (24642)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.56/0.55  % (24655)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)
% 1.56/0.56  % (24643)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.56/0.56  % (24634)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.56/0.56  % (24634)Refutation not found, incomplete strategy% (24634)------------------------------
% 1.56/0.56  % (24634)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.56/0.56  % (24634)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.56/0.56  % (24634)Termination reason: Refutation not found, incomplete strategy
% 1.56/0.56  
% 1.56/0.56  % (24634)Memory used [KB]: 5373
% 1.56/0.56  % (24634)Time elapsed: 0.161 s
% 1.56/0.56  % (24634)Instructions burned: 2 (million)
% 1.56/0.56  % (24634)------------------------------
% 1.56/0.56  % (24634)------------------------------
% 1.56/0.56  % (24659)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.56/0.56  % (24656)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)
% 1.56/0.56  % (24643)First to succeed.
% 1.56/0.57  % (24648)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.56/0.57  % (24651)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.56/0.57  % (24635)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.73/0.57  % (24640)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.73/0.57  % (24655)Also succeeded, but the first one will report.
% 1.73/0.57  % (24643)Refutation found. Thanks to Tanya!
% 1.73/0.57  % SZS status Theorem for theBenchmark
% 1.73/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 1.73/0.57  % (24643)------------------------------
% 1.73/0.57  % (24643)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.73/0.57  % (24643)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.73/0.57  % (24643)Termination reason: Refutation
% 1.73/0.57  
% 1.73/0.57  % (24643)Memory used [KB]: 5373
% 1.73/0.57  % (24643)Time elapsed: 0.156 s
% 1.73/0.57  % (24643)Instructions burned: 3 (million)
% 1.73/0.57  % (24643)------------------------------
% 1.73/0.57  % (24643)------------------------------
% 1.73/0.57  % (24632)Success in time 0.224 s
%------------------------------------------------------------------------------