%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET017-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 : n014.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 18:18:25 EDT 2022

% Result   : Unsatisfiable 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   40 (  12 unt;   0 def)
%            Number of atoms       :   76 (  18 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   65 (  29   ~;  32   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   5 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   27 (  27   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f141,plain,
    $false,
    inference(avatar_sat_refutation,[],[f112,f124,f128,f130,f140]) ).

fof(f140,plain,
    ( ~ spl0_1
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f139]) ).

fof(f139,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f138,f132]) ).

fof(f132,plain,
    ( x != z
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f94,f119]) ).

fof(f119,plain,
    ( x = y
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f117]) ).

fof(f117,plain,
    ( spl0_3
  <=> x = y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f94,axiom,
    y != z,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_3) ).

fof(f138,plain,
    ( x = z
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(duplicate_literal_removal,[],[f137]) ).

fof(f137,plain,
    ( x = z
    | x = z
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(resolution,[],[f136,f8]) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( ~ member(X2,unordered_pair(X0,X1))
      | X0 = X2
      | X1 = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).

fof(f136,plain,
    ( member(z,unordered_pair(x,x))
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(forward_demodulation,[],[f107,f119]) ).

fof(f107,plain,
    ( member(z,unordered_pair(x,y))
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f105]) ).

fof(f105,plain,
    ( spl0_1
  <=> member(z,unordered_pair(x,y)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f130,plain,
    spl0_4,
    inference(avatar_contradiction_clause,[],[f129]) ).

fof(f129,plain,
    ( $false
    | spl0_4 ),
    inference(subsumption_resolution,[],[f126,f123]) ).

fof(f123,plain,
    ( ~ member(y,universal_class)
    | spl0_4 ),
    inference(avatar_component_clause,[],[f121]) ).

fof(f121,plain,
    ( spl0_4
  <=> member(y,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f126,plain,
    member(y,universal_class),
    inference(resolution,[],[f97,f96]) ).

fof(f96,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
      | member(X2,X0) ),
    inference(definition_unfolding,[],[f14,f95]) ).

fof(f95,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
    inference(definition_unfolding,[],[f13,f12,f12]) ).

fof(f12,axiom,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).

fof(f13,axiom,
    ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).

fof(f14,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X2,X0)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).

fof(f97,plain,
    member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(universal_class,universal_class)),
    inference(definition_unfolding,[],[f93,f95]) ).

fof(f93,axiom,
    member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_2) ).

fof(f128,plain,
    spl0_2,
    inference(avatar_contradiction_clause,[],[f127]) ).

fof(f127,plain,
    ( $false
    | spl0_2 ),
    inference(subsumption_resolution,[],[f125,f111]) ).

fof(f111,plain,
    ( ~ member(z,universal_class)
    | spl0_2 ),
    inference(avatar_component_clause,[],[f109]) ).

fof(f109,plain,
    ( spl0_2
  <=> member(z,universal_class) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f125,plain,
    member(z,universal_class),
    inference(resolution,[],[f97,f99]) ).

fof(f99,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
      | member(X3,X1) ),
    inference(definition_unfolding,[],[f15,f95]) ).

fof(f15,axiom,
    ! [X2,X3,X0,X1] :
      ( member(X3,X1)
      | ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).

fof(f124,plain,
    ( spl0_3
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f115,f121,f117]) ).

fof(f115,plain,
    ( ~ member(y,universal_class)
    | x = y ),
    inference(subsumption_resolution,[],[f113,f94]) ).

fof(f113,plain,
    ( x = y
    | ~ member(y,universal_class)
    | y = z ),
    inference(resolution,[],[f103,f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( member(X1,unordered_pair(X0,X1))
      | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).

fof(f103,plain,
    ! [X0] :
      ( ~ member(X0,unordered_pair(x,y))
      | x = X0
      | z = X0 ),
    inference(superposition,[],[f8,f92]) ).

fof(f92,axiom,
    unordered_pair(x,y) = unordered_pair(x,z),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_1) ).

fof(f112,plain,
    ( spl0_1
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f102,f109,f105]) ).

fof(f102,plain,
    ( ~ member(z,universal_class)
    | member(z,unordered_pair(x,y)) ),
    inference(superposition,[],[f10,f92]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SET017-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 12:54:48 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (9716)fmb+10_1:1_fmbes=contour:fmbsr=2.0:fmbsso=input_usage:i=6:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.19/0.50  % (9708)lrs+1010_1:4_amm=off:bce=on:sd=1:sos=on:ss=included:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (9716)Instruction limit reached!
% 0.19/0.50  % (9716)------------------------------
% 0.19/0.50  % (9716)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (9723)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=97:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/97Mi)
% 0.19/0.51  % (9708)First to succeed.
% 0.19/0.51  % (9716)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (9716)Termination reason: Unknown
% 0.19/0.51  % (9716)Termination phase: Finite model building preprocessing
% 0.19/0.51  
% 0.19/0.51  % (9716)Memory used [KB]: 1535
% 0.19/0.51  % (9716)Time elapsed: 0.005 s
% 0.19/0.51  % (9716)Instructions burned: 7 (million)
% 0.19/0.51  % (9716)------------------------------
% 0.19/0.51  % (9716)------------------------------
% 0.19/0.51  % (9708)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (9708)------------------------------
% 0.19/0.51  % (9708)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (9708)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (9708)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (9708)Memory used [KB]: 5884
% 0.19/0.51  % (9708)Time elapsed: 0.102 s
% 0.19/0.51  % (9708)Instructions burned: 3 (million)
% 0.19/0.51  % (9708)------------------------------
% 0.19/0.51  % (9708)------------------------------
% 0.19/0.51  % (9700)Success in time 0.165 s
%------------------------------------------------------------------------------