%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : COL074-3 : TPTP v8.1.0. Released v1.2.0.
% 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 : n025.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 15:52:43 EDT 2022

% Result   : Unsatisfiable 0.19s 0.47s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   35 (  17 unt;   0 def)
%            Number of atoms       :   54 (  34 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   31 (  12   ~;  17   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   3 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   20 (  20   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f164,plain,
    $false,
    inference(avatar_sat_refutation,[],[f144,f148,f162]) ).

fof(f162,plain,
    ( ~ spl7_1
    | spl7_2 ),
    inference(avatar_contradiction_clause,[],[f161]) ).

fof(f161,plain,
    ( $false
    | ~ spl7_1
    | spl7_2 ),
    inference(subsumption_resolution,[],[f160,f138]) ).

fof(f138,plain,
    ( projection2 != s
    | spl7_2 ),
    inference(avatar_component_clause,[],[f137]) ).

fof(f137,plain,
    ( spl7_2
  <=> projection2 = s ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).

fof(f160,plain,
    ( projection2 = s
    | ~ spl7_1 ),
    inference(forward_demodulation,[],[f151,f60]) ).

fof(f60,plain,
    ! [X0] : projection2 = sF4(k_projection2,X0),
    inference(superposition,[],[f18,f55]) ).

fof(f55,plain,
    ! [X0] : projection2 = apply(k_projection2,X0),
    inference(forward_demodulation,[],[f51,f22]) ).

fof(f22,plain,
    ! [X0,X1] : sF6(X0,X1) = X0,
    inference(definition_folding,[],[f1,f21,f17]) ).

fof(f17,plain,
    ! [X2] : apply(k,X2) = sF3(X2),
    introduced(function_definition,[]) ).

fof(f21,plain,
    ! [X0,X1] : apply(sF3(X0),X1) = sF6(X0,X1),
    introduced(function_definition,[]) ).

fof(f1,axiom,
    ! [X0,X1] : apply(apply(k,X0),X1) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).

fof(f51,plain,
    ! [X0] : apply(k_projection2,X0) = sF6(projection2,X0),
    inference(superposition,[],[f21,f24]) ).

fof(f24,plain,
    k_projection2 = sF3(projection2),
    inference(superposition,[],[f17,f12]) ).

fof(f12,axiom,
    apply(k,projection2) = k_projection2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_projection2) ).

fof(f18,plain,
    ! [X2,X0] : sF4(X0,X2) = apply(X0,sF3(X2)),
    introduced(function_definition,[]) ).

fof(f151,plain,
    ( ! [X0] : s = sF4(k_projection2,X0)
    | ~ spl7_1 ),
    inference(superposition,[],[f57,f135]) ).

fof(f135,plain,
    ( k_projection2 = sF3(s)
    | ~ spl7_1 ),
    inference(avatar_component_clause,[],[f133]) ).

fof(f133,plain,
    ( spl7_1
  <=> k_projection2 = sF3(s) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).

fof(f57,plain,
    ! [X0,X1] : sF4(sF3(X0),X1) = X0,
    inference(forward_demodulation,[],[f54,f22]) ).

fof(f54,plain,
    ! [X0,X1] : sF4(sF3(X0),X1) = sF6(X0,sF3(X1)),
    inference(superposition,[],[f18,f21]) ).

fof(f148,plain,
    ~ spl7_2,
    inference(avatar_contradiction_clause,[],[f147]) ).

fof(f147,plain,
    ( $false
    | ~ spl7_2 ),
    inference(subsumption_resolution,[],[f146,f10]) ).

fof(f10,axiom,
    projection1 != projection2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',different_projections) ).

fof(f146,plain,
    ( projection1 = projection2
    | ~ spl7_2 ),
    inference(forward_demodulation,[],[f145,f7]) ).

fof(f7,axiom,
    ! [X0] : projection1 = apply(eq,pair(X0,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality) ).

fof(f145,plain,
    ( projection2 = apply(eq,pair(apply(k,projection2),apply(k,projection2)))
    | ~ spl7_2 ),
    inference(superposition,[],[f13,f139]) ).

fof(f139,plain,
    ( projection2 = s
    | ~ spl7_2 ),
    inference(avatar_component_clause,[],[f137]) ).

fof(f13,axiom,
    s = apply(eq,pair(apply(k,s),apply(k,projection2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',self_referential) ).

fof(f144,plain,
    ( spl7_2
    | spl7_1 ),
    inference(avatar_split_clause,[],[f143,f133,f137]) ).

fof(f143,plain,
    ( k_projection2 = sF3(s)
    | projection2 = s ),
    inference(forward_demodulation,[],[f142,f24]) ).

fof(f142,plain,
    ( projection2 = s
    | sF3(s) = sF3(projection2) ),
    inference(forward_demodulation,[],[f141,f17]) ).

fof(f141,plain,
    ( projection2 = s
    | apply(k,projection2) = sF3(s) ),
    inference(forward_demodulation,[],[f123,f17]) ).

fof(f123,plain,
    ( projection2 = s
    | apply(k,projection2) = apply(k,s) ),
    inference(superposition,[],[f8,f13]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( projection2 = apply(eq,pair(X0,X1))
      | X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem    : COL074-3 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Aug 29 16:57:14 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.44  % (25286)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)
% 0.19/0.44  % (25309)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.45  % (25293)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)
% 0.19/0.46  % (25300)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.46  % (25309)First to succeed.
% 0.19/0.47  % (25309)Refutation found. Thanks to Tanya!
% 0.19/0.47  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.47  % (25309)------------------------------
% 0.19/0.47  % (25309)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.47  % (25309)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.47  % (25309)Termination reason: Refutation
% 0.19/0.47  
% 0.19/0.47  % (25309)Memory used [KB]: 5500
% 0.19/0.47  % (25309)Time elapsed: 0.072 s
% 0.19/0.47  % (25309)Instructions burned: 7 (million)
% 0.19/0.47  % (25309)------------------------------
% 0.19/0.47  % (25309)------------------------------
% 0.19/0.47  % (25283)Success in time 0.127 s
%------------------------------------------------------------------------------