%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : CAT009-4 : TPTP v8.1.0. Released v1.0.0.
% 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 : n016.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 15:51:16 EDT 2022

% Result   : Unsatisfiable 0.17s 0.57s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   39 (  20 unt;   0 def)
%            Number of atoms       :   58 (  23 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   38 (  19   ~;  17   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   10 (  10   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f155,plain,
    $false,
    inference(avatar_sat_refutation,[],[f70,f77,f154]) ).

fof(f154,plain,
    ~ spl3_3,
    inference(avatar_contradiction_clause,[],[f153]) ).

fof(f153,plain,
    ( $false
    | ~ spl3_3 ),
    inference(subsumption_resolution,[],[f152,f18]) ).

fof(f18,plain,
    sF1 != sF2,
    inference(definition_folding,[],[f13,f17,f16,f15]) ).

fof(f15,plain,
    compose(a,b) = sF0,
    introduced(function_definition,[]) ).

fof(f16,plain,
    domain(sF0) = sF1,
    introduced(function_definition,[]) ).

fof(f17,plain,
    domain(b) = sF2,
    introduced(function_definition,[]) ).

fof(f13,axiom,
    domain(compose(a,b)) != domain(b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_ab_equals_domain_of_b) ).

fof(f152,plain,
    ( sF1 = sF2
    | ~ spl3_3 ),
    inference(forward_demodulation,[],[f151,f16]) ).

fof(f151,plain,
    ( domain(sF0) = sF2
    | ~ spl3_3 ),
    inference(forward_demodulation,[],[f150,f76]) ).

fof(f76,plain,
    ( codomain(sF2) = sF2
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f74]) ).

fof(f74,plain,
    ( spl3_3
  <=> codomain(sF2) = sF2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f150,plain,
    domain(sF0) = codomain(sF2),
    inference(subsumption_resolution,[],[f148,f19]) ).

fof(f19,plain,
    there_exists(sF0),
    inference(backward_demodulation,[],[f12,f15]) ).

fof(f12,axiom,
    there_exists(compose(a,b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_exists) ).

fof(f148,plain,
    ( domain(sF0) = codomain(sF2)
    | ~ there_exists(sF0) ),
    inference(superposition,[],[f7,f137]) ).

fof(f137,plain,
    compose(sF0,sF2) = sF0,
    inference(forward_demodulation,[],[f136,f15]) ).

fof(f136,plain,
    compose(a,b) = compose(sF0,sF2),
    inference(forward_demodulation,[],[f132,f17]) ).

fof(f132,plain,
    compose(a,b) = compose(sF0,domain(b)),
    inference(superposition,[],[f56,f10]) ).

fof(f10,axiom,
    ! [X0] : compose(X0,domain(X0)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_domain) ).

fof(f56,plain,
    ! [X8] : compose(sF0,X8) = compose(a,compose(b,X8)),
    inference(superposition,[],[f9,f15]) ).

fof(f9,axiom,
    ! [X2,X0,X1] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_compose) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ there_exists(compose(X0,X1))
      | domain(X0) = codomain(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition1) ).

fof(f77,plain,
    ( spl3_3
    | ~ spl3_1 ),
    inference(avatar_split_clause,[],[f72,f23,f74]) ).

fof(f23,plain,
    ( spl3_1
  <=> there_exists(b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

fof(f72,plain,
    ( ~ there_exists(b)
    | codomain(sF2) = sF2 ),
    inference(forward_demodulation,[],[f47,f17]) ).

fof(f47,plain,
    ( domain(b) = codomain(sF2)
    | ~ there_exists(b) ),
    inference(superposition,[],[f7,f34]) ).

fof(f34,plain,
    b = compose(b,sF2),
    inference(superposition,[],[f10,f17]) ).

fof(f70,plain,
    spl3_1,
    inference(avatar_contradiction_clause,[],[f69]) ).

fof(f69,plain,
    ( $false
    | spl3_1 ),
    inference(subsumption_resolution,[],[f68,f43]) ).

fof(f43,plain,
    there_exists(domain(a)),
    inference(subsumption_resolution,[],[f37,f19]) ).

fof(f37,plain,
    ( there_exists(domain(a))
    | ~ there_exists(sF0) ),
    inference(superposition,[],[f6,f15]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ~ there_exists(compose(X0,X1))
      | there_exists(domain(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_domain) ).

fof(f68,plain,
    ( ~ there_exists(domain(a))
    | spl3_1 ),
    inference(subsumption_resolution,[],[f67,f24]) ).

fof(f24,plain,
    ( ~ there_exists(b)
    | spl3_1 ),
    inference(avatar_component_clause,[],[f23]) ).

fof(f67,plain,
    ( ~ there_exists(domain(a))
    | there_exists(b) ),
    inference(superposition,[],[f5,f51]) ).

fof(f51,plain,
    codomain(b) = domain(a),
    inference(subsumption_resolution,[],[f46,f19]) ).

fof(f46,plain,
    ( ~ there_exists(sF0)
    | codomain(b) = domain(a) ),
    inference(superposition,[],[f7,f15]) ).

fof(f5,axiom,
    ! [X0] :
      ( ~ there_exists(codomain(X0))
      | there_exists(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_has_elements) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : CAT009-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.11/0.33  % Computer : n016.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Mon Aug 29 16:39:59 EDT 2022
% 0.11/0.33  % CPUTime    : 
% 0.17/0.53  % (3883)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)
% 0.17/0.54  % (3890)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.17/0.55  % (3897)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.17/0.55  % (3890)First to succeed.
% 0.17/0.57  % (3890)Refutation found. Thanks to Tanya!
% 0.17/0.57  % SZS status Unsatisfiable for theBenchmark
% 0.17/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.57  % (3890)------------------------------
% 0.17/0.57  % (3890)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.57  % (3890)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.57  % (3890)Termination reason: Refutation
% 0.17/0.57  
% 0.17/0.57  % (3890)Memory used [KB]: 5500
% 0.17/0.57  % (3890)Time elapsed: 0.148 s
% 0.17/0.57  % (3890)Instructions burned: 6 (million)
% 0.17/0.57  % (3890)------------------------------
% 0.17/0.57  % (3890)------------------------------
% 0.17/0.57  % (3871)Success in time 0.221 s
%------------------------------------------------------------------------------