%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : GRP021-1 : 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_uns --cores 0 -t %d %s

% Computer : n024.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 16:13:43 EDT 2022

% Result   : Unsatisfiable 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    5
% Syntax   : Number of formulae    :    8 (   5 unt;   0 def)
%            Number of atoms       :   13 (   3 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   11 (   6   ~;   4   |;   0   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   13 (  13   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f34,plain,
    $false,
    inference(unit_resulting_resolution,[],[f4,f5,f16,f15]) ).

fof(f15,plain,
    ! [X2,X3,X0,X1] :
      ( ~ product(X0,X1,X3)
      | sQ2_eqProxy(X2,X3)
      | ~ product(X0,X1,X2) ),
    inference(equality_proxy_replacement,[],[f6,f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( sQ2_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ2_eqProxy])]) ).

fof(f6,axiom,
    ! [X2,X3,X0,X1] :
      ( X2 = X3
      | ~ product(X0,X1,X2)
      | ~ product(X0,X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).

fof(f16,plain,
    ~ sQ2_eqProxy(identity,multiply(a,inverse(a))),
    inference(equality_proxy_replacement,[],[f9,f14]) ).

fof(f9,axiom,
    identity != multiply(a,inverse(a)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_X_times_inverse_X_is_id) ).

fof(f5,axiom,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).

fof(f4,axiom,
    ! [X0] : product(X0,inverse(X0),identity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : GRP021-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n024.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 22:09:49 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.49  % (12742)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/34Mi)
% 0.19/0.49  % (12740)lrs+10_1:16_awrs=converge:awrsf=40:br=off:ep=RSTC:flr=on:gsp=on:nwc=3.0:sos=on:urr=on:i=4:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.49  % (12740)First to succeed.
% 0.19/0.50  % (12740)Refutation found. Thanks to Tanya!
% 0.19/0.50  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50  % (12740)------------------------------
% 0.19/0.50  % (12740)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (12740)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (12740)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (12740)Memory used [KB]: 5756
% 0.19/0.50  % (12740)Time elapsed: 0.100 s
% 0.19/0.50  % (12740)Instructions burned: 1 (million)
% 0.19/0.50  % (12740)------------------------------
% 0.19/0.50  % (12740)------------------------------
% 0.19/0.50  % (12737)Success in time 0.155 s
%------------------------------------------------------------------------------