%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : GRP031-1 : 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_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 16:19:11 EDT 2022

% Result   : Unsatisfiable 0.18s 0.47s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   14 (   7 unt;   0 def)
%            Number of atoms       :   25 (   5 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   23 (  12   ~;  11   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   30 (  30   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f55,plain,
    $false,
    inference(resolution,[],[f45,f7]) ).

fof(f7,axiom,
    ! [X6] : ~ product(a,X6,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_has_an_inverse) ).

fof(f45,plain,
    ! [X0] : product(X0,inverse(X0),identity),
    inference(superposition,[],[f1,f36]) ).

fof(f36,plain,
    ! [X0] : identity = multiply(X0,inverse(X0)),
    inference(resolution,[],[f34,f1]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ product(X1,inverse(X1),X0)
      | identity = X0 ),
    inference(resolution,[],[f28,f24]) ).

fof(f24,plain,
    ! [X2,X3,X4] :
      ( product(inverse(X2),X3,X4)
      | ~ product(X2,X4,X3) ),
    inference(resolution,[],[f20,f6]) ).

fof(f6,axiom,
    ! [X6] : product(inverse(X6),X6,identity),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).

fof(f20,plain,
    ! [X2,X3,X0,X1] :
      ( ~ product(X3,X0,identity)
      | product(X3,X2,X1)
      | ~ product(X0,X1,X2) ),
    inference(resolution,[],[f3,f5]) ).

fof(f5,axiom,
    ! [X6] : product(identity,X6,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).

fof(f3,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ product(X4,X2,X3)
      | ~ product(X1,X2,X5)
      | product(X0,X5,X3)
      | ~ product(X0,X1,X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity1) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ~ product(X0,X1,X0)
      | identity = X1 ),
    inference(resolution,[],[f24,f9]) ).

fof(f9,plain,
    ! [X2,X3] :
      ( ~ product(inverse(X3),X3,X2)
      | identity = X2 ),
    inference(resolution,[],[f2,f6]) ).

fof(f2,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ product(X0,X1,X3)
      | X2 = X3
      | ~ product(X0,X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).

fof(f1,axiom,
    ! [X0,X1] : product(X0,X1,multiply(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem    : GRP031-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : n008.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 22:12:55 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.18/0.47  % (2173)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)
% 0.18/0.47  % (2173)First to succeed.
% 0.18/0.47  % (2173)Refutation found. Thanks to Tanya!
% 0.18/0.47  % SZS status Unsatisfiable for theBenchmark
% 0.18/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47  % (2173)------------------------------
% 0.18/0.47  % (2173)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.47  % (2173)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.47  % (2173)Termination reason: Refutation
% 0.18/0.47  
% 0.18/0.47  % (2173)Memory used [KB]: 5373
% 0.18/0.47  % (2173)Time elapsed: 0.091 s
% 0.18/0.47  % (2173)Instructions burned: 2 (million)
% 0.18/0.47  % (2173)------------------------------
% 0.18/0.47  % (2173)------------------------------
% 0.18/0.47  % (2159)Success in time 0.133 s
%------------------------------------------------------------------------------