%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM001-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n009.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 : Tue May 21 01:47:45 EDT 2024

% Result   : Unsatisfiable 0.15s 0.37s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   11 (   8 unt;   0 def)
%            Number of atoms       :   15 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :    9 (   5   ~;   4   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   27 (  27   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f372,plain,
    $false,
    inference(resolution,[],[f363,f13]) ).

fof(f13,axiom,
    ~ equalish(add(add(a,b),c),add(a,add(b,c))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).

fof(f363,plain,
    ! [X2,X0,X1] : equalish(add(add(X0,X1),X2),add(X0,add(X1,X2))),
    inference(resolution,[],[f325,f16]) ).

fof(f16,plain,
    ! [X2,X0,X1] :
      ( ~ equalish(add(X0,X1),X2)
      | equalish(add(X1,X0),X2) ),
    inference(resolution,[],[f2,f3]) ).

fof(f3,axiom,
    ! [X0,X1] : equalish(add(X0,X1),add(X1,X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).

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

fof(f325,plain,
    ! [X2,X0,X1] : equalish(add(X0,add(X1,X2)),add(X1,add(X2,X0))),
    inference(resolution,[],[f305,f30]) ).

fof(f30,plain,
    ! [X2,X3,X0,X1] :
      ( ~ equalish(add(add(X0,X1),X2),X3)
      | equalish(add(X0,add(X1,X2)),X3) ),
    inference(resolution,[],[f4,f2]) ).

fof(f4,axiom,
    ! [X2,X0,X1] : equalish(add(X0,add(X1,X2)),add(add(X0,X1),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition) ).

fof(f305,plain,
    ! [X2,X0,X1] : equalish(add(add(X0,X1),X2),add(X1,add(X2,X0))),
    inference(resolution,[],[f284,f16]) ).

fof(f284,plain,
    ! [X2,X0,X1] : equalish(add(X0,add(X1,X2)),add(X2,add(X0,X1))),
    inference(resolution,[],[f30,f3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM001-1 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n009.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon May 20 05:01:08 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (21682)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (21687)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.37  % (21687)First to succeed.
% 0.15/0.37  % (21687)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-21682"
% 0.15/0.37  % (21687)Refutation found. Thanks to Tanya!
% 0.15/0.37  % SZS status Unsatisfiable for theBenchmark
% 0.15/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.37  % (21687)------------------------------
% 0.15/0.37  % (21687)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.37  % (21687)Termination reason: Refutation
% 0.15/0.37  
% 0.15/0.37  % (21687)Memory used [KB]: 890
% 0.15/0.37  % (21687)Time elapsed: 0.006 s
% 0.15/0.37  % (21687)Instructions burned: 17 (million)
% 0.15/0.37  % (21682)Success in time 0.005 s
%------------------------------------------------------------------------------