%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUM027-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 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 : n027.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 18:03:18 EDT 2022

% Result   : Unsatisfiable 0.21s 0.54s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   33 (   8 unt;   0 def)
%            Number of atoms       :   64 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   58 (  27   ~;  28   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   19 (  19   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f555,plain,
    $false,
    inference(avatar_sat_refutation,[],[f62,f123,f125,f554]) ).

fof(f554,plain,
    ~ spl0_1,
    inference(avatar_contradiction_clause,[],[f553]) ).

fof(f553,plain,
    ( $false
    | ~ spl0_1 ),
    inference(subsumption_resolution,[],[f552,f16]) ).

fof(f16,axiom,
    ! [X0] : ~ less(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',number_not_less_than_itself) ).

fof(f552,plain,
    ( less(multiply(a,c),multiply(a,c))
    | ~ spl0_1 ),
    inference(subsumption_resolution,[],[f546,f21]) ).

fof(f21,axiom,
    ~ equalish(c,n0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_is_0) ).

fof(f546,plain,
    ( equalish(c,n0)
    | less(multiply(a,c),multiply(a,c))
    | ~ spl0_1 ),
    inference(resolution,[],[f153,f27]) ).

fof(f27,plain,
    ! [X0] :
      ( ~ less(X0,multiply(b,c))
      | less(X0,multiply(a,c)) ),
    inference(resolution,[],[f7,f20]) ).

fof(f20,axiom,
    less(multiply(b,c),multiply(a,c)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_c_less_than_a_times_c) ).

fof(f7,axiom,
    ! [X2,X0,X1] :
      ( ~ less(X0,X1)
      | ~ less(X2,X0)
      | less(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).

fof(f153,plain,
    ( ! [X7] :
        ( less(multiply(a,X7),multiply(b,X7))
        | equalish(X7,n0) )
    | ~ spl0_1 ),
    inference(resolution,[],[f18,f52]) ).

fof(f52,plain,
    ( less(a,b)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f50]) ).

fof(f50,plain,
    ( spl0_1
  <=> less(a,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f18,axiom,
    ! [X2,X0,X1] :
      ( ~ less(X0,X1)
      | equalish(X2,n0)
      | less(multiply(X0,X2),multiply(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_lemma) ).

fof(f125,plain,
    ( spl0_2
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f124]) ).

fof(f124,plain,
    ( $false
    | spl0_2
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f71,f55]) ).

fof(f55,plain,
    ( ~ equalish(b,a)
    | spl0_2 ),
    inference(avatar_component_clause,[],[f54]) ).

fof(f54,plain,
    ( spl0_2
  <=> equalish(b,a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f71,plain,
    ( equalish(b,a)
    | ~ spl0_3 ),
    inference(resolution,[],[f61,f11]) ).

fof(f11,axiom,
    ! [X3,X4] :
      ( ~ equalish(X3,X4)
      | equalish(X4,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).

fof(f61,plain,
    ( equalish(a,b)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f59]) ).

fof(f59,plain,
    ( spl0_3
  <=> equalish(a,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f123,plain,
    ~ spl0_2,
    inference(avatar_contradiction_clause,[],[f118]) ).

fof(f118,plain,
    ( $false
    | ~ spl0_2 ),
    inference(resolution,[],[f84,f26]) ).

fof(f26,plain,
    ~ equalish(multiply(b,c),multiply(a,c)),
    inference(resolution,[],[f14,f20]) ).

fof(f14,axiom,
    ! [X0,X1] :
      ( ~ less(X0,X1)
      | ~ equalish(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_less_and_equal) ).

fof(f84,plain,
    ( ! [X15] : equalish(multiply(b,X15),multiply(a,X15))
    | ~ spl0_2 ),
    inference(resolution,[],[f13,f56]) ).

fof(f56,plain,
    ( equalish(b,a)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f54]) ).

fof(f13,axiom,
    ! [X2,X0,X1] :
      ( ~ equalish(X0,X1)
      | equalish(multiply(X0,X2),multiply(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality_preserved_over_times) ).

fof(f62,plain,
    ( spl0_3
    | spl0_1 ),
    inference(avatar_split_clause,[],[f44,f50,f59]) ).

fof(f44,plain,
    ( less(a,b)
    | equalish(a,b) ),
    inference(resolution,[],[f15,f19]) ).

fof(f19,axiom,
    ~ less(b,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_not_less_than_a) ).

fof(f15,axiom,
    ! [X0,X1] :
      ( less(X1,X0)
      | less(X0,X1)
      | equalish(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',numbers_either_less_or_equal) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM027-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34  % Computer : n027.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 06:05:46 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.21/0.45  % (30691)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.21/0.47  % (30683)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.52  % (30697)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.53  % (30683)First to succeed.
% 0.21/0.54  % (30683)Refutation found. Thanks to Tanya!
% 0.21/0.54  % SZS status Unsatisfiable for theBenchmark
% 0.21/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.55  % (30683)------------------------------
% 0.21/0.55  % (30683)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.55  % (30683)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.55  % (30683)Termination reason: Refutation
% 0.21/0.55  
% 0.21/0.55  % (30683)Memory used [KB]: 5756
% 0.21/0.55  % (30683)Time elapsed: 0.151 s
% 0.21/0.55  % (30683)Instructions burned: 25 (million)
% 0.21/0.55  % (30683)------------------------------
% 0.21/0.55  % (30683)------------------------------
% 0.21/0.55  % (30678)Success in time 0.195 s
%------------------------------------------------------------------------------