%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWV019-1 : TPTP v8.1.0. Released v2.4.0.
% 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 : n018.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 18:55:15 EDT 2022

% Result   : Unsatisfiable 0.22s 0.51s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   53 (  12 unt;   0 def)
%            Number of atoms       :  111 (   3 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   99 (  41   ~;  48   |;   0   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   14 (  12 usr;  11 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   11 (  11   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f89,plain,
    $false,
    inference(avatar_sat_refutation,[],[f19,f40,f47,f49,f55,f61,f71,f77,f82,f85,f88]) ).

fof(f88,plain,
    ( spl0_10
    | ~ spl0_5 ),
    inference(avatar_split_clause,[],[f86,f29,f68]) ).

fof(f68,plain,
    ( spl0_10
  <=> less_than(upper_bound,an_index) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f29,plain,
    ( spl0_5
  <=> less_than(successor(upper_bound),successor(an_index)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f86,plain,
    ( less_than(upper_bound,an_index)
    | ~ spl0_5 ),
    inference(resolution,[],[f31,f2]) ).

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

fof(f31,plain,
    ( less_than(successor(upper_bound),successor(an_index))
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f29]) ).

fof(f85,plain,
    ~ spl0_10,
    inference(avatar_contradiction_clause,[],[f83]) ).

fof(f83,plain,
    ( $false
    | ~ spl0_10 ),
    inference(resolution,[],[f70,f8]) ).

fof(f8,axiom,
    ~ less_than(upper_bound,an_index),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',somewhere_below_upper_bound) ).

fof(f70,plain,
    ( less_than(upper_bound,an_index)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f82,plain,
    ~ spl0_9,
    inference(avatar_contradiction_clause,[],[f80]) ).

fof(f80,plain,
    ( $false
    | ~ spl0_9 ),
    inference(resolution,[],[f66,f7]) ).

fof(f7,axiom,
    ~ less_than(an_index,lower_bound),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',somewhere_above_lower_bound) ).

fof(f66,plain,
    ( less_than(an_index,lower_bound)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f64]) ).

fof(f64,plain,
    ( spl0_9
  <=> less_than(an_index,lower_bound) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f77,plain,
    ( spl0_9
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f75,f21,f64]) ).

fof(f21,plain,
    ( spl0_3
  <=> less_than(successor(an_index),lower_bound) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f75,plain,
    ( less_than(an_index,lower_bound)
    | ~ spl0_3 ),
    inference(resolution,[],[f72,f4]) ).

fof(f4,axiom,
    ! [X1] : less_than(X1,successor(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_greater) ).

fof(f72,plain,
    ( ! [X0] :
        ( ~ less_than(X0,successor(an_index))
        | less_than(X0,lower_bound) )
    | ~ spl0_3 ),
    inference(resolution,[],[f23,f3]) ).

fof(f3,axiom,
    ! [X2,X3,X1] :
      ( ~ less_than(X2,X3)
      | ~ less_than(X1,X2)
      | less_than(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).

fof(f23,plain,
    ( less_than(successor(an_index),lower_bound)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f21]) ).

fof(f71,plain,
    ( spl0_9
    | spl0_10
    | spl0_7 ),
    inference(avatar_split_clause,[],[f62,f37,f68,f64]) ).

fof(f37,plain,
    ( spl0_7
  <=> in_array_bounds(array,an_index) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f62,plain,
    ( less_than(upper_bound,an_index)
    | less_than(an_index,lower_bound)
    | spl0_7 ),
    inference(resolution,[],[f39,f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( in_array_bounds(array,X0)
      | less_than(upper_bound,X0)
      | less_than(X0,lower_bound) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_bounds) ).

fof(f39,plain,
    ( ~ in_array_bounds(array,an_index)
    | spl0_7 ),
    inference(avatar_component_clause,[],[f37]) ).

fof(f61,plain,
    spl0_6,
    inference(avatar_contradiction_clause,[],[f59]) ).

fof(f59,plain,
    ( $false
    | spl0_6 ),
    inference(resolution,[],[f58,f6]) ).

fof(f6,axiom,
    less_than(index_of_maximal,an_index),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_before_somewhere) ).

fof(f58,plain,
    ( ~ less_than(index_of_maximal,an_index)
    | spl0_6 ),
    inference(resolution,[],[f51,f35]) ).

fof(f35,plain,
    ( ~ less_than(index_of_maximal,successor(an_index))
    | spl0_6 ),
    inference(avatar_component_clause,[],[f33]) ).

fof(f33,plain,
    ( spl0_6
  <=> less_than(index_of_maximal,successor(an_index)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f51,plain,
    ! [X2,X1] :
      ( less_than(X1,successor(X2))
      | ~ less_than(X1,X2) ),
    inference(resolution,[],[f3,f4]) ).

fof(f55,plain,
    ~ spl0_8,
    inference(avatar_split_clause,[],[f54,f44]) ).

fof(f44,plain,
    ( spl0_8
  <=> less_than(upper_bound,index_of_maximal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f54,plain,
    ~ less_than(upper_bound,index_of_maximal),
    inference(resolution,[],[f50,f8]) ).

fof(f50,plain,
    ! [X0] :
      ( less_than(X0,an_index)
      | ~ less_than(X0,index_of_maximal) ),
    inference(resolution,[],[f3,f6]) ).

fof(f49,plain,
    ~ spl0_4,
    inference(avatar_contradiction_clause,[],[f48]) ).

fof(f48,plain,
    ( $false
    | ~ spl0_4 ),
    inference(resolution,[],[f27,f9]) ).

fof(f9,axiom,
    ~ less_than(index_of_maximal,lower_bound),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_above_lower_bound) ).

fof(f27,plain,
    ( less_than(index_of_maximal,lower_bound)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f25]) ).

fof(f25,plain,
    ( spl0_4
  <=> less_than(index_of_maximal,lower_bound) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f47,plain,
    ( spl0_8
    | spl0_4
    | spl0_2 ),
    inference(avatar_split_clause,[],[f42,f16,f25,f44]) ).

fof(f16,plain,
    ( spl0_2
  <=> in_array_bounds(array,index_of_maximal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f42,plain,
    ( less_than(index_of_maximal,lower_bound)
    | less_than(upper_bound,index_of_maximal)
    | spl0_2 ),
    inference(resolution,[],[f1,f18]) ).

fof(f18,plain,
    ( ~ in_array_bounds(array,index_of_maximal)
    | spl0_2 ),
    inference(avatar_component_clause,[],[f16]) ).

fof(f40,plain,
    ( spl0_3
    | spl0_4
    | spl0_5
    | ~ spl0_2
    | ~ spl0_6
    | ~ spl0_1
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f10,f37,f12,f33,f16,f29,f25,f21]) ).

fof(f12,plain,
    ( spl0_1
  <=> maximal_value = array_value_at(array,index_of_maximal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f10,axiom,
    ( ~ in_array_bounds(array,an_index)
    | maximal_value != array_value_at(array,index_of_maximal)
    | ~ less_than(index_of_maximal,successor(an_index))
    | ~ in_array_bounds(array,index_of_maximal)
    | less_than(successor(upper_bound),successor(an_index))
    | less_than(index_of_maximal,lower_bound)
    | less_than(successor(an_index),lower_bound) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

fof(f19,plain,
    ( spl0_1
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f5,f16,f12]) ).

fof(f5,axiom,
    ( ~ in_array_bounds(array,index_of_maximal)
    | maximal_value = array_value_at(array,index_of_maximal) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',this_is_maximal) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SWV019-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.15/0.36  % Computer : n018.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Aug 30 19:00:10 EDT 2022
% 0.15/0.36  % CPUTime    : 
% 0.22/0.50  % (22440)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.22/0.50  % (22434)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.22/0.50  % (22443)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.22/0.50  % (22440)First to succeed.
% 0.22/0.51  % (22454)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.22/0.51  % (22440)Refutation found. Thanks to Tanya!
% 0.22/0.51  % SZS status Unsatisfiable for theBenchmark
% 0.22/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.51  % (22440)------------------------------
% 0.22/0.51  % (22440)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.51  % (22440)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.51  % (22440)Termination reason: Refutation
% 0.22/0.51  
% 0.22/0.51  % (22440)Memory used [KB]: 5373
% 0.22/0.51  % (22440)Time elapsed: 0.090 s
% 0.22/0.51  % (22440)Instructions burned: 2 (million)
% 0.22/0.51  % (22440)------------------------------
% 0.22/0.51  % (22440)------------------------------
% 0.22/0.51  % (22429)Success in time 0.145 s
%------------------------------------------------------------------------------