TSTP Solution File: ANA003-4 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : ANA003-4 : 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 : 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 15:44:53 EDT 2022

% Result   : Unsatisfiable 1.85s 0.61s
% Output   : Refutation 1.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   43 (   3 unt;   0 def)
%            Number of atoms       :  101 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   93 (  35   ~;  53   |;   0   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    7 (   6 usr;   6 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   3 con; 0-2 aty)
%            Number of variables   :   33 (  33   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f213,plain,
    $false,
    inference(avatar_sat_refutation,[],[f96,f135,f164,f203,f205,f212]) ).

fof(f212,plain,
    ( spl0_3
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f211,f200,f61]) ).

fof(f61,plain,
    ( spl0_3
  <=> less_or_equal(half(epsilon_0),n0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f200,plain,
    ( spl0_7
  <=> less_or_equal(delta_1(half(epsilon_0)),n0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f211,plain,
    ( less_or_equal(half(epsilon_0),n0)
    | ~ spl0_7 ),
    inference(resolution,[],[f202,f6]) ).

fof(f6,axiom,
    ! [X3] :
      ( ~ less_or_equal(delta_1(X3),n0)
      | less_or_equal(X3,n0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).

fof(f202,plain,
    ( less_or_equal(delta_1(half(epsilon_0)),n0)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f200]) ).

fof(f205,plain,
    ( spl0_3
    | ~ spl0_1 ),
    inference(avatar_split_clause,[],[f204,f53,f61]) ).

fof(f53,plain,
    ( spl0_1
  <=> less_or_equal(delta_2(half(epsilon_0)),n0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f204,plain,
    ( less_or_equal(half(epsilon_0),n0)
    | ~ spl0_1 ),
    inference(resolution,[],[f55,f7]) ).

fof(f7,axiom,
    ! [X3] :
      ( ~ less_or_equal(delta_2(X3),n0)
      | less_or_equal(X3,n0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).

fof(f55,plain,
    ( less_or_equal(delta_2(half(epsilon_0)),n0)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f53]) ).

fof(f203,plain,
    ( spl0_1
    | spl0_7
    | ~ spl0_6 ),
    inference(avatar_split_clause,[],[f198,f161,f200,f53]) ).

fof(f161,plain,
    ( spl0_6
  <=> less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f198,plain,
    ( less_or_equal(delta_1(half(epsilon_0)),n0)
    | less_or_equal(delta_2(half(epsilon_0)),n0)
    | ~ spl0_6 ),
    inference(resolution,[],[f163,f3]) ).

fof(f3,axiom,
    ! [X2,X1] :
      ( ~ less_or_equal(minimum(X1,X2),n0)
      | less_or_equal(X1,n0)
      | less_or_equal(X2,n0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum9) ).

fof(f163,plain,
    ( less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f161]) ).

fof(f164,plain,
    ( spl0_3
    | spl0_6
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f159,f94,f161,f61]) ).

fof(f94,plain,
    ( spl0_4
  <=> ! [X6] :
        ( ~ less_or_equal(absolute(add(f(xs(minimum(delta_2(half(epsilon_0)),X6))),negate(f(a_real_number)))),half(epsilon_0))
        | less_or_equal(minimum(delta_2(half(epsilon_0)),X6),n0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f159,plain,
    ( less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)
    | less_or_equal(half(epsilon_0),n0)
    | ~ spl0_4 ),
    inference(duplicate_literal_removal,[],[f158]) ).

fof(f158,plain,
    ( less_or_equal(half(epsilon_0),n0)
    | less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)
    | less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)
    | ~ spl0_4 ),
    inference(resolution,[],[f95,f26]) ).

fof(f26,plain,
    ! [X6,X7] :
      ( less_or_equal(absolute(add(f(xs(minimum(X6,delta_1(X7)))),negate(f(a_real_number)))),X7)
      | less_or_equal(minimum(X6,delta_1(X7)),n0)
      | less_or_equal(X7,n0) ),
    inference(resolution,[],[f16,f8]) ).

fof(f8,axiom,
    ! [X3,X0] :
      ( ~ less_or_equal(absolute(add(X0,negate(a_real_number))),delta_1(X3))
      | less_or_equal(X3,n0)
      | less_or_equal(absolute(add(f(X0),negate(f(a_real_number)))),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).

fof(f16,plain,
    ! [X0,X1] :
      ( less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X1)
      | less_or_equal(minimum(X0,X1),n0) ),
    inference(resolution,[],[f2,f11]) ).

fof(f11,axiom,
    ! [X4] :
      ( less_or_equal(absolute(add(xs(X4),negate(a_real_number))),X4)
      | less_or_equal(X4,n0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).

fof(f2,axiom,
    ! [X2,X0,X1] :
      ( ~ less_or_equal(X0,minimum(X1,X2))
      | less_or_equal(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum7) ).

fof(f95,plain,
    ( ! [X6] :
        ( ~ less_or_equal(absolute(add(f(xs(minimum(delta_2(half(epsilon_0)),X6))),negate(f(a_real_number)))),half(epsilon_0))
        | less_or_equal(minimum(delta_2(half(epsilon_0)),X6),n0) )
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f94]) ).

fof(f135,plain,
    ~ spl0_3,
    inference(avatar_contradiction_clause,[],[f134]) ).

fof(f134,plain,
    ( $false
    | ~ spl0_3 ),
    inference(resolution,[],[f117,f10]) ).

fof(f10,axiom,
    ~ less_or_equal(epsilon_0,n0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).

fof(f117,plain,
    ( less_or_equal(epsilon_0,n0)
    | ~ spl0_3 ),
    inference(resolution,[],[f63,f5]) ).

fof(f5,axiom,
    ! [X1] :
      ( ~ less_or_equal(half(X1),n0)
      | less_or_equal(X1,n0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',zero_and_half) ).

fof(f63,plain,
    ( less_or_equal(half(epsilon_0),n0)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f61]) ).

fof(f96,plain,
    ( spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f92,f94,f61]) ).

fof(f92,plain,
    ! [X6] :
      ( ~ less_or_equal(absolute(add(f(xs(minimum(delta_2(half(epsilon_0)),X6))),negate(f(a_real_number)))),half(epsilon_0))
      | less_or_equal(half(epsilon_0),n0)
      | less_or_equal(minimum(delta_2(half(epsilon_0)),X6),n0) ),
    inference(duplicate_literal_removal,[],[f89]) ).

fof(f89,plain,
    ! [X6] :
      ( less_or_equal(minimum(delta_2(half(epsilon_0)),X6),n0)
      | less_or_equal(minimum(delta_2(half(epsilon_0)),X6),n0)
      | less_or_equal(half(epsilon_0),n0)
      | ~ less_or_equal(absolute(add(f(xs(minimum(delta_2(half(epsilon_0)),X6))),negate(f(a_real_number)))),half(epsilon_0)) ),
    inference(resolution,[],[f23,f19]) ).

fof(f19,plain,
    ! [X0] :
      ( ~ less_or_equal(absolute(add(g(xs(X0)),negate(g(a_real_number)))),half(epsilon_0))
      | ~ less_or_equal(absolute(add(f(xs(X0)),negate(f(a_real_number)))),half(epsilon_0))
      | less_or_equal(X0,n0) ),
    inference(resolution,[],[f12,f4]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( less_or_equal(add(X1,X2),X0)
      | ~ less_or_equal(X2,half(X0))
      | ~ less_or_equal(X1,half(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal_sum_of_halves) ).

fof(f12,axiom,
    ! [X4] :
      ( ~ less_or_equal(add(absolute(add(f(xs(X4)),negate(f(a_real_number)))),absolute(add(g(xs(X4)),negate(g(a_real_number))))),epsilon_0)
      | less_or_equal(X4,n0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7_2) ).

fof(f23,plain,
    ! [X8,X9] :
      ( less_or_equal(absolute(add(g(xs(minimum(delta_2(X8),X9))),negate(g(a_real_number)))),X8)
      | less_or_equal(minimum(delta_2(X8),X9),n0)
      | less_or_equal(X8,n0) ),
    inference(resolution,[],[f15,f9]) ).

fof(f9,axiom,
    ! [X3,X0] :
      ( ~ less_or_equal(absolute(add(X0,negate(a_real_number))),delta_2(X3))
      | less_or_equal(absolute(add(g(X0),negate(g(a_real_number)))),X3)
      | less_or_equal(X3,n0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).

fof(f15,plain,
    ! [X0,X1] :
      ( less_or_equal(absolute(add(xs(minimum(X0,X1)),negate(a_real_number))),X0)
      | less_or_equal(minimum(X0,X1),n0) ),
    inference(resolution,[],[f1,f11]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ less_or_equal(X0,minimum(X1,X2))
      | less_or_equal(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',minimum3) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : ANA003-4 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 29 15:26:00 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 1.47/0.56  % (6832)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.47/0.57  % (6825)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)
% 1.47/0.57  % (6817)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.47/0.58  % (6843)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.47/0.58  % (6835)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.47/0.58  % (6814)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.85/0.59  TRYING [1]
% 1.85/0.59  TRYING [2]
% 1.85/0.59  % (6821)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.85/0.59  % (6820)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.85/0.60  % (6843)First to succeed.
% 1.85/0.61  % (6819)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.85/0.61  % (6816)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.85/0.61  % (6843)Refutation found. Thanks to Tanya!
% 1.85/0.61  % SZS status Unsatisfiable for theBenchmark
% 1.85/0.61  % SZS output start Proof for theBenchmark
% See solution above
% 1.85/0.61  % (6843)------------------------------
% 1.85/0.61  % (6843)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.85/0.61  % (6843)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.85/0.61  % (6843)Termination reason: Refutation
% 1.85/0.61  
% 1.85/0.61  % (6843)Memory used [KB]: 5756
% 1.85/0.61  % (6843)Time elapsed: 0.172 s
% 1.85/0.61  % (6843)Instructions burned: 13 (million)
% 1.85/0.61  % (6843)------------------------------
% 1.85/0.61  % (6843)------------------------------
% 1.85/0.61  % (6813)Success in time 0.26 s
%------------------------------------------------------------------------------