TSTP Solution File: ANA140_1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : ANA140_1 : TPTP v8.2.0. Released v8.2.0.
% 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 : n026.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 : Mon May 22 15:23:11 EDT 2023

% Result   : Theorem 1.26s 0.65s
% Output   : Refutation 1.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   25 (   5 unt;   3 typ;   0 def)
%            Number of atoms       :  134 (  10 equ)
%            Maximal formula atoms :   22 (   6 avg)
%            Number of connectives :  177 (  65   ~;  40   |;  52   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number arithmetic     :  430 ( 123 atm; 204 fun;  76 num;  27 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   3 usr;   3 con; 0-2 aty)
%            Number of variables   :   27 (;  16   !;  11   ?;  27   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_0,type,
    a: $real ).

tff(func_def_6,type,
    sK0: $real ).

tff(func_def_7,type,
    sK1: $real > $real ).

tff(f42,plain,
    $false,
    inference(subsumption_resolution,[],[f41,f35]) ).

tff(f35,plain,
    $less($sum(sK1(sK0),$uminus(a)),0.0),
    inference(subsumption_resolution,[],[f34,f20]) ).

tff(f20,plain,
    $less(0.0,sK0),
    inference(cnf_transformation,[],[f19]) ).

tff(f19,plain,
    ( ! [X1: $real] :
        ( ~ $less(0.0,X1)
        | ( ( $less($uminus($sum(sK1(X1),$uminus(a))),X1)
            | ~ $less($sum(sK1(X1),$uminus(a)),0.0) )
          & ( a != sK1(X1) )
          & ( ( ~ $less($uminus($sum(sK1(X1),$uminus(a))),sK0)
              & $less($sum(sK1(X1),$uminus(a)),0.0) )
            | ( ~ $less($sum(sK1(X1),$uminus(a)),sK0)
              & ~ $less($sum(sK1(X1),$uminus(a)),0.0) ) )
          & ( $less($sum(sK1(X1),$uminus(a)),X1)
            | $less($sum(sK1(X1),$uminus(a)),0.0) ) ) )
    & $less(0.0,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f18,f17]) ).

tff(f17,plain,
    ( ? [X0: $real] :
        ( ! [X1: $real] :
            ( ~ $less(0.0,X1)
            | ? [X2: $real] :
                ( ( $less($uminus($sum(X2,$uminus(a))),X1)
                  | ~ $less($sum(X2,$uminus(a)),0.0) )
                & ( a != X2 )
                & ( ( ~ $less($uminus($sum(X2,$uminus(a))),X0)
                    & $less($sum(X2,$uminus(a)),0.0) )
                  | ( ~ $less($sum(X2,$uminus(a)),X0)
                    & ~ $less($sum(X2,$uminus(a)),0.0) ) )
                & ( $less($sum(X2,$uminus(a)),X1)
                  | $less($sum(X2,$uminus(a)),0.0) ) ) )
        & $less(0.0,X0) )
   => ( ! [X1: $real] :
          ( ~ $less(0.0,X1)
          | ? [X2: $real] :
              ( ( $less($uminus($sum(X2,$uminus(a))),X1)
                | ~ $less($sum(X2,$uminus(a)),0.0) )
              & ( a != X2 )
              & ( ( ~ $less($uminus($sum(X2,$uminus(a))),sK0)
                  & $less($sum(X2,$uminus(a)),0.0) )
                | ( ~ $less($sum(X2,$uminus(a)),sK0)
                  & ~ $less($sum(X2,$uminus(a)),0.0) ) )
              & ( $less($sum(X2,$uminus(a)),X1)
                | $less($sum(X2,$uminus(a)),0.0) ) ) )
      & $less(0.0,sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f18,plain,
    ! [X1: $real] :
      ( ? [X2: $real] :
          ( ( $less($uminus($sum(X2,$uminus(a))),X1)
            | ~ $less($sum(X2,$uminus(a)),0.0) )
          & ( a != X2 )
          & ( ( ~ $less($uminus($sum(X2,$uminus(a))),sK0)
              & $less($sum(X2,$uminus(a)),0.0) )
            | ( ~ $less($sum(X2,$uminus(a)),sK0)
              & ~ $less($sum(X2,$uminus(a)),0.0) ) )
          & ( $less($sum(X2,$uminus(a)),X1)
            | $less($sum(X2,$uminus(a)),0.0) ) )
     => ( ( $less($uminus($sum(sK1(X1),$uminus(a))),X1)
          | ~ $less($sum(sK1(X1),$uminus(a)),0.0) )
        & ( a != sK1(X1) )
        & ( ( ~ $less($uminus($sum(sK1(X1),$uminus(a))),sK0)
            & $less($sum(sK1(X1),$uminus(a)),0.0) )
          | ( ~ $less($sum(sK1(X1),$uminus(a)),sK0)
            & ~ $less($sum(sK1(X1),$uminus(a)),0.0) ) )
        & ( $less($sum(sK1(X1),$uminus(a)),X1)
          | $less($sum(sK1(X1),$uminus(a)),0.0) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f16,plain,
    ? [X0: $real] :
      ( ! [X1: $real] :
          ( ~ $less(0.0,X1)
          | ? [X2: $real] :
              ( ( $less($uminus($sum(X2,$uminus(a))),X1)
                | ~ $less($sum(X2,$uminus(a)),0.0) )
              & ( a != X2 )
              & ( ( ~ $less($uminus($sum(X2,$uminus(a))),X0)
                  & $less($sum(X2,$uminus(a)),0.0) )
                | ( ~ $less($sum(X2,$uminus(a)),X0)
                  & ~ $less($sum(X2,$uminus(a)),0.0) ) )
              & ( $less($sum(X2,$uminus(a)),X1)
                | $less($sum(X2,$uminus(a)),0.0) ) ) )
      & $less(0.0,X0) ),
    inference(flattening,[],[f15]) ).

tff(f15,plain,
    ? [X0: $real] :
      ( ! [X1: $real] :
          ( ? [X2: $real] :
              ( ( ( ~ $less($uminus($sum(X2,$uminus(a))),X0)
                  & $less($sum(X2,$uminus(a)),0.0) )
                | ( ~ $less($sum(X2,$uminus(a)),X0)
                  & ~ $less($sum(X2,$uminus(a)),0.0) ) )
              & ( a != X2 )
              & ( $less($sum(X2,$uminus(a)),X1)
                | $less($sum(X2,$uminus(a)),0.0) )
              & ( $less($uminus($sum(X2,$uminus(a))),X1)
                | ~ $less($sum(X2,$uminus(a)),0.0) ) )
          | ~ $less(0.0,X1) )
      & $less(0.0,X0) ),
    inference(ennf_transformation,[],[f3]) ).

tff(f3,plain,
    ~ ! [X0: $real] :
        ( $less(0.0,X0)
       => ? [X1: $real] :
            ( ! [X2: $real] :
                ( ( ( a != X2 )
                  & ( ~ $less($sum(X2,$uminus(a)),0.0)
                   => $less($sum(X2,$uminus(a)),X1) )
                  & ( $less($sum(X2,$uminus(a)),0.0)
                   => $less($uminus($sum(X2,$uminus(a))),X1) ) )
               => ( ( ~ $less($sum(X2,$uminus(a)),0.0)
                   => $less($sum(X2,$uminus(a)),X0) )
                  & ( $less($sum(X2,$uminus(a)),0.0)
                   => $less($uminus($sum(X2,$uminus(a))),X0) ) ) )
            & $less(0.0,X1) ) ),
    inference(theory_normalization,[],[f2]) ).

tff(f2,negated_conjecture,
    ~ ! [X0: $real] :
        ( $less(0.0,X0)
       => ? [X1: $real] :
            ( ! [X2: $real] :
                ( ( ( a != X2 )
                  & ( $greatereq($difference(X2,a),0.0)
                   => $less($difference(X2,a),X1) )
                  & ( ~ $greatereq($difference(X2,a),0.0)
                   => $less($uminus($difference(X2,a)),X1) ) )
               => ( ( ~ $greatereq($difference(X2,a),0.0)
                   => $less($uminus($difference(X2,a)),X0) )
                  & ( $greatereq($difference(X2,a),0.0)
                   => $less($difference(X2,a),X0) ) ) )
            & $less(0.0,X1) ) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ! [X0: $real] :
      ( $less(0.0,X0)
     => ? [X1: $real] :
          ( ! [X2: $real] :
              ( ( ( a != X2 )
                & ( $greatereq($difference(X2,a),0.0)
                 => $less($difference(X2,a),X1) )
                & ( ~ $greatereq($difference(X2,a),0.0)
                 => $less($uminus($difference(X2,a)),X1) ) )
             => ( ( ~ $greatereq($difference(X2,a),0.0)
                 => $less($uminus($difference(X2,a)),X0) )
                & ( $greatereq($difference(X2,a),0.0)
                 => $less($difference(X2,a),X0) ) ) )
          & $less(0.0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_1) ).

tff(f34,plain,
    ( ~ $less(0.0,sK0)
    | $less($sum(sK1(sK0),$uminus(a)),0.0) ),
    inference(duplicate_literal_removal,[],[f33]) ).

tff(f33,plain,
    ( ~ $less(0.0,sK0)
    | $less($sum(sK1(sK0),$uminus(a)),0.0)
    | $less($sum(sK1(sK0),$uminus(a)),0.0) ),
    inference(resolution,[],[f29,f23]) ).

tff(f23,plain,
    ! [X1: $real] :
      ( ~ $less($sum(sK1(X1),$uminus(a)),sK0)
      | ~ $less(0.0,X1)
      | $less($sum(sK1(X1),$uminus(a)),0.0) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f29,plain,
    ( $less($sum(sK1(sK0),$uminus(a)),sK0)
    | $less($sum(sK1(sK0),$uminus(a)),0.0) ),
    inference(resolution,[],[f21,f20]) ).

tff(f21,plain,
    ! [X1: $real] :
      ( ~ $less(0.0,X1)
      | $less($sum(sK1(X1),$uminus(a)),0.0)
      | $less($sum(sK1(X1),$uminus(a)),X1) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f41,plain,
    ~ $less($sum(sK1(sK0),$uminus(a)),0.0),
    inference(subsumption_resolution,[],[f39,f20]) ).

tff(f39,plain,
    ( ~ $less(0.0,sK0)
    | ~ $less($sum(sK1(sK0),$uminus(a)),0.0) ),
    inference(resolution,[],[f37,f24]) ).

tff(f24,plain,
    ! [X1: $real] :
      ( ~ $less($uminus($sum(sK1(X1),$uminus(a))),sK0)
      | ~ $less(0.0,X1)
      | ~ $less($sum(sK1(X1),$uminus(a)),0.0) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f37,plain,
    $less($uminus($sum(sK1(sK0),$uminus(a))),sK0),
    inference(subsumption_resolution,[],[f36,f20]) ).

tff(f36,plain,
    ( $less($uminus($sum(sK1(sK0),$uminus(a))),sK0)
    | ~ $less(0.0,sK0) ),
    inference(resolution,[],[f35,f27]) ).

tff(f27,plain,
    ! [X1: $real] :
      ( ~ $less($sum(sK1(X1),$uminus(a)),0.0)
      | ~ $less(0.0,X1)
      | $less($uminus($sum(sK1(X1),$uminus(a))),X1) ),
    inference(cnf_transformation,[],[f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : ANA140_1 : TPTP v8.2.0. Released v8.2.0.
% 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 : n026.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 May 22 11:13:38 EDT 2023
% 0.12/0.34  % CPUTime    : 
% 0.12/0.36  ipcrm: permission denied for id (869859331)
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% 0.19/0.50  ipcrm: permission denied for id (873005179)
% 1.08/0.63  % (16879)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 (2998ds/37Mi)
% 1.26/0.65  % (16879)First to succeed.
% 1.26/0.65  % (16879)Refutation found. Thanks to Tanya!
% 1.26/0.65  % SZS status Theorem for theBenchmark
% 1.26/0.65  % SZS output start Proof for theBenchmark
% See solution above
% 1.26/0.65  % (16879)------------------------------
% 1.26/0.65  % (16879)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.26/0.65  % (16879)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.26/0.65  % (16879)Termination reason: Refutation
% 1.26/0.65  
% 1.26/0.65  % (16879)Memory used [KB]: 895
% 1.26/0.65  % (16879)Time elapsed: 0.102 s
% 1.26/0.65  % (16879)Instructions burned: 2 (million)
% 1.26/0.65  % (16879)------------------------------
% 1.26/0.65  % (16879)------------------------------
% 1.26/0.65  % (16742)Success in time 0.3 s
%------------------------------------------------------------------------------