TSTP Solution File: SET592+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n008.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 18:25:00 EDT 2022

% Result   : Theorem 0.20s 0.48s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (   9 unt;   0 def)
%            Number of atoms       :   77 (  26 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   72 (  24   ~;  15   |;  26   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   44 (  32   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f139,plain,
    $false,
    inference(subsumption_resolution,[],[f137,f57]) ).

fof(f57,plain,
    empty_set != sK2,
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ( empty_set != sK2
    & subset(sK2,sK4)
    & subset(sK2,sK3)
    & empty_set = intersection(sK4,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f34,f35]) ).

fof(f35,plain,
    ( ? [X0,X1,X2] :
        ( empty_set != X0
        & subset(X0,X2)
        & subset(X0,X1)
        & empty_set = intersection(X2,X1) )
   => ( empty_set != sK2
      & subset(sK2,sK4)
      & subset(sK2,sK3)
      & empty_set = intersection(sK4,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ? [X0,X1,X2] :
      ( empty_set != X0
      & subset(X0,X2)
      & subset(X0,X1)
      & empty_set = intersection(X2,X1) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ? [X2,X1,X0] :
      ( empty_set != X2
      & subset(X2,X0)
      & subset(X2,X1)
      & empty_set = intersection(X0,X1) ),
    inference(flattening,[],[f21]) ).

fof(f21,plain,
    ? [X1,X0,X2] :
      ( empty_set != X2
      & empty_set = intersection(X0,X1)
      & subset(X2,X0)
      & subset(X2,X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ~ ! [X1,X0,X2] :
        ( ( empty_set = intersection(X0,X1)
          & subset(X2,X0)
          & subset(X2,X1) )
       => empty_set = X2 ),
    inference(rectify,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X1,X2,X0] :
        ( ( subset(X0,X2)
          & subset(X0,X1)
          & empty_set = intersection(X1,X2) )
       => empty_set = X0 ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X1,X2,X0] :
      ( ( subset(X0,X2)
        & subset(X0,X1)
        & empty_set = intersection(X1,X2) )
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th51) ).

fof(f137,plain,
    empty_set = sK2,
    inference(resolution,[],[f127,f46]) ).

fof(f46,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | empty_set = X0 ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( subset(X0,empty_set)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_empty_set_is_empty_set) ).

fof(f127,plain,
    subset(sK2,empty_set),
    inference(subsumption_resolution,[],[f124,f55]) ).

fof(f55,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f36]) ).

fof(f124,plain,
    ( subset(sK2,empty_set)
    | ~ subset(sK2,sK3) ),
    inference(resolution,[],[f123,f56]) ).

fof(f56,plain,
    subset(sK2,sK4),
    inference(cnf_transformation,[],[f36]) ).

fof(f123,plain,
    ! [X0] :
      ( ~ subset(X0,sK4)
      | subset(X0,empty_set)
      | ~ subset(X0,sK3) ),
    inference(forward_demodulation,[],[f119,f69]) ).

fof(f69,plain,
    empty_set = sF5,
    inference(definition_folding,[],[f54,f68]) ).

fof(f68,plain,
    sF5 = intersection(sK4,sK3),
    introduced(function_definition,[]) ).

fof(f54,plain,
    empty_set = intersection(sK4,sK3),
    inference(cnf_transformation,[],[f36]) ).

fof(f119,plain,
    ! [X0] :
      ( subset(X0,sF5)
      | ~ subset(X0,sK4)
      | ~ subset(X0,sK3) ),
    inference(superposition,[],[f42,f68]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( subset(X2,intersection(X0,X1))
      | ~ subset(X2,X1)
      | ~ subset(X2,X0) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X2,X0)
      | ~ subset(X2,X1)
      | subset(X2,intersection(X0,X1)) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X2,X1,X0] :
      ( ~ subset(X0,X2)
      | ~ subset(X0,X1)
      | subset(X0,intersection(X2,X1)) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ! [X1,X0,X2] :
      ( subset(X0,intersection(X2,X1))
      | ~ subset(X0,X1)
      | ~ subset(X0,X2) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X1,X0,X2] :
      ( ( subset(X0,X1)
        & subset(X0,X2) )
     => subset(X0,intersection(X2,X1)) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X2,X1] :
      ( ( subset(X0,X2)
        & subset(X0,X1) )
     => subset(X0,intersection(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subsets) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33  % Computer : n008.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 30 14:04:55 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  % (22108)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.47  % (22092)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.47  % (22092)First to succeed.
% 0.20/0.48  % (22101)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.48  % (22092)Refutation found. Thanks to Tanya!
% 0.20/0.48  % SZS status Theorem for theBenchmark
% 0.20/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.48  % (22092)------------------------------
% 0.20/0.48  % (22092)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48  % (22092)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48  % (22092)Termination reason: Refutation
% 0.20/0.48  
% 0.20/0.48  % (22092)Memory used [KB]: 5500
% 0.20/0.48  % (22092)Time elapsed: 0.092 s
% 0.20/0.48  % (22092)Instructions burned: 2 (million)
% 0.20/0.48  % (22092)------------------------------
% 0.20/0.48  % (22092)------------------------------
% 0.20/0.48  % (22079)Success in time 0.138 s
%------------------------------------------------------------------------------