TSTP Solution File: SET002+4 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET002+4 : 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 : n003.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 18:23:00 EDT 2022

% Result   : Theorem 0.19s 0.48s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   42 (  11 unt;   0 def)
%            Number of atoms       :  112 (   1 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  116 (  46   ~;  43   |;  16   &)
%                                         (   6 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   69 (  64   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f258,plain,
    $false,
    inference(subsumption_resolution,[],[f255,f144]) ).

fof(f144,plain,
    subset(sK2,sF4),
    inference(duplicate_literal_removal,[],[f143]) ).

fof(f143,plain,
    ( subset(sK2,sF4)
    | subset(sK2,sF4) ),
    inference(resolution,[],[f131,f87]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( member(sK3(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( member(sK3(X0,X1),X1)
          & ~ member(sK3(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f58,f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X1)
          & ~ member(X3,X0) )
     => ( member(sK3(X0,X1),X1)
        & ~ member(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X0) ) ) ),
    inference(rectify,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( member(X2,X1)
            & ~ member(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ member(X2,X1)
          | member(X2,X0) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).

fof(f131,plain,
    ! [X0] :
      ( ~ member(sK3(sF4,X0),sK2)
      | subset(X0,sF4) ),
    inference(resolution,[],[f95,f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ~ member(sK3(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f95,plain,
    ! [X0] :
      ( member(X0,sF4)
      | ~ member(X0,sK2) ),
    inference(superposition,[],[f83,f92]) ).

fof(f92,plain,
    union(sK2,sK2) = sF4,
    introduced(function_definition,[]) ).

fof(f83,plain,
    ! [X2,X0,X1] :
      ( member(X1,union(X2,X0))
      | ~ member(X1,X2) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( ( member(X1,X0)
        | member(X1,X2)
        | ~ member(X1,union(X2,X0)) )
      & ( member(X1,union(X2,X0))
        | ( ~ member(X1,X0)
          & ~ member(X1,X2) ) ) ),
    inference(rectify,[],[f55]) ).

fof(f55,plain,
    ! [X1,X0,X2] :
      ( ( member(X0,X1)
        | member(X0,X2)
        | ~ member(X0,union(X2,X1)) )
      & ( member(X0,union(X2,X1))
        | ( ~ member(X0,X1)
          & ~ member(X0,X2) ) ) ),
    inference(flattening,[],[f54]) ).

fof(f54,plain,
    ! [X1,X0,X2] :
      ( ( member(X0,X1)
        | member(X0,X2)
        | ~ member(X0,union(X2,X1)) )
      & ( member(X0,union(X2,X1))
        | ( ~ member(X0,X1)
          & ~ member(X0,X2) ) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0,X2] :
      ( ( member(X0,X1)
        | member(X0,X2) )
    <=> member(X0,union(X2,X1)) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X2,X1,X0] :
      ( ( member(X2,X0)
        | member(X2,X1) )
    <=> member(X2,union(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).

fof(f255,plain,
    ~ subset(sK2,sF4),
    inference(resolution,[],[f246,f120]) ).

fof(f120,plain,
    ( ~ subset(sF4,sK2)
    | ~ subset(sK2,sF4) ),
    inference(resolution,[],[f72,f93]) ).

fof(f93,plain,
    ~ equal_set(sF4,sK2),
    inference(definition_folding,[],[f82,f92]) ).

fof(f82,plain,
    ~ equal_set(union(sK2,sK2),sK2),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ~ equal_set(union(sK2,sK2),sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f26,f52]) ).

fof(f52,plain,
    ( ? [X0] : ~ equal_set(union(X0,X0),X0)
   => ~ equal_set(union(sK2,sK2),sK2) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0] : ~ equal_set(union(X0,X0),X0),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0] : equal_set(union(X0,X0),X0),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0] : equal_set(union(X0,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI14) ).

fof(f72,plain,
    ! [X0,X1] :
      ( equal_set(X1,X0)
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X1,X0) ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ! [X1,X0] :
      ( ~ subset(X0,X1)
      | ~ subset(X1,X0)
      | equal_set(X0,X1) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ! [X1,X0] :
      ( equal_set(X0,X1)
      | ~ subset(X0,X1)
      | ~ subset(X1,X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

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

fof(f246,plain,
    subset(sF4,sK2),
    inference(duplicate_literal_removal,[],[f242]) ).

fof(f242,plain,
    ( subset(sF4,sK2)
    | subset(sF4,sK2) ),
    inference(resolution,[],[f197,f86]) ).

fof(f197,plain,
    ! [X2] :
      ( member(sK3(X2,sF4),sK2)
      | subset(sF4,X2) ),
    inference(resolution,[],[f194,f87]) ).

fof(f194,plain,
    ! [X0] :
      ( ~ member(X0,sF4)
      | member(X0,sK2) ),
    inference(duplicate_literal_removal,[],[f193]) ).

fof(f193,plain,
    ! [X0] :
      ( member(X0,sK2)
      | ~ member(X0,sF4)
      | member(X0,sK2) ),
    inference(superposition,[],[f85,f92]) ).

fof(f85,plain,
    ! [X2,X0,X1] :
      ( ~ member(X1,union(X2,X0))
      | member(X1,X0)
      | member(X1,X2) ),
    inference(cnf_transformation,[],[f56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET002+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13  % 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 : n003.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   : Tue Aug 30 12:50:52 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.46  % (18984)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.46  % (18992)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.47  % (18984)Instruction limit reached!
% 0.19/0.47  % (18984)------------------------------
% 0.19/0.47  % (18984)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.47  % (18984)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.47  % (18984)Termination reason: Unknown
% 0.19/0.47  % (18984)Termination phase: Saturation
% 0.19/0.47  
% 0.19/0.47  % (18984)Memory used [KB]: 5500
% 0.19/0.47  % (18984)Time elapsed: 0.071 s
% 0.19/0.47  % (18984)Instructions burned: 7 (million)
% 0.19/0.47  % (18984)------------------------------
% 0.19/0.47  % (18984)------------------------------
% 0.19/0.48  % (18992)First to succeed.
% 0.19/0.48  % (18992)Refutation found. Thanks to Tanya!
% 0.19/0.48  % SZS status Theorem for theBenchmark
% 0.19/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48  % (18992)------------------------------
% 0.19/0.48  % (18992)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48  % (18992)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48  % (18992)Termination reason: Refutation
% 0.19/0.48  
% 0.19/0.48  % (18992)Memory used [KB]: 1023
% 0.19/0.48  % (18992)Time elapsed: 0.083 s
% 0.19/0.48  % (18992)Instructions burned: 8 (million)
% 0.19/0.48  % (18992)------------------------------
% 0.19/0.48  % (18992)------------------------------
% 0.19/0.48  % (18976)Success in time 0.129 s
%------------------------------------------------------------------------------