%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU161+2 : TPTP v8.1.0. Released v3.3.0.
% 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 18:32:14 EDT 2022

% Result   : Theorem 1.65s 0.58s
% Output   : Refutation 1.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   29 (  12 unt;   0 def)
%            Number of atoms       :   52 (  21 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   42 (  19   ~;  10   |;   6   &)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   33 (  29   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1139,plain,
    $false,
    inference(subsumption_resolution,[],[f1125,f528]) ).

fof(f528,plain,
    sK20 != sF24,
    inference(definition_folding,[],[f487,f527,f526]) ).

fof(f526,plain,
    unordered_pair(sK21,sK21) = sF23,
    introduced(function_definition,[]) ).

fof(f527,plain,
    set_union2(sF23,sK20) = sF24,
    introduced(function_definition,[]) ).

fof(f487,plain,
    sK20 != set_union2(unordered_pair(sK21,sK21),sK20),
    inference(definition_unfolding,[],[f424,f336]) ).

fof(f336,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

fof(f424,plain,
    sK20 != set_union2(singleton(sK21),sK20),
    inference(cnf_transformation,[],[f285]) ).

fof(f285,plain,
    ( sK20 != set_union2(singleton(sK21),sK20)
    & in(sK21,sK20) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f159,f284]) ).

fof(f284,plain,
    ( ? [X0,X1] :
        ( set_union2(singleton(X1),X0) != X0
        & in(X1,X0) )
   => ( sK20 != set_union2(singleton(sK21),sK20)
      & in(sK21,sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ? [X0,X1] :
      ( set_union2(singleton(X1),X0) != X0
      & in(X1,X0) ),
    inference(ennf_transformation,[],[f117]) ).

fof(f117,plain,
    ~ ! [X1,X0] :
        ( in(X1,X0)
       => set_union2(singleton(X1),X0) = X0 ),
    inference(rectify,[],[f77]) ).

fof(f77,negated_conjecture,
    ~ ! [X1,X0] :
        ( in(X0,X1)
       => set_union2(singleton(X0),X1) = X1 ),
    inference(negated_conjecture,[],[f76]) ).

fof(f76,conjecture,
    ! [X1,X0] :
      ( in(X0,X1)
     => set_union2(singleton(X0),X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).

fof(f1125,plain,
    sK20 = sF24,
    inference(superposition,[],[f527,f1096]) ).

fof(f1096,plain,
    set_union2(sF23,sK20) = sK20,
    inference(resolution,[],[f1084,f327]) ).

fof(f327,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_union2(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f204]) ).

fof(f204,plain,
    ! [X0,X1] :
      ( set_union2(X0,X1) = X1
      | ~ subset(X0,X1) ),
    inference(rectify,[],[f139]) ).

fof(f139,plain,
    ! [X1,X0] :
      ( set_union2(X1,X0) = X0
      | ~ subset(X1,X0) ),
    inference(ennf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
     => set_union2(X1,X0) = X0 ),
    inference(rectify,[],[f52]) ).

fof(f52,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
     => set_union2(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(f1084,plain,
    subset(sF23,sK20),
    inference(resolution,[],[f1077,f423]) ).

fof(f423,plain,
    in(sK21,sK20),
    inference(cnf_transformation,[],[f285]) ).

fof(f1077,plain,
    ! [X0] :
      ( ~ in(sK21,X0)
      | subset(sF23,X0) ),
    inference(superposition,[],[f460,f526]) ).

fof(f460,plain,
    ! [X0,X1] :
      ( subset(unordered_pair(X1,X1),X0)
      | ~ in(X1,X0) ),
    inference(definition_unfolding,[],[f337,f336]) ).

fof(f337,plain,
    ! [X0,X1] :
      ( subset(singleton(X1),X0)
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[],[f210]) ).

fof(f210,plain,
    ! [X0,X1] :
      ( ( in(X1,X0)
        | ~ subset(singleton(X1),X0) )
      & ( subset(singleton(X1),X0)
        | ~ in(X1,X0) ) ),
    inference(rectify,[],[f209]) ).

fof(f209,plain,
    ! [X1,X0] :
      ( ( in(X0,X1)
        | ~ subset(singleton(X0),X1) )
      & ( subset(singleton(X0),X1)
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f67]) ).

fof(f67,axiom,
    ! [X1,X0] :
      ( in(X0,X1)
    <=> subset(singleton(X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU161+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 14:47:10 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.52  % (5656)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)
% 0.21/0.53  % (5664)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.65/0.57  % (5664)First to succeed.
% 1.65/0.58  % (5664)Refutation found. Thanks to Tanya!
% 1.65/0.58  % SZS status Theorem for theBenchmark
% 1.65/0.58  % SZS output start Proof for theBenchmark
% See solution above
% 1.65/0.58  % (5664)------------------------------
% 1.65/0.58  % (5664)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.58  % (5664)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.58  % (5664)Termination reason: Refutation
% 1.65/0.58  
% 1.65/0.58  % (5664)Memory used [KB]: 5884
% 1.65/0.58  % (5664)Time elapsed: 0.133 s
% 1.65/0.58  % (5664)Instructions burned: 26 (million)
% 1.65/0.58  % (5664)------------------------------
% 1.65/0.58  % (5664)------------------------------
% 1.65/0.58  % (5650)Success in time 0.218 s
%------------------------------------------------------------------------------