TSTP Solution File: SEU153+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU153+1 : 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 : n006.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 18:32:11 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   47 (  12 unt;   0 def)
%            Number of atoms       :  187 (  51 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  221 (  81   ~;  82   |;  47   &)
%                                         (   6 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :   97 (  81   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f148,plain,
    $false,
    inference(subsumption_resolution,[],[f147,f71]) ).

fof(f71,plain,
    ! [X1] : ~ in(X1,empty_set),
    inference(equality_resolution,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | in(sK5(X0),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f36,f37]) ).

fof(f37,plain,
    ! [X0] :
      ( ? [X2] : in(X2,X0)
     => in(sK5(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | ? [X2] : in(X2,X0) ) ),
    inference(rectify,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | ? [X1] : in(X1,X0) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ! [X1] : ~ in(X1,X0)
    <=> empty_set = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(f147,plain,
    in(sK2,empty_set),
    inference(forward_demodulation,[],[f146,f105]) ).

fof(f105,plain,
    empty_set = set_intersection2(sK1,sF7),
    inference(resolution,[],[f57,f78]) ).

fof(f78,plain,
    disjoint(sK1,sF7),
    inference(resolution,[],[f46,f76]) ).

fof(f76,plain,
    disjoint(sF7,sK1),
    inference(definition_folding,[],[f47,f75]) ).

fof(f75,plain,
    singleton(sK2) = sF7,
    introduced(function_definition,[]) ).

fof(f47,plain,
    disjoint(singleton(sK2),sK1),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ( in(sK2,sK1)
    & disjoint(singleton(sK2),sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f25,f26]) ).

fof(f26,plain,
    ( ? [X0,X1] :
        ( in(X1,X0)
        & disjoint(singleton(X1),X0) )
   => ( in(sK2,sK1)
      & disjoint(singleton(sK2),sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ? [X0,X1] :
      ( in(X1,X0)
      & disjoint(singleton(X1),X0) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ? [X1,X0] :
      ( in(X0,X1)
      & disjoint(singleton(X0),X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X1,X0] :
        ~ ( in(X0,X1)
          & disjoint(singleton(X0),X1) ),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X1,X0] :
      ~ ( in(X0,X1)
        & disjoint(singleton(X0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ~ disjoint(X1,X0)
      | disjoint(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ~ disjoint(X1,X0)
      | disjoint(X0,X1) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1,X0] :
      ( ~ disjoint(X0,X1)
      | disjoint(X1,X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X1,X0] :
      ( disjoint(X0,X1)
     => disjoint(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | set_intersection2(X0,X1) = empty_set ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( set_intersection2(X0,X1) = empty_set
        | ~ disjoint(X0,X1) )
      & ( disjoint(X0,X1)
        | set_intersection2(X0,X1) != empty_set ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) = empty_set
    <=> disjoint(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).

fof(f146,plain,
    in(sK2,set_intersection2(sK1,sF7)),
    inference(forward_demodulation,[],[f145,f75]) ).

fof(f145,plain,
    in(sK2,set_intersection2(sK1,singleton(sK2))),
    inference(resolution,[],[f139,f69]) ).

fof(f69,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f68]) ).

fof(f68,plain,
    ! [X3,X0] :
      ( in(X3,X0)
      | singleton(X3) != X0 ),
    inference(equality_resolution,[],[f52]) ).

fof(f52,plain,
    ! [X3,X0,X1] :
      ( in(X3,X0)
      | X1 != X3
      | singleton(X1) != X0 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( singleton(X1) = X0
        | ( ( sK4(X0,X1) != X1
            | ~ in(sK4(X0,X1),X0) )
          & ( sK4(X0,X1) = X1
            | in(sK4(X0,X1),X0) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X0)
              | X1 != X3 )
            & ( X1 = X3
              | ~ in(X3,X0) ) )
        | singleton(X1) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f31,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X1 != X2
            | ~ in(X2,X0) )
          & ( X1 = X2
            | in(X2,X0) ) )
     => ( ( sK4(X0,X1) != X1
          | ~ in(sK4(X0,X1),X0) )
        & ( sK4(X0,X1) = X1
          | in(sK4(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( singleton(X1) = X0
        | ? [X2] :
            ( ( X1 != X2
              | ~ in(X2,X0) )
            & ( X1 = X2
              | in(X2,X0) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X0)
              | X1 != X3 )
            & ( X1 = X3
              | ~ in(X3,X0) ) )
        | singleton(X1) != X0 ) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ! [X1,X0] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f139,plain,
    ! [X2] :
      ( ~ in(sK2,X2)
      | in(sK2,set_intersection2(sK1,X2)) ),
    inference(resolution,[],[f72,f48]) ).

fof(f48,plain,
    in(sK2,sK1),
    inference(cnf_transformation,[],[f27]) ).

fof(f72,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,X1)
      | ~ in(X4,X0)
      | in(X4,set_intersection2(X1,X0)) ),
    inference(equality_resolution,[],[f62]) ).

fof(f62,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X1)
      | ~ in(X4,X0)
      | set_intersection2(X1,X0) != X2 ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X1,X0) = X2
        | ( ( ~ in(sK6(X0,X1,X2),X1)
            | ~ in(sK6(X0,X1,X2),X0)
            | ~ in(sK6(X0,X1,X2),X2) )
          & ( ( in(sK6(X0,X1,X2),X1)
              & in(sK6(X0,X1,X2),X0) )
            | in(sK6(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X1,X0) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f41,f42]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ~ in(X3,X0)
            | ~ in(X3,X2) )
          & ( ( in(X3,X1)
              & in(X3,X0) )
            | in(X3,X2) ) )
     => ( ( ~ in(sK6(X0,X1,X2),X1)
          | ~ in(sK6(X0,X1,X2),X0)
          | ~ in(sK6(X0,X1,X2),X2) )
        & ( ( in(sK6(X0,X1,X2),X1)
            & in(sK6(X0,X1,X2),X0) )
          | in(sK6(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X1,X0) = X2
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ~ in(X3,X0)
              | ~ in(X3,X2) )
            & ( ( in(X3,X1)
                & in(X3,X0) )
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ in(X4,X1)
              | ~ in(X4,X0) )
            & ( ( in(X4,X1)
                & in(X4,X0) )
              | ~ in(X4,X2) ) )
        | set_intersection2(X1,X0) != X2 ) ),
    inference(rectify,[],[f40]) ).

fof(f40,plain,
    ! [X1,X0,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ~ in(X3,X1)
              | ~ in(X3,X2) )
            & ( ( in(X3,X0)
                & in(X3,X1) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X0)
              | ~ in(X3,X1) )
            & ( ( in(X3,X0)
                & in(X3,X1) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(flattening,[],[f39]) ).

fof(f39,plain,
    ! [X1,X0,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ~ in(X3,X1)
              | ~ in(X3,X2) )
            & ( ( in(X3,X0)
                & in(X3,X1) )
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ in(X3,X0)
              | ~ in(X3,X1) )
            & ( ( in(X3,X0)
                & in(X3,X1) )
              | ~ in(X3,X2) ) )
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X0)
            & in(X3,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SEU153+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 14:41:10 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.50  % (5572)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52  % (5600)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.52  % (5572)Refutation not found, incomplete strategy% (5572)------------------------------
% 0.20/0.52  % (5572)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (5572)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (5572)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.52  
% 0.20/0.52  % (5572)Memory used [KB]: 5500
% 0.20/0.52  % (5572)Time elapsed: 0.100 s
% 0.20/0.52  % (5572)Instructions burned: 3 (million)
% 0.20/0.52  % (5572)------------------------------
% 0.20/0.52  % (5572)------------------------------
% 0.20/0.52  % (5583)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.52  % (5586)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)
% 0.20/0.52  % (5584)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52  % (5574)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)
% 0.20/0.53  % (5600)First to succeed.
% 0.20/0.53  % (5580)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (5600)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (5600)------------------------------
% 0.20/0.53  % (5600)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (5600)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (5600)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (5600)Memory used [KB]: 5500
% 0.20/0.53  % (5600)Time elapsed: 0.112 s
% 0.20/0.53  % (5600)Instructions burned: 5 (million)
% 0.20/0.53  % (5600)------------------------------
% 0.20/0.53  % (5600)------------------------------
% 0.20/0.53  % (5568)Success in time 0.174 s
%------------------------------------------------------------------------------