TSTP Solution File: SET591+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET591+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_uns --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 18:21:31 EDT 2022

% Result   : Theorem 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   37 (   8 unt;   0 def)
%            Number of atoms       :  116 (  17 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  131 (  52   ~;  42   |;  27   &)
%                                         (   5 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   79 (  72   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f134,plain,
    $false,
    inference(subsumption_resolution,[],[f131,f36]) ).

fof(f36,plain,
    empty_set != sK1,
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ( empty_set != sK1
    & subset(sK1,difference(sK2,sK1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f10,f22]) ).

fof(f22,plain,
    ( ? [X0,X1] :
        ( empty_set != X0
        & subset(X0,difference(X1,X0)) )
   => ( empty_set != sK1
      & subset(sK1,difference(sK2,sK1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ? [X0,X1] :
      ( empty_set != X0
      & subset(X0,difference(X1,X0)) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(X0,difference(X1,X0))
       => empty_set = X0 ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0,X1] :
      ( subset(X0,difference(X1,X0))
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th50) ).

fof(f131,plain,
    empty_set = sK1,
    inference(resolution,[],[f126,f47]) ).

fof(f47,plain,
    ! [X1] :
      ( ~ subset(X1,empty_set)
      | empty_set = X1 ),
    inference(resolution,[],[f30,f39]) ).

fof(f39,plain,
    ! [X0] : subset(empty_set,X0),
    inference(resolution,[],[f28,f34]) ).

fof(f34,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f28,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

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

fof(f30,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ! [X1,X0] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
    <=> X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(f126,plain,
    ! [X1] : subset(sK1,X1),
    inference(resolution,[],[f123,f35]) ).

fof(f35,plain,
    subset(sK1,difference(sK2,sK1)),
    inference(cnf_transformation,[],[f23]) ).

fof(f123,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X0,difference(X1,X0))
      | subset(X0,X2) ),
    inference(duplicate_literal_removal,[],[f118]) ).

fof(f118,plain,
    ! [X2,X0,X1] :
      ( subset(X0,X2)
      | ~ subset(X0,difference(X1,X0))
      | subset(X0,X2) ),
    inference(resolution,[],[f65,f28]) ).

fof(f65,plain,
    ! [X6,X7,X4,X5] :
      ( ~ member(sK0(X4,X7),X6)
      | ~ subset(X4,difference(X5,X6))
      | subset(X4,X7) ),
    inference(resolution,[],[f44,f25]) ).

fof(f25,plain,
    ! [X2,X0,X1] :
      ( ~ member(X1,difference(X0,X2))
      | ~ member(X1,X2) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ( member(X1,difference(X0,X2))
        | member(X1,X2)
        | ~ member(X1,X0) )
      & ( ( ~ member(X1,X2)
          & member(X1,X0) )
        | ~ member(X1,difference(X0,X2)) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,plain,
    ! [X1,X2,X0] :
      ( ( member(X2,difference(X1,X0))
        | member(X2,X0)
        | ~ member(X2,X1) )
      & ( ( ~ member(X2,X0)
          & member(X2,X1) )
        | ~ member(X2,difference(X1,X0)) ) ),
    inference(flattening,[],[f12]) ).

fof(f12,plain,
    ! [X1,X2,X0] :
      ( ( member(X2,difference(X1,X0))
        | member(X2,X0)
        | ~ member(X2,X1) )
      & ( ( ~ member(X2,X0)
          & member(X2,X1) )
        | ~ member(X2,difference(X1,X0)) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X1,X2,X0] :
      ( member(X2,difference(X1,X0))
    <=> ( ~ member(X2,X0)
        & member(X2,X1) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0,X2] :
      ( member(X2,difference(X0,X1))
    <=> ( member(X2,X0)
        & ~ member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( member(sK0(X0,X2),X1)
      | ~ subset(X0,X1)
      | subset(X0,X2) ),
    inference(resolution,[],[f27,f28]) ).

fof(f27,plain,
    ! [X3,X0,X1] :
      ( ~ member(X3,X0)
      | ~ subset(X0,X1)
      | member(X3,X1) ),
    inference(cnf_transformation,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : SET591+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 14:07:10 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.49  % (30109)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.49  % (30101)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.49  % (30093)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.49  % (30101)Instruction limit reached!
% 0.19/0.49  % (30101)------------------------------
% 0.19/0.49  % (30101)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (30101)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (30101)Termination reason: Unknown
% 0.19/0.50  % (30101)Termination phase: Saturation
% 0.19/0.50  
% 0.19/0.50  % (30101)Memory used [KB]: 6012
% 0.19/0.50  % (30101)Time elapsed: 0.057 s
% 0.19/0.50  % (30101)Instructions burned: 4 (million)
% 0.19/0.50  % (30101)------------------------------
% 0.19/0.50  % (30101)------------------------------
% 0.19/0.50  % (30093)First to succeed.
% 0.19/0.50  % (30098)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.50  % (30100)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (30099)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.50  % (30093)Refutation found. Thanks to Tanya!
% 0.19/0.50  % SZS status Theorem for theBenchmark
% 0.19/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50  % (30093)------------------------------
% 0.19/0.50  % (30093)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (30093)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (30093)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (30093)Memory used [KB]: 6012
% 0.19/0.50  % (30093)Time elapsed: 0.061 s
% 0.19/0.50  % (30093)Instructions burned: 5 (million)
% 0.19/0.50  % (30093)------------------------------
% 0.19/0.50  % (30093)------------------------------
% 0.19/0.50  % (30086)Success in time 0.16 s
%------------------------------------------------------------------------------