TSTP Solution File: SEU149+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU149+3 : TPTP v8.1.0. Released v3.2.0.
% 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 : n025.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 18:26:54 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   29 (   7 unt;   0 def)
%            Number of atoms       :  148 ( 102 equ)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :  186 (  67   ~;  68   |;  40   &)
%                                         (   6 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   77 (  61   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f89,plain,
    $false,
    inference(trivial_inequality_removal,[],[f88]) ).

fof(f88,plain,
    sK2 != sK2,
    inference(superposition,[],[f38,f72]) ).

fof(f72,plain,
    sK3 = sK2,
    inference(resolution,[],[f49,f55]) ).

fof(f55,plain,
    in(sK2,singleton(sK3)),
    inference(superposition,[],[f52,f37]) ).

fof(f37,plain,
    unordered_pair(sK2,sK4) = singleton(sK3),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ( sK3 != sK2
    & unordered_pair(sK2,sK4) = singleton(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f20,f21]) ).

fof(f21,plain,
    ( ? [X0,X1,X2] :
        ( X0 != X1
        & unordered_pair(X0,X2) = singleton(X1) )
   => ( sK3 != sK2
      & unordered_pair(sK2,sK4) = singleton(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0,X1,X2] :
      ( X0 != X1
      & unordered_pair(X0,X2) = singleton(X1) ),
    inference(rectify,[],[f12]) ).

fof(f12,plain,
    ? [X1,X0,X2] :
      ( X0 != X1
      & singleton(X0) = unordered_pair(X1,X2) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X2,X0,X1] :
        ( singleton(X0) = unordered_pair(X1,X2)
       => X0 = X1 ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X2,X0,X1] :
      ( singleton(X0) = unordered_pair(X1,X2)
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).

fof(f52,plain,
    ! [X2,X4] : in(X4,unordered_pair(X4,X2)),
    inference(equality_resolution,[],[f51]) ).

fof(f51,plain,
    ! [X2,X0,X4] :
      ( in(X4,X0)
      | unordered_pair(X4,X2) != X0 ),
    inference(equality_resolution,[],[f40]) ).

fof(f40,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | X1 != X4
      | unordered_pair(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X1,X2) = X0
        | ( ( ~ in(sK5(X0,X1,X2),X0)
            | ( sK5(X0,X1,X2) != X1
              & sK5(X0,X1,X2) != X2 ) )
          & ( in(sK5(X0,X1,X2),X0)
            | sK5(X0,X1,X2) = X1
            | sK5(X0,X1,X2) = X2 ) ) )
      & ( ! [X4] :
            ( ( X1 = X4
              | X2 = X4
              | ~ in(X4,X0) )
            & ( in(X4,X0)
              | ( X1 != X4
                & X2 != X4 ) ) )
        | unordered_pair(X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f25,f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X0)
            | ( X1 != X3
              & X2 != X3 ) )
          & ( in(X3,X0)
            | X1 = X3
            | X2 = X3 ) )
     => ( ( ~ in(sK5(X0,X1,X2),X0)
          | ( sK5(X0,X1,X2) != X1
            & sK5(X0,X1,X2) != X2 ) )
        & ( in(sK5(X0,X1,X2),X0)
          | sK5(X0,X1,X2) = X1
          | sK5(X0,X1,X2) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( X1 != X3
                & X2 != X3 ) )
            & ( in(X3,X0)
              | X1 = X3
              | X2 = X3 ) ) )
      & ( ! [X4] :
            ( ( X1 = X4
              | X2 = X4
              | ~ in(X4,X0) )
            & ( in(X4,X0)
              | ( X1 != X4
                & X2 != X4 ) ) )
        | unordered_pair(X1,X2) != X0 ) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( X1 != X3
                & X2 != X3 ) )
            & ( in(X3,X0)
              | X1 = X3
              | X2 = X3 ) ) )
      & ( ! [X3] :
            ( ( X1 = X3
              | X2 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( X1 != X3
                & X2 != X3 ) ) )
        | unordered_pair(X1,X2) != X0 ) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( X1 != X3
                & X2 != X3 ) )
            & ( in(X3,X0)
              | X1 = X3
              | X2 = X3 ) ) )
      & ( ! [X3] :
            ( ( X1 = X3
              | X2 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( X1 != X3
                & X2 != X3 ) ) )
        | unordered_pair(X1,X2) != X0 ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X0,X1,X2] :
      ( unordered_pair(X1,X2) = X0
    <=> ! [X3] :
          ( ( X1 = X3
            | X2 = X3 )
        <=> in(X3,X0) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(f49,plain,
    ! [X3,X1] :
      ( ~ in(X3,singleton(X1))
      | X1 = X3 ),
    inference(equality_resolution,[],[f33]) ).

fof(f33,plain,
    ! [X3,X0,X1] :
      ( X1 = X3
      | ~ in(X3,X0)
      | singleton(X1) != X0 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( singleton(X1) = X0
        | ( ( sK1(X0,X1) != X1
            | ~ in(sK1(X0,X1),X0) )
          & ( sK1(X0,X1) = X1
            | in(sK1(X0,X1),X0) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X0)
              | X1 != X3 )
            & ( X1 = X3
              | ~ in(X3,X0) ) )
        | singleton(X1) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f17,f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X1 != X2
            | ~ in(X2,X0) )
          & ( X1 = X2
            | in(X2,X0) ) )
     => ( ( sK1(X0,X1) != X1
          | ~ in(sK1(X0,X1),X0) )
        & ( sK1(X0,X1) = X1
          | in(sK1(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f17,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,[],[f16]) ).

fof(f16,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(f38,plain,
    sK3 != sK2,
    inference(cnf_transformation,[],[f22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SEU149+3 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n025.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 14:55:00 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (3691)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.49  % (3704)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)
% 0.19/0.50  % (3696)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)
% 0.19/0.50  % (3704)First to succeed.
% 0.19/0.50  % (3696)Instruction limit reached!
% 0.19/0.50  % (3696)------------------------------
% 0.19/0.50  % (3696)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (3696)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (3696)Termination reason: Unknown
% 0.19/0.50  % (3696)Termination phase: Saturation
% 0.19/0.50  
% 0.19/0.50  % (3696)Memory used [KB]: 5884
% 0.19/0.50  % (3696)Time elapsed: 0.055 s
% 0.19/0.50  % (3696)Instructions burned: 3 (million)
% 0.19/0.50  % (3696)------------------------------
% 0.19/0.50  % (3696)------------------------------
% 0.19/0.50  % (3692)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.50  % (3693)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  % (3688)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)
% 0.19/0.51  % (3704)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (3704)------------------------------
% 0.19/0.51  % (3704)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (3704)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (3704)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (3704)Memory used [KB]: 5884
% 0.19/0.51  % (3704)Time elapsed: 0.059 s
% 0.19/0.51  % (3704)Instructions burned: 2 (million)
% 0.19/0.51  % (3704)------------------------------
% 0.19/0.51  % (3704)------------------------------
% 0.19/0.51  % (3681)Success in time 0.16 s
%------------------------------------------------------------------------------