TSTP Solution File: SEU143+2 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU143+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 : n029.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 18:32:07 EDT 2022

% Result   : Theorem 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   31 (  15 unt;   0 def)
%            Number of atoms       :  116 (  78 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  135 (  50   ~;  50   |;  27   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 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   :   61 (  52   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f354,plain,
    $false,
    inference(subsumption_resolution,[],[f353,f339]) ).

fof(f339,plain,
    ! [X1] : ~ in(X1,empty_set),
    inference(equality_resolution,[],[f284]) ).

fof(f284,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f191]) ).

fof(f191,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | in(sK9(X0),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f189,f190]) ).

fof(f190,plain,
    ! [X0] :
      ( ? [X2] : in(X2,X0)
     => in(sK9(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f189,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | ? [X2] : in(X2,X0) ) ),
    inference(rectify,[],[f188]) ).

fof(f188,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | ? [X1] : in(X1,X0) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( ! [X1] : ~ in(X1,X0)
    <=> empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(f353,plain,
    in(sK1,empty_set),
    inference(superposition,[],[f328,f342]) ).

fof(f342,plain,
    empty_set = unordered_pair(sK1,sK1),
    inference(forward_demodulation,[],[f340,f341]) ).

fof(f341,plain,
    empty_set = sF13,
    inference(definition_folding,[],[f299,f340]) ).

fof(f299,plain,
    empty_set = unordered_pair(sK1,sK1),
    inference(definition_unfolding,[],[f222,f206]) ).

fof(f206,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).

fof(f222,plain,
    empty_set = singleton(sK1),
    inference(cnf_transformation,[],[f144]) ).

fof(f144,plain,
    empty_set = singleton(sK1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f115,f143]) ).

fof(f143,plain,
    ( ? [X0] : singleton(X0) = empty_set
   => empty_set = singleton(sK1) ),
    introduced(choice_axiom,[]) ).

fof(f115,plain,
    ? [X0] : singleton(X0) = empty_set,
    inference(ennf_transformation,[],[f29]) ).

fof(f29,negated_conjecture,
    ~ ! [X0] : singleton(X0) != empty_set,
    inference(negated_conjecture,[],[f28]) ).

fof(f28,conjecture,
    ! [X0] : singleton(X0) != empty_set,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).

fof(f340,plain,
    sF13 = unordered_pair(sK1,sK1),
    introduced(function_definition,[]) ).

fof(f328,plain,
    ! [X3,X1] : in(X3,unordered_pair(X1,X3)),
    inference(equality_resolution,[],[f327]) ).

fof(f327,plain,
    ! [X2,X3,X1] :
      ( in(X3,X2)
      | unordered_pair(X1,X3) != X2 ),
    inference(equality_resolution,[],[f250]) ).

fof(f250,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X2)
      | X0 != X3
      | unordered_pair(X1,X0) != X2 ),
    inference(cnf_transformation,[],[f165]) ).

fof(f165,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( X0 = X3
              | X1 = X3
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ( X0 != X3
                & X1 != X3 ) ) )
        | unordered_pair(X1,X0) != X2 )
      & ( unordered_pair(X1,X0) = X2
        | ( ( ~ in(sK5(X0,X1,X2),X2)
            | ( sK5(X0,X1,X2) != X0
              & sK5(X0,X1,X2) != X1 ) )
          & ( in(sK5(X0,X1,X2),X2)
            | sK5(X0,X1,X2) = X0
            | sK5(X0,X1,X2) = X1 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f163,f164]) ).

fof(f164,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X2)
            | ( X0 != X4
              & X1 != X4 ) )
          & ( in(X4,X2)
            | X0 = X4
            | X1 = X4 ) )
     => ( ( ~ in(sK5(X0,X1,X2),X2)
          | ( sK5(X0,X1,X2) != X0
            & sK5(X0,X1,X2) != X1 ) )
        & ( in(sK5(X0,X1,X2),X2)
          | sK5(X0,X1,X2) = X0
          | sK5(X0,X1,X2) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f163,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( X0 = X3
              | X1 = X3
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ( X0 != X3
                & X1 != X3 ) ) )
        | unordered_pair(X1,X0) != X2 )
      & ( unordered_pair(X1,X0) = X2
        | ? [X4] :
            ( ( ~ in(X4,X2)
              | ( X0 != X4
                & X1 != X4 ) )
            & ( in(X4,X2)
              | X0 = X4
              | X1 = X4 ) ) ) ),
    inference(rectify,[],[f162]) ).

fof(f162,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3] :
            ( ( X2 = X3
              | X1 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) ) )
        | unordered_pair(X1,X2) != X0 )
      & ( unordered_pair(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) )
            & ( in(X3,X0)
              | X2 = X3
              | X1 = X3 ) ) ) ),
    inference(flattening,[],[f161]) ).

fof(f161,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3] :
            ( ( X2 = X3
              | X1 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) ) )
        | unordered_pair(X1,X2) != X0 )
      & ( unordered_pair(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) )
            & ( in(X3,X0)
              | X2 = X3
              | X1 = X3 ) ) ) ),
    inference(nnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X2,X1,X0] :
      ( ! [X3] :
          ( ( X2 = X3
            | X1 = X3 )
        <=> in(X3,X0) )
    <=> unordered_pair(X1,X2) = X0 ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X2,X0,X1] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X0 = X3
            | X1 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SEU143+2 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 14:53:57 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.19/0.50  % (5582)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.51  % (5574)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.51  % (5565)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.51  % (5568)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.51  % (5569)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.52  % (5582)First to succeed.
% 0.19/0.52  % (5565)Instruction limit reached!
% 0.19/0.52  % (5565)------------------------------
% 0.19/0.52  % (5565)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (5565)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (5565)Termination reason: Unknown
% 0.19/0.52  % (5565)Termination phase: Unused predicate definition removal
% 0.19/0.52  
% 0.19/0.52  % (5565)Memory used [KB]: 895
% 0.19/0.52  % (5565)Time elapsed: 0.003 s
% 0.19/0.52  % (5565)Instructions burned: 2 (million)
% 0.19/0.52  % (5565)------------------------------
% 0.19/0.52  % (5565)------------------------------
% 0.19/0.52  % (5557)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.52  TRYING [1]
% 0.19/0.52  % (5582)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Theorem for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (5582)------------------------------
% 0.19/0.52  % (5582)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (5582)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (5582)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (5582)Memory used [KB]: 5628
% 0.19/0.52  % (5582)Time elapsed: 0.120 s
% 0.19/0.52  % (5582)Instructions burned: 7 (million)
% 0.19/0.52  % (5582)------------------------------
% 0.19/0.52  % (5582)------------------------------
% 0.19/0.52  % (5556)Success in time 0.167 s
%------------------------------------------------------------------------------