TSTP Solution File: SET790+4 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET790+4 : 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_sat --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 18:25:39 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   39 (   8 unt;   0 def)
%            Number of atoms       :  193 (  23 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  235 (  81   ~;  67   |;  55   &)
%                                         (   4 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :  117 (  99   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f64,plain,
    $false,
    inference(subsumption_resolution,[],[f63,f47]) ).

fof(f47,plain,
    member(sK0,sK2),
    inference(resolution,[],[f42,f39]) ).

fof(f39,plain,
    least(sK0,sK1,sK2),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ( order(sK1,sK2)
    & least(sK0,sK1,sK2)
    & least(sK3,sK1,sK2)
    & sK3 != sK0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f31,f33,f32]) ).

fof(f32,plain,
    ( ? [X0,X1,X2] :
        ( order(X1,X2)
        & least(X0,X1,X2)
        & ? [X3] :
            ( least(X3,X1,X2)
            & X0 != X3 ) )
   => ( order(sK1,sK2)
      & least(sK0,sK1,sK2)
      & ? [X3] :
          ( least(X3,sK1,sK2)
          & sK0 != X3 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ( ? [X3] :
        ( least(X3,sK1,sK2)
        & sK0 != X3 )
   => ( least(sK3,sK1,sK2)
      & sK3 != sK0 ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ? [X0,X1,X2] :
      ( order(X1,X2)
      & least(X0,X1,X2)
      & ? [X3] :
          ( least(X3,X1,X2)
          & X0 != X3 ) ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ? [X2,X1,X0] :
      ( order(X1,X0)
      & least(X2,X1,X0)
      & ? [X3] :
          ( least(X3,X1,X0)
          & X2 != X3 ) ),
    inference(flattening,[],[f28]) ).

fof(f28,plain,
    ? [X1,X0,X2] :
      ( ? [X3] :
          ( least(X3,X1,X0)
          & X2 != X3 )
      & order(X1,X0)
      & least(X2,X1,X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ~ ! [X1,X0,X2] :
        ( ( order(X1,X0)
          & least(X2,X1,X0) )
       => ! [X3] :
            ( least(X3,X1,X0)
           => X2 = X3 ) ),
    inference(rectify,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X1,X0,X5] :
        ( ( order(X0,X1)
          & least(X5,X0,X1) )
       => ! [X2] :
            ( least(X2,X0,X1)
           => X2 = X5 ) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X1,X0,X5] :
      ( ( order(X0,X1)
        & least(X5,X0,X1) )
     => ! [X2] :
          ( least(X2,X0,X1)
         => X2 = X5 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV2) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( ~ least(X2,X1,X0)
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ~ least(X2,X1,X0)
      | ( member(X2,X0)
        & ! [X3] :
            ( ~ member(X3,X0)
            | apply(X1,X2,X3) ) ) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( ~ least(X1,X0,X2)
      | ( member(X1,X2)
        & ! [X3] :
            ( ~ member(X3,X2)
            | apply(X0,X1,X3) ) ) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( least(X1,X0,X2)
     => ( ! [X3] :
            ( member(X3,X2)
           => apply(X0,X1,X3) )
        & member(X1,X2) ) ),
    inference(unused_predicate_definition_removal,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( member(X3,X2)
           => apply(X0,X1,X3) )
        & member(X1,X2) )
    <=> least(X1,X0,X2) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X5,X1] :
      ( least(X5,X0,X1)
    <=> ( ! [X2] :
            ( member(X2,X1)
           => apply(X0,X5,X2) )
        & member(X5,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',least) ).

fof(f63,plain,
    ~ member(sK0,sK2),
    inference(subsumption_resolution,[],[f62,f40]) ).

fof(f40,plain,
    order(sK1,sK2),
    inference(cnf_transformation,[],[f34]) ).

fof(f62,plain,
    ( ~ order(sK1,sK2)
    | ~ member(sK0,sK2) ),
    inference(resolution,[],[f61,f46]) ).

fof(f46,plain,
    member(sK3,sK2),
    inference(resolution,[],[f42,f38]) ).

fof(f38,plain,
    least(sK3,sK1,sK2),
    inference(cnf_transformation,[],[f34]) ).

fof(f61,plain,
    ! [X1] :
      ( ~ member(sK3,X1)
      | ~ order(sK1,X1)
      | ~ member(sK0,X1) ),
    inference(subsumption_resolution,[],[f60,f37]) ).

fof(f37,plain,
    sK3 != sK0,
    inference(cnf_transformation,[],[f34]) ).

fof(f60,plain,
    ! [X1] :
      ( ~ order(sK1,X1)
      | ~ member(sK0,X1)
      | ~ member(sK3,X1)
      | sK3 = sK0 ),
    inference(subsumption_resolution,[],[f59,f47]) ).

fof(f59,plain,
    ! [X1] :
      ( ~ member(sK0,sK2)
      | sK3 = sK0
      | ~ order(sK1,X1)
      | ~ member(sK0,X1)
      | ~ member(sK3,X1) ),
    inference(subsumption_resolution,[],[f55,f46]) ).

fof(f55,plain,
    ! [X1] :
      ( ~ order(sK1,X1)
      | ~ member(sK0,X1)
      | ~ member(sK3,sK2)
      | sK3 = sK0
      | ~ member(sK0,sK2)
      | ~ member(sK3,X1) ),
    inference(resolution,[],[f51,f49]) ).

fof(f49,plain,
    ! [X1] :
      ( apply(sK1,sK0,X1)
      | ~ member(X1,sK2) ),
    inference(resolution,[],[f41,f39]) ).

fof(f41,plain,
    ! [X2,X3,X0,X1] :
      ( ~ least(X2,X1,X0)
      | apply(X1,X2,X3)
      | ~ member(X3,X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f51,plain,
    ! [X4,X5] :
      ( ~ apply(sK1,X5,sK3)
      | ~ order(sK1,X4)
      | ~ member(X5,X4)
      | ~ member(sK3,X4)
      | sK3 = X5
      | ~ member(X5,sK2) ),
    inference(resolution,[],[f44,f48]) ).

fof(f48,plain,
    ! [X0] :
      ( apply(sK1,sK3,X0)
      | ~ member(X0,sK2) ),
    inference(resolution,[],[f41,f38]) ).

fof(f44,plain,
    ! [X3,X0,X1,X4] :
      ( ~ apply(X0,X4,X3)
      | ~ order(X0,X1)
      | ~ member(X3,X1)
      | X3 = X4
      | ~ apply(X0,X3,X4)
      | ~ member(X4,X1) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( apply(X0,X2,X2)
            | ~ member(X2,X1) )
        & ! [X3,X4] :
            ( ~ apply(X0,X3,X4)
            | ~ member(X4,X1)
            | ~ member(X3,X1)
            | X3 = X4
            | ~ apply(X0,X4,X3) )
        & ! [X5,X6,X7] :
            ( ~ member(X6,X1)
            | ~ apply(X0,X7,X5)
            | ~ apply(X0,X6,X7)
            | apply(X0,X6,X5)
            | ~ member(X5,X1)
            | ~ member(X7,X1) ) )
      | ~ order(X0,X1) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ! [X1,X0] :
      ( ( ! [X5] :
            ( apply(X1,X5,X5)
            | ~ member(X5,X0) )
        & ! [X7,X6] :
            ( ~ apply(X1,X7,X6)
            | ~ member(X6,X0)
            | ~ member(X7,X0)
            | X6 = X7
            | ~ apply(X1,X6,X7) )
        & ! [X2,X4,X3] :
            ( ~ member(X4,X0)
            | ~ apply(X1,X3,X2)
            | ~ apply(X1,X4,X3)
            | apply(X1,X4,X2)
            | ~ member(X2,X0)
            | ~ member(X3,X0) ) )
      | ~ order(X1,X0) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( ! [X6,X7] :
            ( X6 = X7
            | ~ apply(X1,X6,X7)
            | ~ apply(X1,X7,X6)
            | ~ member(X7,X0)
            | ~ member(X6,X0) )
        & ! [X4,X3,X2] :
            ( apply(X1,X4,X2)
            | ~ apply(X1,X4,X3)
            | ~ apply(X1,X3,X2)
            | ~ member(X3,X0)
            | ~ member(X2,X0)
            | ~ member(X4,X0) )
        & ! [X5] :
            ( apply(X1,X5,X5)
            | ~ member(X5,X0) ) )
      | ~ order(X1,X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( order(X1,X0)
     => ( ! [X6,X7] :
            ( ( member(X7,X0)
              & member(X6,X0) )
           => ( ( apply(X1,X6,X7)
                & apply(X1,X7,X6) )
             => X6 = X7 ) )
        & ! [X4,X3,X2] :
            ( ( member(X3,X0)
              & member(X2,X0)
              & member(X4,X0) )
           => ( ( apply(X1,X4,X3)
                & apply(X1,X3,X2) )
             => apply(X1,X4,X2) ) )
        & ! [X5] :
            ( member(X5,X0)
           => apply(X1,X5,X5) ) ) ),
    inference(unused_predicate_definition_removal,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( order(X1,X0)
    <=> ( ! [X6,X7] :
            ( ( member(X7,X0)
              & member(X6,X0) )
           => ( ( apply(X1,X6,X7)
                & apply(X1,X7,X6) )
             => X6 = X7 ) )
        & ! [X4,X3,X2] :
            ( ( member(X3,X0)
              & member(X2,X0)
              & member(X4,X0) )
           => ( ( apply(X1,X4,X3)
                & apply(X1,X3,X2) )
             => apply(X1,X4,X2) ) )
        & ! [X5] :
            ( member(X5,X0)
           => apply(X1,X5,X5) ) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( ( ! [X4,X3,X2] :
            ( ( member(X4,X1)
              & member(X3,X1)
              & member(X2,X1) )
           => ( ( apply(X0,X3,X4)
                & apply(X0,X2,X3) )
             => apply(X0,X2,X4) ) )
        & ! [X2] :
            ( member(X2,X1)
           => apply(X0,X2,X2) )
        & ! [X3,X2] :
            ( ( member(X2,X1)
              & member(X3,X1) )
           => ( ( apply(X0,X3,X2)
                & apply(X0,X2,X3) )
             => X2 = X3 ) ) )
    <=> order(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SET790+4 : TPTP v8.1.0. Released v3.2.0.
% 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
% 0.13/0.34  % Computer : n025.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 14:29:30 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.49  % (20530)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.49  % (20530)First to succeed.
% 0.20/0.50  % (20546)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.50  % (20530)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Theorem for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (20530)------------------------------
% 0.20/0.50  % (20530)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (20530)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (20530)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (20530)Memory used [KB]: 5500
% 0.20/0.50  % (20530)Time elapsed: 0.074 s
% 0.20/0.50  % (20530)Instructions burned: 3 (million)
% 0.20/0.50  % (20530)------------------------------
% 0.20/0.50  % (20530)------------------------------
% 0.20/0.50  % (20516)Success in time 0.151 s
%------------------------------------------------------------------------------