TSTP Solution File: PHI012+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : PHI012+1 : TPTP v8.1.0. Released v7.2.0.
% 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 : n003.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 18:08:23 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   49 (   5 unt;   0 def)
%            Number of atoms       :  258 (  33 equ)
%            Maximal formula atoms :   11 (   5 avg)
%            Number of connectives :  345 ( 136   ~; 135   |;  57   &)
%                                         (   2 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-1 aty)
%            Number of variables   :   73 (  54   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f94,plain,
    $false,
    inference(resolution,[],[f89,f28]) ).

fof(f28,plain,
    object(sK2),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ( ! [X0] :
        ( ~ exemplifies_property(none_greater,X0)
        | ~ object(X0)
        | ( sK1(X0) != X0
          & exemplifies_property(none_greater,sK1(X0))
          & object(sK1(X0)) ) )
    & exemplifies_property(none_greater,sK2)
    & object(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f18,f20,f19]) ).

fof(f19,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 != X1
          & exemplifies_property(none_greater,X1)
          & object(X1) )
     => ( sK1(X0) != X0
        & exemplifies_property(none_greater,sK1(X0))
        & object(sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ( ? [X2] :
        ( exemplifies_property(none_greater,X2)
        & object(X2) )
   => ( exemplifies_property(none_greater,sK2)
      & object(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ( ! [X0] :
        ( ~ exemplifies_property(none_greater,X0)
        | ~ object(X0)
        | ? [X1] :
            ( X0 != X1
            & exemplifies_property(none_greater,X1)
            & object(X1) ) )
    & ? [X2] :
        ( exemplifies_property(none_greater,X2)
        & object(X2) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ( ! [X1] :
        ( ~ exemplifies_property(none_greater,X1)
        | ~ object(X1)
        | ? [X2] :
            ( X1 != X2
            & exemplifies_property(none_greater,X2)
            & object(X2) ) )
    & ? [X0] :
        ( exemplifies_property(none_greater,X0)
        & object(X0) ) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ( ! [X1] :
        ( ? [X2] :
            ( X1 != X2
            & exemplifies_property(none_greater,X2)
            & object(X2) )
        | ~ object(X1)
        | ~ exemplifies_property(none_greater,X1) )
    & ? [X0] :
        ( exemplifies_property(none_greater,X0)
        & object(X0) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,plain,
    ~ ( ? [X0] :
          ( exemplifies_property(none_greater,X0)
          & object(X0) )
     => ? [X1] :
          ( ! [X2] :
              ( object(X2)
             => ( exemplifies_property(none_greater,X2)
               => X1 = X2 ) )
          & object(X1)
          & exemplifies_property(none_greater,X1) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,negated_conjecture,
    ~ ( ? [X0] :
          ( exemplifies_property(none_greater,X0)
          & object(X0) )
     => ? [X0] :
          ( object(X0)
          & exemplifies_property(none_greater,X0)
          & ! [X1] :
              ( object(X1)
             => ( exemplifies_property(none_greater,X1)
               => X0 = X1 ) ) ) ),
    inference(negated_conjecture,[],[f3]) ).

fof(f3,conjecture,
    ( ? [X0] :
        ( exemplifies_property(none_greater,X0)
        & object(X0) )
   => ? [X0] :
        ( object(X0)
        & exemplifies_property(none_greater,X0)
        & ! [X1] :
            ( object(X1)
           => ( exemplifies_property(none_greater,X1)
             => X0 = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_2) ).

fof(f89,plain,
    ~ object(sK2),
    inference(resolution,[],[f88,f29]) ).

fof(f29,plain,
    exemplifies_property(none_greater,sK2),
    inference(cnf_transformation,[],[f21]) ).

fof(f88,plain,
    ( ~ exemplifies_property(none_greater,sK2)
    | ~ object(sK2) ),
    inference(trivial_inequality_removal,[],[f85]) ).

fof(f85,plain,
    ( ~ exemplifies_property(none_greater,sK2)
    | ~ object(sK2)
    | sK2 != sK2 ),
    inference(superposition,[],[f32,f82]) ).

fof(f82,plain,
    sK2 = sK1(sK2),
    inference(resolution,[],[f77,f28]) ).

fof(f77,plain,
    ( ~ object(sK2)
    | sK2 = sK1(sK2) ),
    inference(resolution,[],[f76,f29]) ).

fof(f76,plain,
    ( ~ exemplifies_property(none_greater,sK2)
    | ~ object(sK2)
    | sK2 = sK1(sK2) ),
    inference(duplicate_literal_removal,[],[f75]) ).

fof(f75,plain,
    ( ~ object(sK2)
    | sK2 = sK1(sK2)
    | ~ object(sK2)
    | ~ exemplifies_property(none_greater,sK2) ),
    inference(resolution,[],[f73,f30]) ).

fof(f30,plain,
    ! [X0] :
      ( object(sK1(X0))
      | ~ exemplifies_property(none_greater,X0)
      | ~ object(X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f73,plain,
    ( ~ object(sK1(sK2))
    | sK2 = sK1(sK2)
    | ~ object(sK2) ),
    inference(duplicate_literal_removal,[],[f68]) ).

fof(f68,plain,
    ( sK2 = sK1(sK2)
    | ~ object(sK2)
    | ~ object(sK1(sK2))
    | ~ object(sK2) ),
    inference(resolution,[],[f62,f29]) ).

fof(f62,plain,
    ! [X0] :
      ( ~ exemplifies_property(none_greater,X0)
      | ~ object(X0)
      | sK1(X0) = sK2
      | ~ object(sK2)
      | ~ object(sK1(X0)) ),
    inference(resolution,[],[f58,f31]) ).

fof(f31,plain,
    ! [X0] :
      ( exemplifies_property(none_greater,sK1(X0))
      | ~ exemplifies_property(none_greater,X0)
      | ~ object(X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f58,plain,
    ! [X0] :
      ( ~ exemplifies_property(none_greater,X0)
      | ~ object(sK2)
      | ~ object(X0)
      | sK2 = X0 ),
    inference(duplicate_literal_removal,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ~ object(sK2)
      | ~ exemplifies_property(none_greater,X0)
      | ~ object(X0)
      | sK2 = X0
      | ~ object(X0)
      | ~ exemplifies_property(none_greater,X0) ),
    inference(resolution,[],[f47,f22]) ).

fof(f22,plain,
    ! [X0] :
      ( exemplifies_property(conceivable,X0)
      | ~ object(X0)
      | ~ exemplifies_property(none_greater,X0) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0] :
      ( ( ( exemplifies_property(none_greater,X0)
          | ( exemplifies_property(conceivable,sK0(X0))
            & exemplifies_relation(greater_than,sK0(X0),X0)
            & object(sK0(X0)) )
          | ~ exemplifies_property(conceivable,X0) )
        & ( ( ! [X2] :
                ( ~ exemplifies_property(conceivable,X2)
                | ~ exemplifies_relation(greater_than,X2,X0)
                | ~ object(X2) )
            & exemplifies_property(conceivable,X0) )
          | ~ exemplifies_property(none_greater,X0) ) )
      | ~ object(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f14,f15]) ).

fof(f15,plain,
    ! [X0] :
      ( ? [X1] :
          ( exemplifies_property(conceivable,X1)
          & exemplifies_relation(greater_than,X1,X0)
          & object(X1) )
     => ( exemplifies_property(conceivable,sK0(X0))
        & exemplifies_relation(greater_than,sK0(X0),X0)
        & object(sK0(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ! [X0] :
      ( ( ( exemplifies_property(none_greater,X0)
          | ? [X1] :
              ( exemplifies_property(conceivable,X1)
              & exemplifies_relation(greater_than,X1,X0)
              & object(X1) )
          | ~ exemplifies_property(conceivable,X0) )
        & ( ( ! [X2] :
                ( ~ exemplifies_property(conceivable,X2)
                | ~ exemplifies_relation(greater_than,X2,X0)
                | ~ object(X2) )
            & exemplifies_property(conceivable,X0) )
          | ~ exemplifies_property(none_greater,X0) ) )
      | ~ object(X0) ),
    inference(rectify,[],[f13]) ).

fof(f13,plain,
    ! [X0] :
      ( ( ( exemplifies_property(none_greater,X0)
          | ? [X1] :
              ( exemplifies_property(conceivable,X1)
              & exemplifies_relation(greater_than,X1,X0)
              & object(X1) )
          | ~ exemplifies_property(conceivable,X0) )
        & ( ( ! [X1] :
                ( ~ exemplifies_property(conceivable,X1)
                | ~ exemplifies_relation(greater_than,X1,X0)
                | ~ object(X1) )
            & exemplifies_property(conceivable,X0) )
          | ~ exemplifies_property(none_greater,X0) ) )
      | ~ object(X0) ),
    inference(flattening,[],[f12]) ).

fof(f12,plain,
    ! [X0] :
      ( ( ( exemplifies_property(none_greater,X0)
          | ? [X1] :
              ( exemplifies_property(conceivable,X1)
              & exemplifies_relation(greater_than,X1,X0)
              & object(X1) )
          | ~ exemplifies_property(conceivable,X0) )
        & ( ( ! [X1] :
                ( ~ exemplifies_property(conceivable,X1)
                | ~ exemplifies_relation(greater_than,X1,X0)
                | ~ object(X1) )
            & exemplifies_property(conceivable,X0) )
          | ~ exemplifies_property(none_greater,X0) ) )
      | ~ object(X0) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X0] :
      ( ( exemplifies_property(none_greater,X0)
      <=> ( ! [X1] :
              ( ~ exemplifies_property(conceivable,X1)
              | ~ exemplifies_relation(greater_than,X1,X0)
              | ~ object(X1) )
          & exemplifies_property(conceivable,X0) ) )
      | ~ object(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( object(X0)
     => ( ( exemplifies_property(conceivable,X0)
          & ~ ? [X1] :
                ( object(X1)
                & exemplifies_property(conceivable,X1)
                & exemplifies_relation(greater_than,X1,X0) ) )
      <=> exemplifies_property(none_greater,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_none_greater) ).

fof(f47,plain,
    ! [X0] :
      ( ~ exemplifies_property(conceivable,X0)
      | ~ exemplifies_property(none_greater,X0)
      | sK2 = X0
      | ~ object(X0)
      | ~ object(sK2) ),
    inference(resolution,[],[f45,f29]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ~ exemplifies_property(none_greater,X1)
      | ~ exemplifies_property(conceivable,X0)
      | ~ object(X0)
      | ~ object(X1)
      | X0 = X1
      | ~ exemplifies_property(none_greater,X0) ),
    inference(duplicate_literal_removal,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ object(X0)
      | ~ object(X1)
      | ~ exemplifies_property(conceivable,X0)
      | ~ exemplifies_property(none_greater,X1)
      | ~ exemplifies_property(none_greater,X0)
      | X0 = X1
      | ~ object(X1)
      | ~ exemplifies_property(none_greater,X1) ),
    inference(resolution,[],[f38,f22]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ exemplifies_property(conceivable,X0)
      | ~ exemplifies_property(conceivable,X1)
      | X0 = X1
      | ~ exemplifies_property(none_greater,X1)
      | ~ exemplifies_property(none_greater,X0)
      | ~ object(X1)
      | ~ object(X0) ),
    inference(duplicate_literal_removal,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ exemplifies_property(conceivable,X0)
      | ~ object(X0)
      | ~ exemplifies_property(none_greater,X0)
      | ~ exemplifies_property(none_greater,X1)
      | ~ object(X1)
      | ~ exemplifies_property(conceivable,X1)
      | ~ object(X1)
      | ~ object(X0) ),
    inference(resolution,[],[f36,f23]) ).

fof(f23,plain,
    ! [X2,X0] :
      ( ~ exemplifies_relation(greater_than,X2,X0)
      | ~ exemplifies_property(conceivable,X2)
      | ~ exemplifies_property(none_greater,X0)
      | ~ object(X2)
      | ~ object(X0) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( exemplifies_relation(greater_than,X0,X1)
      | ~ object(X1)
      | ~ object(X0)
      | ~ exemplifies_property(conceivable,X1)
      | ~ exemplifies_property(none_greater,X0)
      | X0 = X1 ),
    inference(duplicate_literal_removal,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ~ object(X0)
      | ~ exemplifies_property(none_greater,X0)
      | X0 = X1
      | ~ object(X1)
      | ~ object(X1)
      | exemplifies_relation(greater_than,X0,X1)
      | ~ exemplifies_property(conceivable,X1)
      | ~ object(X0) ),
    inference(resolution,[],[f27,f23]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( exemplifies_relation(greater_than,X0,X1)
      | exemplifies_relation(greater_than,X1,X0)
      | ~ object(X0)
      | X0 = X1
      | ~ object(X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( exemplifies_relation(greater_than,X0,X1)
      | ~ object(X1)
      | X0 = X1
      | ~ object(X0)
      | exemplifies_relation(greater_than,X1,X0) ),
    inference(rectify,[],[f8]) ).

fof(f8,plain,
    ! [X1,X0] :
      ( exemplifies_relation(greater_than,X1,X0)
      | ~ object(X0)
      | X0 = X1
      | ~ object(X1)
      | exemplifies_relation(greater_than,X0,X1) ),
    inference(flattening,[],[f7]) ).

fof(f7,plain,
    ! [X1,X0] :
      ( exemplifies_relation(greater_than,X0,X1)
      | exemplifies_relation(greater_than,X1,X0)
      | X0 = X1
      | ~ object(X0)
      | ~ object(X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,plain,
    ! [X1,X0] :
      ( ( object(X0)
        & object(X1) )
     => ( exemplifies_relation(greater_than,X0,X1)
        | exemplifies_relation(greater_than,X1,X0)
        | X0 = X1 ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( ( object(X0)
        & object(X1) )
     => ( exemplifies_relation(greater_than,X1,X0)
        | X0 = X1
        | exemplifies_relation(greater_than,X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_of_greater_than) ).

fof(f32,plain,
    ! [X0] :
      ( sK1(X0) != X0
      | ~ exemplifies_property(none_greater,X0)
      | ~ object(X0) ),
    inference(cnf_transformation,[],[f21]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : PHI012+1 : TPTP v8.1.0. Released v7.2.0.
% 0.11/0.13  % 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 : n003.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 10:02:37 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (20531)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)
% 0.19/0.50  % (20531)First to succeed.
% 0.19/0.50  % (20524)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.50  % (20541)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.51  % (20531)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  % (20531)------------------------------
% 0.19/0.51  % (20531)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (20531)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (20531)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (20531)Memory used [KB]: 1023
% 0.19/0.51  % (20531)Time elapsed: 0.110 s
% 0.19/0.51  % (20531)Instructions burned: 3 (million)
% 0.19/0.51  % (20531)------------------------------
% 0.19/0.51  % (20531)------------------------------
% 0.19/0.51  % (20521)Success in time 0.161 s
%------------------------------------------------------------------------------