TSTP Solution File: SWV370+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV370+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n028.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 : Tue Apr 30 16:46:36 EDT 2024

% Result   : Theorem 0.19s 0.39s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   53 (  11 unt;   0 def)
%            Number of atoms       :  165 (  22 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  183 (  71   ~;  72   |;  27   &)
%                                         (   8 <=>;   4  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :  158 ( 124   !;  34   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f344,plain,
    $false,
    inference(resolution,[],[f335,f200]) ).

fof(f200,plain,
    ! [X2,X0] : contains_pq(insert_pq(X0,X2),X2),
    inference(equality_resolution,[],[f174]) ).

fof(f174,plain,
    ! [X2,X0,X1] :
      ( contains_pq(insert_pq(X0,X1),X2)
      | X1 != X2 ),
    inference(cnf_transformation,[],[f124]) ).

fof(f124,plain,
    ! [X0,X1,X2] :
      ( ( contains_pq(insert_pq(X0,X1),X2)
        | ( X1 != X2
          & ~ contains_pq(X0,X2) ) )
      & ( X1 = X2
        | contains_pq(X0,X2)
        | ~ contains_pq(insert_pq(X0,X1),X2) ) ),
    inference(flattening,[],[f123]) ).

fof(f123,plain,
    ! [X0,X1,X2] :
      ( ( contains_pq(insert_pq(X0,X1),X2)
        | ( X1 != X2
          & ~ contains_pq(X0,X2) ) )
      & ( X1 = X2
        | contains_pq(X0,X2)
        | ~ contains_pq(insert_pq(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X2] :
      ( contains_pq(insert_pq(X0,X1),X2)
    <=> ( X1 = X2
        | contains_pq(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).

fof(f335,plain,
    ~ contains_pq(insert_pq(i(triple(sK1,sK0,sK2)),sK3),sK3),
    inference(resolution,[],[f330,f201]) ).

fof(f201,plain,
    ! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2),
    inference(equality_resolution,[],[f191]) ).

fof(f191,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
      | X1 != X2 ),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
        | ( X1 != X2
          & ~ contains_slb(X0,X2) ) )
      & ( X1 = X2
        | contains_slb(X0,X2)
        | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
    inference(flattening,[],[f126]) ).

fof(f126,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
        | ( X1 != X2
          & ~ contains_slb(X0,X2) ) )
      & ( X1 = X2
        | contains_slb(X0,X2)
        | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
    inference(nnf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X1,X2,X3] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
    <=> ( X1 = X2
        | contains_slb(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

fof(f330,plain,
    ( ~ contains_slb(insert_slb(sK0,pair(sK3,sK4)),sK3)
    | ~ contains_pq(insert_pq(i(triple(sK1,sK0,sK2)),sK3),sK3) ),
    inference(forward_demodulation,[],[f324,f320]) ).

fof(f320,plain,
    sK3 = sK5,
    inference(resolution,[],[f319,f282]) ).

fof(f282,plain,
    ~ contains_slb(sK0,sK5),
    inference(resolution,[],[f280,f188]) ).

fof(f188,plain,
    ! [X2,X3,X0,X1] :
      ( contains_cpq(triple(X0,X1,X2),X3)
      | ~ contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f125]) ).

fof(f125,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_cpq(triple(X0,X1,X2),X3)
        | ~ contains_slb(X1,X3) )
      & ( contains_slb(X1,X3)
        | ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
    inference(nnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ! [X0,X1,X2,X3] :
      ( contains_cpq(triple(X0,X1,X2),X3)
    <=> contains_slb(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).

fof(f280,plain,
    ~ contains_cpq(triple(sK1,sK0,sK2),sK5),
    inference(resolution,[],[f279,f131]) ).

fof(f131,plain,
    ! [X8,X6,X7] :
      ( contains_pq(i(triple(X6,sK0,X7)),X8)
      | ~ contains_cpq(triple(X6,sK0,X7),X8) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ( ( ~ contains_pq(i(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)),sK5)
      | ~ contains_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2),sK5) )
    & ( contains_pq(i(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)),sK5)
      | contains_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2),sK5) )
    & ! [X6,X7,X8] :
        ( ( contains_cpq(triple(X6,sK0,X7),X8)
          | ~ contains_pq(i(triple(X6,sK0,X7)),X8) )
        & ( contains_pq(i(triple(X6,sK0,X7)),X8)
          | ~ contains_cpq(triple(X6,sK0,X7),X8) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f117,f119,f118]) ).

fof(f118,plain,
    ( ? [X0] :
        ( ? [X1,X2,X3,X4,X5] :
            ( ( ~ contains_pq(i(triple(X1,insert_slb(X0,pair(X3,X4)),X2)),X5)
              | ~ contains_cpq(triple(X1,insert_slb(X0,pair(X3,X4)),X2),X5) )
            & ( contains_pq(i(triple(X1,insert_slb(X0,pair(X3,X4)),X2)),X5)
              | contains_cpq(triple(X1,insert_slb(X0,pair(X3,X4)),X2),X5) ) )
        & ! [X6,X7,X8] :
            ( ( contains_cpq(triple(X6,X0,X7),X8)
              | ~ contains_pq(i(triple(X6,X0,X7)),X8) )
            & ( contains_pq(i(triple(X6,X0,X7)),X8)
              | ~ contains_cpq(triple(X6,X0,X7),X8) ) ) )
   => ( ? [X5,X4,X3,X2,X1] :
          ( ( ~ contains_pq(i(triple(X1,insert_slb(sK0,pair(X3,X4)),X2)),X5)
            | ~ contains_cpq(triple(X1,insert_slb(sK0,pair(X3,X4)),X2),X5) )
          & ( contains_pq(i(triple(X1,insert_slb(sK0,pair(X3,X4)),X2)),X5)
            | contains_cpq(triple(X1,insert_slb(sK0,pair(X3,X4)),X2),X5) ) )
      & ! [X8,X7,X6] :
          ( ( contains_cpq(triple(X6,sK0,X7),X8)
            | ~ contains_pq(i(triple(X6,sK0,X7)),X8) )
          & ( contains_pq(i(triple(X6,sK0,X7)),X8)
            | ~ contains_cpq(triple(X6,sK0,X7),X8) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f119,plain,
    ( ? [X5,X4,X3,X2,X1] :
        ( ( ~ contains_pq(i(triple(X1,insert_slb(sK0,pair(X3,X4)),X2)),X5)
          | ~ contains_cpq(triple(X1,insert_slb(sK0,pair(X3,X4)),X2),X5) )
        & ( contains_pq(i(triple(X1,insert_slb(sK0,pair(X3,X4)),X2)),X5)
          | contains_cpq(triple(X1,insert_slb(sK0,pair(X3,X4)),X2),X5) ) )
   => ( ( ~ contains_pq(i(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)),sK5)
        | ~ contains_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2),sK5) )
      & ( contains_pq(i(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)),sK5)
        | contains_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2),sK5) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f117,plain,
    ? [X0] :
      ( ? [X1,X2,X3,X4,X5] :
          ( ( ~ contains_pq(i(triple(X1,insert_slb(X0,pair(X3,X4)),X2)),X5)
            | ~ contains_cpq(triple(X1,insert_slb(X0,pair(X3,X4)),X2),X5) )
          & ( contains_pq(i(triple(X1,insert_slb(X0,pair(X3,X4)),X2)),X5)
            | contains_cpq(triple(X1,insert_slb(X0,pair(X3,X4)),X2),X5) ) )
      & ! [X6,X7,X8] :
          ( ( contains_cpq(triple(X6,X0,X7),X8)
            | ~ contains_pq(i(triple(X6,X0,X7)),X8) )
          & ( contains_pq(i(triple(X6,X0,X7)),X8)
            | ~ contains_cpq(triple(X6,X0,X7),X8) ) ) ),
    inference(rectify,[],[f116]) ).

fof(f116,plain,
    ? [X0] :
      ( ? [X4,X5,X6,X7,X8] :
          ( ( ~ contains_pq(i(triple(X4,insert_slb(X0,pair(X6,X7)),X5)),X8)
            | ~ contains_cpq(triple(X4,insert_slb(X0,pair(X6,X7)),X5),X8) )
          & ( contains_pq(i(triple(X4,insert_slb(X0,pair(X6,X7)),X5)),X8)
            | contains_cpq(triple(X4,insert_slb(X0,pair(X6,X7)),X5),X8) ) )
      & ! [X1,X2,X3] :
          ( ( contains_cpq(triple(X1,X0,X2),X3)
            | ~ contains_pq(i(triple(X1,X0,X2)),X3) )
          & ( contains_pq(i(triple(X1,X0,X2)),X3)
            | ~ contains_cpq(triple(X1,X0,X2),X3) ) ) ),
    inference(nnf_transformation,[],[f75]) ).

fof(f75,plain,
    ? [X0] :
      ( ? [X4,X5,X6,X7,X8] :
          ( contains_cpq(triple(X4,insert_slb(X0,pair(X6,X7)),X5),X8)
        <~> contains_pq(i(triple(X4,insert_slb(X0,pair(X6,X7)),X5)),X8) )
      & ! [X1,X2,X3] :
          ( contains_cpq(triple(X1,X0,X2),X3)
        <=> contains_pq(i(triple(X1,X0,X2)),X3) ) ),
    inference(ennf_transformation,[],[f64]) ).

fof(f64,negated_conjecture,
    ~ ! [X0] :
        ( ! [X1,X2,X3] :
            ( contains_cpq(triple(X1,X0,X2),X3)
          <=> contains_pq(i(triple(X1,X0,X2)),X3) )
       => ! [X4,X5,X6,X7,X8] :
            ( contains_cpq(triple(X4,insert_slb(X0,pair(X6,X7)),X5),X8)
          <=> contains_pq(i(triple(X4,insert_slb(X0,pair(X6,X7)),X5)),X8) ) ),
    inference(negated_conjecture,[],[f63]) ).

fof(f63,conjecture,
    ! [X0] :
      ( ! [X1,X2,X3] :
          ( contains_cpq(triple(X1,X0,X2),X3)
        <=> contains_pq(i(triple(X1,X0,X2)),X3) )
     => ! [X4,X5,X6,X7,X8] :
          ( contains_cpq(triple(X4,insert_slb(X0,pair(X6,X7)),X5),X8)
        <=> contains_pq(i(triple(X4,insert_slb(X0,pair(X6,X7)),X5)),X8) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l6_co) ).

fof(f279,plain,
    ~ contains_pq(i(triple(sK1,sK0,sK2)),sK5),
    inference(factoring,[],[f274]) ).

fof(f274,plain,
    ! [X0,X1] :
      ( ~ contains_pq(i(triple(X0,sK0,X1)),sK5)
      | ~ contains_pq(i(triple(sK1,sK0,sK2)),sK5) ),
    inference(resolution,[],[f272,f173]) ).

fof(f173,plain,
    ! [X2,X0,X1] :
      ( contains_pq(insert_pq(X0,X1),X2)
      | ~ contains_pq(X0,X2) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f272,plain,
    ! [X0,X1] :
      ( ~ contains_pq(insert_pq(i(triple(sK1,sK0,sK2)),sK3),sK5)
      | ~ contains_pq(i(triple(X0,sK0,X1)),sK5) ),
    inference(resolution,[],[f271,f211]) ).

fof(f211,plain,
    ! [X2,X0,X1] :
      ( contains_slb(sK0,X0)
      | ~ contains_pq(i(triple(X1,sK0,X2)),X0) ),
    inference(resolution,[],[f187,f132]) ).

fof(f132,plain,
    ! [X8,X6,X7] :
      ( contains_cpq(triple(X6,sK0,X7),X8)
      | ~ contains_pq(i(triple(X6,sK0,X7)),X8) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f187,plain,
    ! [X2,X3,X0,X1] :
      ( ~ contains_cpq(triple(X0,X1,X2),X3)
      | contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f125]) ).

fof(f271,plain,
    ( ~ contains_slb(sK0,sK5)
    | ~ contains_pq(insert_pq(i(triple(sK1,sK0,sK2)),sK3),sK5) ),
    inference(resolution,[],[f270,f190]) ).

fof(f190,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
      | ~ contains_slb(X0,X2) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f270,plain,
    ( ~ contains_slb(insert_slb(sK0,pair(sK3,sK4)),sK5)
    | ~ contains_pq(insert_pq(i(triple(sK1,sK0,sK2)),sK3),sK5) ),
    inference(resolution,[],[f205,f188]) ).

fof(f205,plain,
    ( ~ contains_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2),sK5)
    | ~ contains_pq(insert_pq(i(triple(sK1,sK0,sK2)),sK3),sK5) ),
    inference(backward_demodulation,[],[f134,f192]) ).

fof(f192,plain,
    ! [X2,X3,X0,X1,X4] : i(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) = insert_pq(i(triple(X0,X1,X2)),X3),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,axiom,
    ! [X0,X1,X2,X3,X4] : i(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) = insert_pq(i(triple(X0,X1,X2)),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).

fof(f134,plain,
    ( ~ contains_pq(i(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)),sK5)
    | ~ contains_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2),sK5) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f319,plain,
    ( contains_slb(sK0,sK5)
    | sK3 = sK5 ),
    inference(resolution,[],[f318,f283]) ).

fof(f283,plain,
    ! [X0,X1] : ~ contains_pq(i(triple(X0,sK0,X1)),sK5),
    inference(resolution,[],[f282,f211]) ).

fof(f318,plain,
    ( contains_pq(i(triple(sK1,sK0,sK2)),sK5)
    | sK3 = sK5
    | contains_slb(sK0,sK5) ),
    inference(duplicate_literal_removal,[],[f317]) ).

fof(f317,plain,
    ( contains_slb(sK0,sK5)
    | sK3 = sK5
    | contains_pq(i(triple(sK1,sK0,sK2)),sK5)
    | sK3 = sK5 ),
    inference(resolution,[],[f189,f268]) ).

fof(f268,plain,
    ( contains_slb(insert_slb(sK0,pair(sK3,sK4)),sK5)
    | contains_pq(i(triple(sK1,sK0,sK2)),sK5)
    | sK3 = sK5 ),
    inference(resolution,[],[f267,f172]) ).

fof(f172,plain,
    ! [X2,X0,X1] :
      ( ~ contains_pq(insert_pq(X0,X1),X2)
      | contains_pq(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[],[f124]) ).

fof(f267,plain,
    ( contains_pq(insert_pq(i(triple(sK1,sK0,sK2)),sK3),sK5)
    | contains_slb(insert_slb(sK0,pair(sK3,sK4)),sK5) ),
    inference(resolution,[],[f204,f187]) ).

fof(f204,plain,
    ( contains_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2),sK5)
    | contains_pq(insert_pq(i(triple(sK1,sK0,sK2)),sK3),sK5) ),
    inference(backward_demodulation,[],[f133,f192]) ).

fof(f133,plain,
    ( contains_pq(i(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)),sK5)
    | contains_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2),sK5) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f189,plain,
    ! [X2,X3,X0,X1] :
      ( ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2)
      | contains_slb(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[],[f127]) ).

fof(f324,plain,
    ( ~ contains_pq(insert_pq(i(triple(sK1,sK0,sK2)),sK3),sK3)
    | ~ contains_slb(insert_slb(sK0,pair(sK3,sK4)),sK5) ),
    inference(backward_demodulation,[],[f270,f320]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWV370+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.35  % Computer : n028.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit   : 300
% 0.12/0.35  % WCLimit    : 300
% 0.12/0.35  % DateTime   : Tue Apr 30 05:03:14 EDT 2024
% 0.12/0.35  % CPUTime    : 
% 0.19/0.36  % (8915)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.37  % (8918)WARNING: value z3 for option sas not known
% 0.19/0.37  % (8918)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.19/0.37  % (8919)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.37  % (8920)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.19/0.37  % (8922)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.19/0.37  % (8917)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.37  % (8921)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.19/0.38  % (8916)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.38  TRYING [1]
% 0.19/0.38  TRYING [2]
% 0.19/0.38  % (8921)First to succeed.
% 0.19/0.39  % (8921)Refutation found. Thanks to Tanya!
% 0.19/0.39  % SZS status Theorem for theBenchmark
% 0.19/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.39  % (8921)------------------------------
% 0.19/0.39  % (8921)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.39  % (8921)Termination reason: Refutation
% 0.19/0.39  
% 0.19/0.39  % (8921)Memory used [KB]: 1034
% 0.19/0.39  % (8921)Time elapsed: 0.012 s
% 0.19/0.39  % (8921)Instructions burned: 20 (million)
% 0.19/0.39  % (8921)------------------------------
% 0.19/0.39  % (8921)------------------------------
% 0.19/0.39  % (8915)Success in time 0.029 s
%------------------------------------------------------------------------------