TSTP Solution File: SYN069+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYN069+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -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 : Tue Apr 30 18:02:04 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   48 (   7 unt;   0 def)
%            Number of atoms       :  160 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  167 (  55   ~;  49   |;  54   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   71 (  53   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f65,plain,
    $false,
    inference(resolution,[],[f64,f42]) ).

fof(f42,plain,
    ~ big_k(sK2(sK4)),
    inference(resolution,[],[f41,f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ~ big_l(X0)
      | ~ big_k(X0) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X0] :
      ( ~ big_k(X0)
      | ~ big_l(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,plain,
    ~ ? [X0] :
        ( big_k(X0)
        & big_l(X0) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ~ ? [X1] :
        ( big_k(X1)
        & big_l(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45_2) ).

fof(f41,plain,
    big_l(sK2(sK4)),
    inference(resolution,[],[f37,f40]) ).

fof(f40,plain,
    big_h(sK4,sK2(sK4)),
    inference(resolution,[],[f27,f36]) ).

fof(f36,plain,
    big_f(sK4),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ( ! [X1] :
        ( big_j(sK4,X1)
        | ~ big_h(sK4,X1)
        | ~ big_g(X1) )
    & ! [X2] :
        ( big_l(X2)
        | ~ big_h(sK4,X2) )
    & big_f(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f13,f24]) ).

fof(f24,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( big_j(X0,X1)
            | ~ big_h(X0,X1)
            | ~ big_g(X1) )
        & ! [X2] :
            ( big_l(X2)
            | ~ big_h(X0,X2) )
        & big_f(X0) )
   => ( ! [X1] :
          ( big_j(sK4,X1)
          | ~ big_h(sK4,X1)
          | ~ big_g(X1) )
      & ! [X2] :
          ( big_l(X2)
          | ~ big_h(sK4,X2) )
      & big_f(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0] :
      ( ! [X1] :
          ( big_j(X0,X1)
          | ~ big_h(X0,X1)
          | ~ big_g(X1) )
      & ! [X2] :
          ( big_l(X2)
          | ~ big_h(X0,X2) )
      & big_f(X0) ),
    inference(flattening,[],[f12]) ).

fof(f12,plain,
    ? [X0] :
      ( ! [X1] :
          ( big_j(X0,X1)
          | ~ big_h(X0,X1)
          | ~ big_g(X1) )
      & ! [X2] :
          ( big_l(X2)
          | ~ big_h(X0,X2) )
      & big_f(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,plain,
    ? [X0] :
      ( ! [X1] :
          ( ( big_h(X0,X1)
            & big_g(X1) )
         => big_j(X0,X1) )
      & ! [X2] :
          ( big_h(X0,X2)
         => big_l(X2) )
      & big_f(X0) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ? [X0] :
      ( ! [X2] :
          ( ( big_h(X0,X2)
            & big_g(X2) )
         => big_j(X0,X2) )
      & ! [X1] :
          ( big_h(X0,X1)
         => big_l(X1) )
      & big_f(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45_3) ).

fof(f27,plain,
    ! [X0] :
      ( ~ big_f(X0)
      | big_h(X0,sK2(X0)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0] :
      ( ( big_h(X0,sK2(X0))
        & big_g(sK2(X0)) )
      | ~ big_f(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f8,f17]) ).

fof(f17,plain,
    ! [X0] :
      ( ? [X1] :
          ( big_h(X0,X1)
          & big_g(X1) )
     => ( big_h(X0,sK2(X0))
        & big_g(sK2(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f8,plain,
    ! [X0] :
      ( ? [X1] :
          ( big_h(X0,X1)
          & big_g(X1) )
      | ~ big_f(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,negated_conjecture,
    ~ ? [X0] :
        ( ~ ? [X1] :
              ( big_h(X0,X1)
              & big_g(X1) )
        & big_f(X0) ),
    inference(negated_conjecture,[],[f4]) ).

fof(f4,conjecture,
    ? [X0] :
      ( ~ ? [X1] :
            ( big_h(X0,X1)
            & big_g(X1) )
      & big_f(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45) ).

fof(f37,plain,
    ! [X2] :
      ( ~ big_h(sK4,X2)
      | big_l(X2) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f64,plain,
    ! [X0] : big_k(X0),
    inference(subsumption_resolution,[],[f63,f45]) ).

fof(f45,plain,
    ! [X0] :
      ( sP0(sK4)
      | big_k(X0) ),
    inference(resolution,[],[f43,f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ sP1(X0)
      | big_k(X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0] :
      ( ! [X1] :
          ( big_k(X1)
          & big_h(X0,X1)
          & big_g(X1) )
      | ~ sP1(X0) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X0] :
      ( ! [X2] :
          ( big_k(X2)
          & big_h(X0,X2)
          & big_g(X2) )
      | ~ sP1(X0) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0] :
      ( ! [X2] :
          ( big_k(X2)
          & big_h(X0,X2)
          & big_g(X2) )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f43,plain,
    ( sP1(sK4)
    | sP0(sK4) ),
    inference(resolution,[],[f35,f36]) ).

fof(f35,plain,
    ! [X0] :
      ( ~ big_f(X0)
      | sP0(X0)
      | sP1(X0) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0] :
      ( sP1(X0)
      | sP0(X0)
      | ~ big_f(X0) ),
    inference(definition_folding,[],[f11,f15,f14]) ).

fof(f14,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ big_j(X0,X1)
          & big_h(X0,X1)
          & big_g(X1) )
      | ~ sP0(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f11,plain,
    ! [X0] :
      ( ! [X2] :
          ( big_k(X2)
          & big_h(X0,X2)
          & big_g(X2) )
      | ? [X1] :
          ( ~ big_j(X0,X1)
          & big_h(X0,X1)
          & big_g(X1) )
      | ~ big_f(X0) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ! [X0] :
      ( ! [X2] :
          ( big_k(X2)
          & big_h(X0,X2)
          & big_g(X2) )
      | ? [X1] :
          ( ~ big_j(X0,X1)
          & big_h(X0,X1)
          & big_g(X1) )
      | ~ big_f(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( ( ! [X1] :
            ( ( big_h(X0,X1)
              & big_g(X1) )
           => big_j(X0,X1) )
        & big_f(X0) )
     => ! [X2] :
          ( big_k(X2)
          & big_h(X0,X2)
          & big_g(X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel45_1) ).

fof(f63,plain,
    ! [X0] :
      ( big_k(X0)
      | ~ sP0(sK4) ),
    inference(resolution,[],[f62,f34]) ).

fof(f34,plain,
    ! [X0] :
      ( ~ big_j(X0,sK3(X0))
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0] :
      ( ( ~ big_j(X0,sK3(X0))
        & big_h(X0,sK3(X0))
        & big_g(sK3(X0)) )
      | ~ sP0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f21,f22]) ).

fof(f22,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ big_j(X0,X1)
          & big_h(X0,X1)
          & big_g(X1) )
     => ( ~ big_j(X0,sK3(X0))
        & big_h(X0,sK3(X0))
        & big_g(sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ big_j(X0,X1)
          & big_h(X0,X1)
          & big_g(X1) )
      | ~ sP0(X0) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f62,plain,
    ! [X0] :
      ( big_j(sK4,sK3(sK4))
      | big_k(X0) ),
    inference(subsumption_resolution,[],[f60,f54]) ).

fof(f54,plain,
    big_g(sK3(sK4)),
    inference(resolution,[],[f48,f42]) ).

fof(f48,plain,
    ! [X0] :
      ( big_k(X0)
      | big_g(sK3(sK4)) ),
    inference(resolution,[],[f45,f32]) ).

fof(f32,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | big_g(sK3(X0)) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f60,plain,
    ! [X0] :
      ( big_k(X0)
      | big_j(sK4,sK3(sK4))
      | ~ big_g(sK3(sK4)) ),
    inference(resolution,[],[f47,f38]) ).

fof(f38,plain,
    ! [X1] :
      ( ~ big_h(sK4,X1)
      | big_j(sK4,X1)
      | ~ big_g(X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f47,plain,
    ! [X0] :
      ( big_h(sK4,sK3(sK4))
      | big_k(X0) ),
    inference(resolution,[],[f45,f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ~ sP0(X0)
      | big_h(X0,sK3(X0)) ),
    inference(cnf_transformation,[],[f23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SYN069+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n003.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Tue Apr 30 01:54:03 EDT 2024
% 0.14/0.37  % CPUTime    : 
% 0.14/0.37  % (19843)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39  % (19851)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.39  % (19847)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39  % (19850)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.39  % (19849)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.39  % (19848)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.39  Detected minimum model sizes of [1,1]
% 0.14/0.39  Detected maximum model sizes of [max,1]
% 0.14/0.39  Detected minimum model sizes of [1,1]
% 0.14/0.39  Detected maximum model sizes of [max,1]
% 0.14/0.39  TRYING [1,1]
% 0.14/0.39  TRYING [1,1]
% 0.14/0.39  TRYING [2,1]
% 0.14/0.39  TRYING [2,1]
% 0.14/0.39  % (19850)First to succeed.
% 0.14/0.39  % (19852)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.39  TRYING [3,1]
% 0.14/0.39  TRYING [3,1]
% 0.14/0.39  TRYING [4,1]
% 0.14/0.39  TRYING [4,1]
% 0.14/0.39  % (19846)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.39  TRYING [5,1]
% 0.14/0.39  TRYING [5,1]
% 0.14/0.39  % (19851)Also succeeded, but the first one will report.
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  TRYING [6,1]
% 0.14/0.39  TRYING [6,1]
% 0.14/0.39  TRYING [3]
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [7,1]
% 0.14/0.39  TRYING [7,1]
% 0.14/0.39  TRYING [2]
% 0.14/0.39  % (19852)Also succeeded, but the first one will report.
% 0.14/0.39  % (19850)Refutation found. Thanks to Tanya!
% 0.14/0.39  % SZS status Theorem for theBenchmark
% 0.14/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39  % (19850)------------------------------
% 0.14/0.39  % (19850)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.39  % (19850)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (19850)Memory used [KB]: 751
% 0.14/0.39  % (19850)Time elapsed: 0.004 s
% 0.14/0.39  % (19850)Instructions burned: 4 (million)
% 0.14/0.39  % (19850)------------------------------
% 0.14/0.39  % (19850)------------------------------
% 0.14/0.39  % (19843)Success in time 0.019 s
%------------------------------------------------------------------------------