TSTP Solution File: NUM762_8 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM762_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -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 : Tue Apr 30 14:37:35 EDT 2024

% Result   : Theorem 0.17s 0.35s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   64 (  12 unt;   9 typ;   0 def)
%            Number of atoms       :  128 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  135 (  62   ~;  51   |;   0   &)
%                                         (   5 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    8 (   4   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   96 (  96   !;   0   ?;  93   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    frac: $tType ).

tff(func_def_0,type,
    x: frac ).

tff(func_def_1,type,
    y: frac ).

tff(func_def_2,type,
    z: frac ).

tff(func_def_3,type,
    u: frac ).

tff(func_def_4,type,
    pf: ( frac * frac ) > frac ).

tff(pred_def_1,type,
    moref: ( frac * frac ) > $o ).

tff(pred_def_2,type,
    eq: ( frac * frac ) > $o ).

tff(pred_def_3,type,
    sP0: ( frac * frac ) > $o ).

tff(f472,plain,
    $false,
    inference(avatar_sat_refutation,[],[f54,f106,f319,f458,f471]) ).

tff(f471,plain,
    spl1_3,
    inference(avatar_contradiction_clause,[],[f467]) ).

tff(f467,plain,
    ( $false
    | spl1_3 ),
    inference(resolution,[],[f105,f32]) ).

tff(f32,plain,
    moref(x,y),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    moref(x,y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).

tff(f105,plain,
    ( ~ moref(x,y)
    | spl1_3 ),
    inference(avatar_component_clause,[],[f103]) ).

tff(f103,plain,
    ( spl1_3
  <=> moref(x,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

tff(f458,plain,
    ~ spl1_11,
    inference(avatar_contradiction_clause,[],[f454]) ).

tff(f454,plain,
    ( $false
    | ~ spl1_11 ),
    inference(resolution,[],[f453,f32]) ).

tff(f453,plain,
    ( ~ moref(x,y)
    | ~ spl1_11 ),
    inference(resolution,[],[f318,f34]) ).

tff(f34,plain,
    ! [X0: frac] : eq(X0,X0),
    inference(cnf_transformation,[],[f16]) ).

tff(f16,plain,
    ! [X0: frac] : eq(X0,X0),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X1: frac] : eq(X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37) ).

tff(f318,plain,
    ( ! [X0: frac] :
        ( ~ eq(X0,y)
        | ~ moref(x,X0) )
    | ~ spl1_11 ),
    inference(avatar_component_clause,[],[f317]) ).

tff(f317,plain,
    ( spl1_11
  <=> ! [X0: frac] :
        ( ~ eq(X0,y)
        | ~ moref(x,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).

tff(f319,plain,
    ( spl1_11
    | ~ spl1_2 ),
    inference(avatar_split_clause,[],[f302,f51,f317]) ).

tff(f51,plain,
    ( spl1_2
  <=> eq(z,u) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).

tff(f302,plain,
    ! [X0: frac] :
      ( ~ eq(z,u)
      | ~ eq(X0,y)
      | ~ moref(x,X0) ),
    inference(resolution,[],[f234,f36]) ).

tff(f36,plain,
    ! [X2: frac,X0: frac,X1: frac] :
      ( moref(pf(X0,X2),pf(X1,X2))
      | ~ moref(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

tff(f24,plain,
    ! [X0: frac,X1: frac,X2: frac] :
      ( moref(pf(X0,X2),pf(X1,X2))
      | ~ moref(X0,X1) ),
    inference(ennf_transformation,[],[f18]) ).

tff(f18,plain,
    ! [X0: frac,X1: frac,X2: frac] :
      ( moref(X0,X1)
     => moref(pf(X0,X2),pf(X1,X2)) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X1: frac,X2: frac,X3: frac] :
      ( moref(X1,X2)
     => moref(pf(X1,X3),pf(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz61) ).

tff(f234,plain,
    ! [X0: frac,X1: frac] :
      ( ~ moref(pf(x,z),pf(X0,X1))
      | ~ eq(X1,u)
      | ~ eq(X0,y) ),
    inference(resolution,[],[f205,f37]) ).

tff(f37,plain,
    ! [X2: frac,X3: frac,X0: frac,X1: frac] :
      ( eq(pf(X0,X2),pf(X1,X3))
      | ~ eq(X2,X3)
      | ~ eq(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

tff(f26,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( eq(pf(X0,X2),pf(X1,X3))
      | ~ eq(X2,X3)
      | ~ eq(X0,X1) ),
    inference(flattening,[],[f25]) ).

tff(f25,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( eq(pf(X0,X2),pf(X1,X3))
      | ~ eq(X2,X3)
      | ~ eq(X0,X1) ),
    inference(ennf_transformation,[],[f19]) ).

tff(f19,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( eq(X0,X1)
     => ( eq(X2,X3)
       => eq(pf(X0,X2),pf(X1,X3)) ) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X1: frac,X2: frac,X3: frac,X4: frac] :
      ( eq(X1,X2)
     => ( eq(X3,X4)
       => eq(pf(X1,X3),pf(X2,X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz56) ).

tff(f205,plain,
    ! [X0: frac] :
      ( ~ eq(X0,pf(y,u))
      | ~ moref(pf(x,z),X0) ),
    inference(resolution,[],[f111,f34]) ).

tff(f111,plain,
    ! [X0: frac,X1: frac] :
      ( ~ moref(X0,X1)
      | ~ eq(X0,pf(x,z))
      | ~ eq(X1,pf(y,u)) ),
    inference(resolution,[],[f58,f31]) ).

tff(f31,plain,
    ~ moref(pf(x,z),pf(y,u)),
    inference(cnf_transformation,[],[f15]) ).

tff(f15,plain,
    ~ moref(pf(x,z),pf(y,u)),
    inference(flattening,[],[f10]) ).

tff(f10,negated_conjecture,
    ~ moref(pf(x,z),pf(y,u)),
    inference(negated_conjecture,[],[f9]) ).

tff(f9,conjecture,
    moref(pf(x,z),pf(y,u)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz65b) ).

tff(f58,plain,
    ! [X2: frac,X3: frac,X0: frac,X1: frac] :
      ( moref(X3,X1)
      | ~ moref(X2,X0)
      | ~ eq(X2,X3)
      | ~ eq(X0,X1) ),
    inference(resolution,[],[f42,f41]) ).

tff(f41,plain,
    ! [X2: frac,X3: frac,X0: frac] :
      ( sP0(X0,X3)
      | ~ eq(X0,X2)
      | moref(X2,X3) ),
    inference(cnf_transformation,[],[f41_D]) ).

tff(f41_D,plain,
    ! [X3,X0] :
      ( ! [X2] :
          ( ~ eq(X0,X2)
          | moref(X2,X3) )
    <=> ~ sP0(X0,X3) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP0])]) ).

tff(f42,plain,
    ! [X3: frac,X0: frac,X1: frac] :
      ( ~ eq(X1,X3)
      | ~ moref(X0,X1)
      | ~ sP0(X0,X3) ),
    inference(general_splitting,[],[f38,f41_D]) ).

tff(f38,plain,
    ! [X2: frac,X3: frac,X0: frac,X1: frac] :
      ( moref(X2,X3)
      | ~ eq(X1,X3)
      | ~ eq(X0,X2)
      | ~ moref(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

tff(f28,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( moref(X2,X3)
      | ~ eq(X1,X3)
      | ~ eq(X0,X2)
      | ~ moref(X0,X1) ),
    inference(flattening,[],[f27]) ).

tff(f27,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( moref(X2,X3)
      | ~ eq(X1,X3)
      | ~ eq(X0,X2)
      | ~ moref(X0,X1) ),
    inference(ennf_transformation,[],[f20]) ).

tff(f20,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( moref(X0,X1)
     => ( eq(X0,X2)
       => ( eq(X1,X3)
         => moref(X2,X3) ) ) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X1: frac,X2: frac,X3: frac,X4: frac] :
      ( moref(X1,X2)
     => ( eq(X1,X3)
       => ( eq(X2,X4)
         => moref(X3,X4) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44) ).

tff(f106,plain,
    ( ~ spl1_3
    | ~ spl1_1 ),
    inference(avatar_split_clause,[],[f100,f47,f103]) ).

tff(f47,plain,
    ( spl1_1
  <=> moref(z,u) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).

tff(f100,plain,
    ( ~ moref(z,u)
    | ~ moref(x,y) ),
    inference(resolution,[],[f39,f31]) ).

tff(f39,plain,
    ! [X2: frac,X3: frac,X0: frac,X1: frac] :
      ( moref(pf(X0,X2),pf(X1,X3))
      | ~ moref(X2,X3)
      | ~ moref(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

tff(f30,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( moref(pf(X0,X2),pf(X1,X3))
      | ~ moref(X2,X3)
      | ~ moref(X0,X1) ),
    inference(flattening,[],[f29]) ).

tff(f29,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( moref(pf(X0,X2),pf(X1,X3))
      | ~ moref(X2,X3)
      | ~ moref(X0,X1) ),
    inference(ennf_transformation,[],[f21]) ).

tff(f21,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( moref(X0,X1)
     => ( moref(X2,X3)
       => moref(pf(X0,X2),pf(X1,X3)) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X1: frac,X2: frac,X3: frac,X4: frac] :
      ( moref(X1,X2)
     => ( moref(X3,X4)
       => moref(pf(X1,X3),pf(X2,X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz64) ).

tff(f54,plain,
    ( spl1_1
    | spl1_2 ),
    inference(avatar_split_clause,[],[f33,f51,f47]) ).

tff(f33,plain,
    ( eq(z,u)
    | moref(z,u) ),
    inference(cnf_transformation,[],[f22]) ).

tff(f22,plain,
    ( eq(z,u)
    | moref(z,u) ),
    inference(ennf_transformation,[],[f2]) ).

tff(f2,axiom,
    ( ~ moref(z,u)
   => eq(z,u) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem    : NUM762_8 : TPTP v8.1.2. Released v8.0.0.
% 0.03/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32  % Computer : n025.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Apr 30 00:13:56 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  % (19369)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34  % (19371)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.34  % (19374)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.11/0.34  % (19373)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.11/0.34  % (19370)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.11/0.34  Detected minimum model sizes of [1,1]
% 0.11/0.34  Detected maximum model sizes of [max,2]
% 0.11/0.34  TRYING [1,1]
% 0.11/0.34  % (19376)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)
% 0.11/0.34  TRYING [1,2]
% 0.11/0.34  TRYING [2,2]
% 0.11/0.34  % (19372)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)
% 0.11/0.34  % (19375)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.11/0.34  Detected minimum model sizes of [1,1]
% 0.11/0.34  Detected maximum model sizes of [max,2]
% 0.11/0.34  TRYING [1,1]
% 0.11/0.34  Detected minimum model sizes of [1,1]
% 0.11/0.34  Detected maximum model sizes of [max,2]
% 0.11/0.34  TRYING [1,1]
% 0.11/0.34  TRYING [1,2]
% 0.11/0.34  TRYING [1,2]
% 0.11/0.34  Detected minimum model sizes of [1,1]
% 0.11/0.34  Detected maximum model sizes of [max,2]
% 0.11/0.34  TRYING [3,2]
% 0.11/0.34  TRYING [2,2]
% 0.11/0.34  TRYING [1,1]
% 0.11/0.34  TRYING [2,2]
% 0.11/0.34  TRYING [1,2]
% 0.11/0.34  TRYING [2,2]
% 0.11/0.34  TRYING [3,2]
% 0.11/0.34  TRYING [3,2]
% 0.11/0.34  TRYING [3,2]
% 0.11/0.34  TRYING [4,2]
% 0.11/0.35  TRYING [4,2]
% 0.11/0.35  TRYING [4,2]
% 0.17/0.35  TRYING [4,2]
% 0.17/0.35  % (19372)First to succeed.
% 0.17/0.35  TRYING [5,2]
% 0.17/0.35  % (19372)Refutation found. Thanks to Tanya!
% 0.17/0.35  % SZS status Theorem for theBenchmark
% 0.17/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.35  % (19372)------------------------------
% 0.17/0.35  % (19372)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.17/0.35  % (19372)Termination reason: Refutation
% 0.17/0.35  
% 0.17/0.35  % (19372)Memory used [KB]: 916
% 0.17/0.35  % (19372)Time elapsed: 0.013 s
% 0.17/0.35  % (19372)Instructions burned: 23 (million)
% 0.17/0.35  % (19372)------------------------------
% 0.17/0.35  % (19372)------------------------------
% 0.17/0.35  % (19369)Success in time 0.027 s
%------------------------------------------------------------------------------