TSTP Solution File: NUM765_8 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM765_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n012.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 May 21 02:13:19 EDT 2024

% Result   : Theorem 0.22s 0.38s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   50 (   3 unt;   8 typ;   0 def)
%            Number of atoms       :  105 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  116 (  53   ~;  34   |;   5   &)
%                                         (   4 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   64 (  64   !;   0   ?;  64   :)

% 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(f101,plain,
    $false,
    inference(avatar_sat_refutation,[],[f49,f58,f60,f62,f99,f100]) ).

tff(f100,plain,
    ( ~ spl0_1
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f97,f55,f42]) ).

tff(f42,plain,
    ( spl0_1
  <=> moref(x,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

tff(f55,plain,
    ( spl0_4
  <=> eq(z,u) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

tff(f97,plain,
    ( ~ eq(z,u)
    | ~ moref(x,y) ),
    inference(resolution,[],[f34,f27]) ).

tff(f27,plain,
    ~ moref(pf(x,z),pf(y,u)),
    inference(cnf_transformation,[],[f17]) ).

tff(f17,plain,
    ( ~ eq(pf(x,z),pf(y,u))
    & ~ moref(pf(x,z),pf(y,u)) ),
    inference(ennf_transformation,[],[f8]) ).

tff(f8,negated_conjecture,
    ~ ( ~ moref(pf(x,z),pf(y,u))
     => eq(pf(x,z),pf(y,u)) ),
    inference(negated_conjecture,[],[f7]) ).

tff(f7,conjecture,
    ( ~ moref(pf(x,z),pf(y,u))
   => eq(pf(x,z),pf(y,u)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz66) ).

tff(f34,plain,
    ! [X2: frac,X3: frac,X0: frac,X1: frac] :
      ( moref(pf(X0,X2),pf(X1,X3))
      | ~ eq(X2,X3)
      | ~ moref(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

tff(f24,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( moref(pf(X0,X2),pf(X1,X3))
      | ( ~ eq(X2,X3)
        & ~ moref(X2,X3) )
      | ~ moref(X0,X1) ),
    inference(flattening,[],[f23]) ).

tff(f23,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( moref(pf(X0,X2),pf(X1,X3))
      | ( ~ eq(X2,X3)
        & ~ moref(X2,X3) )
      | ~ moref(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

tff(f15,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( moref(X0,X1)
     => ( ( ~ moref(X2,X3)
         => eq(X2,X3) )
       => moref(pf(X0,X2),pf(X1,X3)) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X1: frac,X2: frac,X3: frac,X4: frac] :
      ( moref(X1,X2)
     => ( ( ~ moref(X3,X4)
         => eq(X3,X4) )
       => moref(pf(X1,X3),pf(X2,X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz65b) ).

tff(f99,plain,
    ( ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f98,f51,f46]) ).

tff(f46,plain,
    ( spl0_2
  <=> eq(x,y) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

tff(f51,plain,
    ( spl0_3
  <=> moref(z,u) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

tff(f98,plain,
    ( ~ moref(z,u)
    | ~ eq(x,y) ),
    inference(resolution,[],[f36,f27]) ).

tff(f36,plain,
    ! [X2: frac,X3: frac,X0: frac,X1: frac] :
      ( moref(pf(X0,X2),pf(X1,X3))
      | ~ moref(X2,X3)
      | ~ eq(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

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

tff(f25,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( moref(pf(X0,X2),pf(X1,X3))
      | ~ moref(X2,X3)
      | ( ~ eq(X0,X1)
        & ~ moref(X0,X1) ) ),
    inference(ennf_transformation,[],[f16]) ).

tff(f16,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( ( ~ moref(X0,X1)
       => eq(X0,X1) )
     => ( moref(X2,X3)
       => moref(pf(X0,X2),pf(X1,X3)) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X1: frac,X2: frac,X3: frac,X4: frac] :
      ( ( ~ moref(X1,X2)
       => eq(X1,X2) )
     => ( moref(X3,X4)
       => moref(pf(X1,X3),pf(X2,X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz65a) ).

tff(f62,plain,
    ( ~ spl0_1
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f61,f51,f42]) ).

tff(f61,plain,
    ( ~ moref(z,u)
    | ~ moref(x,y) ),
    inference(resolution,[],[f33,f27]) ).

tff(f33,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,[],[f24]) ).

tff(f60,plain,
    ( ~ spl0_2
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f59,f55,f46]) ).

tff(f59,plain,
    ( ~ eq(z,u)
    | ~ eq(x,y) ),
    inference(resolution,[],[f32,f28]) ).

tff(f28,plain,
    ~ eq(pf(x,z),pf(y,u)),
    inference(cnf_transformation,[],[f17]) ).

tff(f32,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,[],[f22]) ).

tff(f22,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( eq(pf(X0,X2),pf(X1,X3))
      | ~ eq(X2,X3)
      | ~ eq(X0,X1) ),
    inference(flattening,[],[f21]) ).

tff(f21,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,[],[f14]) ).

tff(f14,plain,
    ! [X0: frac,X1: frac,X2: frac,X3: frac] :
      ( eq(X0,X1)
     => ( eq(X2,X3)
       => eq(pf(X0,X2),pf(X1,X3)) ) ),
    inference(rectify,[],[f4]) ).

tff(f4,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/sandbox/benchmark/theBenchmark.p',satz56) ).

tff(f58,plain,
    ( spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f30,f55,f51]) ).

tff(f30,plain,
    ( eq(z,u)
    | moref(z,u) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f19,plain,
    ( eq(z,u)
    | moref(z,u) ),
    inference(ennf_transformation,[],[f2]) ).

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

tff(f49,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f29,f46,f42]) ).

tff(f29,plain,
    ( eq(x,y)
    | moref(x,y) ),
    inference(cnf_transformation,[],[f18]) ).

tff(f18,plain,
    ( eq(x,y)
    | moref(x,y) ),
    inference(ennf_transformation,[],[f1]) ).

tff(f1,axiom,
    ( ~ moref(x,y)
   => eq(x,y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM765_8 : TPTP v8.2.0. Released v8.0.0.
% 0.14/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n012.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % 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   : Mon May 20 07:33:08 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.22/0.36  % (17731)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38  % (17732)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.22/0.38  % (17735)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.22/0.38  % (17734)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)
% 0.22/0.38  % (17736)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.22/0.38  % (17737)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.22/0.38  % (17738)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)
% 0.22/0.38  % (17733)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38  Detected minimum model sizes of [1,1]
% 0.22/0.38  Detected minimum model sizes of [1,1]
% 0.22/0.38  Detected maximum model sizes of [max,2]
% 0.22/0.38  Detected maximum model sizes of [max,2]
% 0.22/0.38  TRYING [1,1]
% 0.22/0.38  TRYING [1,1]
% 0.22/0.38  Detected minimum model sizes of [1,1]
% 0.22/0.38  Detected maximum model sizes of [max,2]
% 0.22/0.38  TRYING [1,2]
% 0.22/0.38  Detected minimum model sizes of [1,1]
% 0.22/0.38  Detected maximum model sizes of [max,2]
% 0.22/0.38  TRYING [1,2]
% 0.22/0.38  TRYING [1,1]
% 0.22/0.38  TRYING [1,1]
% 0.22/0.38  TRYING [2,2]
% 0.22/0.38  TRYING [1,2]
% 0.22/0.38  TRYING [2,2]
% 0.22/0.38  TRYING [1,2]
% 0.22/0.38  TRYING [2,2]
% 0.22/0.38  TRYING [2,2]
% 0.22/0.38  % (17737)Also succeeded, but the first one will report.
% 0.22/0.38  % (17734)First to succeed.
% 0.22/0.38  % (17736)Also succeeded, but the first one will report.
% 0.22/0.38  % (17734)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-17731"
% 0.22/0.38  % (17734)Refutation found. Thanks to Tanya!
% 0.22/0.38  % SZS status Theorem for theBenchmark
% 0.22/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.38  % (17734)------------------------------
% 0.22/0.38  % (17734)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38  % (17734)Termination reason: Refutation
% 0.22/0.38  
% 0.22/0.38  % (17734)Memory used [KB]: 767
% 0.22/0.38  % (17734)Time elapsed: 0.006 s
% 0.22/0.38  % (17734)Instructions burned: 5 (million)
% 0.22/0.38  % (17731)Success in time 0.011 s
%------------------------------------------------------------------------------