TSTP Solution File: COM007+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : COM007+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.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 : Mon May 20 19:11:12 EDT 2024

% Result   : Theorem 0.14s 0.39s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   85 (  11 unt;   0 def)
%            Number of atoms       :  220 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  231 (  96   ~; 109   |;  10   &)
%                                         (   8 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  12 usr;  10 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   91 (  87   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f313,plain,
    $false,
    inference(avatar_sat_refutation,[],[f45,f46,f66,f84,f115,f206,f266,f283,f312]) ).

fof(f312,plain,
    ( ~ spl1_1
    | ~ spl1_9
    | ~ spl1_28 ),
    inference(avatar_contradiction_clause,[],[f311]) ).

fof(f311,plain,
    ( $false
    | ~ spl1_1
    | ~ spl1_9
    | ~ spl1_28 ),
    inference(subsumption_resolution,[],[f308,f157]) ).

fof(f157,plain,
    ( ~ reflexive_rewrite(b,sK0(c,b))
    | ~ spl1_1
    | ~ spl1_9 ),
    inference(resolution,[],[f144,f40]) ).

fof(f40,plain,
    ( ! [X0] :
        ( ~ reflexive_rewrite(c,X0)
        | ~ reflexive_rewrite(b,X0) )
    | ~ spl1_1 ),
    inference(avatar_component_clause,[],[f39]) ).

fof(f39,plain,
    ( spl1_1
  <=> ! [X0] :
        ( ~ reflexive_rewrite(c,X0)
        | ~ reflexive_rewrite(b,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).

fof(f144,plain,
    ( reflexive_rewrite(c,sK0(c,b))
    | ~ spl1_9 ),
    inference(resolution,[],[f114,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ rewrite(X0,X1)
      | reflexive_rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( reflexive_rewrite(X0,X1)
      | ~ rewrite(X0,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( rewrite(X0,X1)
     => reflexive_rewrite(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rewrite_in_reflexive_rewrite) ).

fof(f114,plain,
    ( rewrite(c,sK0(c,b))
    | ~ spl1_9 ),
    inference(avatar_component_clause,[],[f112]) ).

fof(f112,plain,
    ( spl1_9
  <=> rewrite(c,sK0(c,b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).

fof(f308,plain,
    ( reflexive_rewrite(b,sK0(c,b))
    | ~ spl1_28 ),
    inference(resolution,[],[f282,f33]) ).

fof(f282,plain,
    ( rewrite(b,sK0(c,b))
    | ~ spl1_28 ),
    inference(avatar_component_clause,[],[f280]) ).

fof(f280,plain,
    ( spl1_28
  <=> rewrite(b,sK0(c,b)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).

fof(f283,plain,
    ( spl1_5
    | spl1_28
    | ~ spl1_7 ),
    inference(avatar_split_clause,[],[f221,f82,f280,f68]) ).

fof(f68,plain,
    ( spl1_5
  <=> equalish(a,c) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).

fof(f82,plain,
    ( spl1_7
  <=> ! [X0] :
        ( equalish(a,X0)
        | rewrite(b,sK0(X0,b))
        | ~ reflexive_rewrite(a,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).

fof(f221,plain,
    ( rewrite(b,sK0(c,b))
    | equalish(a,c)
    | ~ spl1_7 ),
    inference(resolution,[],[f83,f28]) ).

fof(f28,plain,
    reflexive_rewrite(a,c),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ( reflexive_rewrite(a,c)
    & reflexive_rewrite(a,b) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption) ).

fof(f83,plain,
    ( ! [X0] :
        ( ~ reflexive_rewrite(a,X0)
        | rewrite(b,sK0(X0,b))
        | equalish(a,X0) )
    | ~ spl1_7 ),
    inference(avatar_component_clause,[],[f82]) ).

fof(f266,plain,
    ( ~ spl1_1
    | ~ spl1_5 ),
    inference(avatar_contradiction_clause,[],[f265]) ).

fof(f265,plain,
    ( $false
    | ~ spl1_1
    | ~ spl1_5 ),
    inference(subsumption_resolution,[],[f262,f48]) ).

fof(f48,plain,
    ! [X0] : reflexive_rewrite(X0,X0),
    inference(resolution,[],[f32,f29]) ).

fof(f29,plain,
    ! [X0] : equalish(X0,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : equalish(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ equalish(X0,X1)
      | reflexive_rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( reflexive_rewrite(X0,X1)
      | ~ equalish(X0,X1) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( equalish(X0,X1)
     => reflexive_rewrite(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equalish_in_reflexive_rewrite) ).

fof(f262,plain,
    ( ~ reflexive_rewrite(b,b)
    | ~ spl1_1
    | ~ spl1_5 ),
    inference(resolution,[],[f258,f40]) ).

fof(f258,plain,
    ( reflexive_rewrite(c,b)
    | ~ spl1_5 ),
    inference(resolution,[],[f225,f27]) ).

fof(f27,plain,
    reflexive_rewrite(a,b),
    inference(cnf_transformation,[],[f1]) ).

fof(f225,plain,
    ( ! [X0] :
        ( ~ reflexive_rewrite(a,X0)
        | reflexive_rewrite(c,X0) )
    | ~ spl1_5 ),
    inference(resolution,[],[f219,f37]) ).

fof(f37,plain,
    ! [X2,X0,X1] :
      ( ~ equalish(X0,X1)
      | ~ reflexive_rewrite(X1,X2)
      | reflexive_rewrite(X0,X2) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( reflexive_rewrite(X0,X2)
      | ~ reflexive_rewrite(X1,X2)
      | ~ equalish(X0,X1) ),
    inference(flattening,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( reflexive_rewrite(X0,X2)
      | ~ reflexive_rewrite(X1,X2)
      | ~ equalish(X0,X1) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( ( reflexive_rewrite(X1,X2)
        & equalish(X0,X1) )
     => reflexive_rewrite(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution) ).

fof(f219,plain,
    ( equalish(c,a)
    | ~ spl1_5 ),
    inference(resolution,[],[f70,f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ equalish(X0,X1)
      | equalish(X1,X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( equalish(X1,X0)
      | ~ equalish(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( equalish(X0,X1)
     => equalish(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmtery) ).

fof(f70,plain,
    ( equalish(a,c)
    | ~ spl1_5 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f206,plain,
    ( ~ spl1_1
    | ~ spl1_3 ),
    inference(avatar_contradiction_clause,[],[f205]) ).

fof(f205,plain,
    ( $false
    | ~ spl1_1
    | ~ spl1_3 ),
    inference(subsumption_resolution,[],[f203,f49]) ).

fof(f49,plain,
    ( ~ reflexive_rewrite(b,c)
    | ~ spl1_1 ),
    inference(resolution,[],[f40,f48]) ).

fof(f203,plain,
    ( reflexive_rewrite(b,c)
    | ~ spl1_3 ),
    inference(resolution,[],[f127,f28]) ).

fof(f127,plain,
    ( ! [X0] :
        ( ~ reflexive_rewrite(a,X0)
        | reflexive_rewrite(b,X0) )
    | ~ spl1_3 ),
    inference(resolution,[],[f122,f37]) ).

fof(f122,plain,
    ( equalish(b,a)
    | ~ spl1_3 ),
    inference(resolution,[],[f62,f31]) ).

fof(f62,plain,
    ( equalish(a,b)
    | ~ spl1_3 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f60,plain,
    ( spl1_3
  <=> equalish(a,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

fof(f115,plain,
    ( spl1_5
    | spl1_9
    | ~ spl1_4 ),
    inference(avatar_split_clause,[],[f89,f64,f112,f68]) ).

fof(f64,plain,
    ( spl1_4
  <=> ! [X0] :
        ( equalish(a,X0)
        | rewrite(X0,sK0(X0,b))
        | ~ reflexive_rewrite(a,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).

fof(f89,plain,
    ( rewrite(c,sK0(c,b))
    | equalish(a,c)
    | ~ spl1_4 ),
    inference(resolution,[],[f65,f28]) ).

fof(f65,plain,
    ( ! [X0] :
        ( ~ reflexive_rewrite(a,X0)
        | rewrite(X0,sK0(X0,b))
        | equalish(a,X0) )
    | ~ spl1_4 ),
    inference(avatar_component_clause,[],[f64]) ).

fof(f84,plain,
    ( spl1_3
    | spl1_7 ),
    inference(avatar_split_clause,[],[f78,f82,f60]) ).

fof(f78,plain,
    ! [X0] :
      ( equalish(a,X0)
      | ~ reflexive_rewrite(a,X0)
      | equalish(a,b)
      | rewrite(b,sK0(X0,b)) ),
    inference(resolution,[],[f55,f27]) ).

fof(f55,plain,
    ! [X2,X0,X1] :
      ( ~ reflexive_rewrite(X2,X0)
      | equalish(X2,X1)
      | ~ reflexive_rewrite(X2,X1)
      | equalish(X2,X0)
      | rewrite(X0,sK0(X1,X0)) ),
    inference(resolution,[],[f53,f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( rewrite(X0,X1)
      | equalish(X0,X1)
      | ~ reflexive_rewrite(X0,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( rewrite(X0,X1)
      | equalish(X0,X1)
      | ~ reflexive_rewrite(X0,X1) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( rewrite(X0,X1)
      | equalish(X0,X1)
      | ~ reflexive_rewrite(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( reflexive_rewrite(X0,X1)
     => ( rewrite(X0,X1)
        | equalish(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equalish_or_rewrite) ).

fof(f53,plain,
    ! [X2,X0,X1] :
      ( ~ rewrite(X0,X1)
      | rewrite(X1,sK0(X2,X1))
      | equalish(X0,X2)
      | ~ reflexive_rewrite(X0,X2) ),
    inference(resolution,[],[f36,f34]) ).

fof(f36,plain,
    ! [X2,X0,X1] :
      ( ~ rewrite(X0,X1)
      | ~ rewrite(X0,X2)
      | rewrite(X2,sK0(X1,X2)) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( rewrite(X2,sK0(X1,X2))
        & rewrite(X1,sK0(X1,X2)) )
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f24]) ).

fof(f24,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( rewrite(X2,X3)
          & rewrite(X1,X3) )
     => ( rewrite(X2,sK0(X1,X2))
        & rewrite(X1,sK0(X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( rewrite(X2,X3)
          & rewrite(X1,X3) )
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( rewrite(X2,X3)
          & rewrite(X1,X3) )
      | ~ rewrite(X0,X2)
      | ~ rewrite(X0,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X2] :
      ( ( rewrite(X0,X2)
        & rewrite(X0,X1) )
     => ? [X3] :
          ( rewrite(X2,X3)
          & rewrite(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rewrite_diamond) ).

fof(f66,plain,
    ( spl1_3
    | spl1_4 ),
    inference(avatar_split_clause,[],[f56,f64,f60]) ).

fof(f56,plain,
    ! [X0] :
      ( equalish(a,X0)
      | ~ reflexive_rewrite(a,X0)
      | equalish(a,b)
      | rewrite(X0,sK0(X0,b)) ),
    inference(resolution,[],[f54,f27]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( ~ reflexive_rewrite(X2,X1)
      | equalish(X2,X0)
      | ~ reflexive_rewrite(X2,X0)
      | equalish(X2,X1)
      | rewrite(X0,sK0(X0,X1)) ),
    inference(resolution,[],[f52,f34]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( ~ rewrite(X0,X1)
      | rewrite(X2,sK0(X2,X1))
      | equalish(X0,X2)
      | ~ reflexive_rewrite(X0,X2) ),
    inference(resolution,[],[f35,f34]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( ~ rewrite(X0,X1)
      | ~ rewrite(X0,X2)
      | rewrite(X1,sK0(X1,X2)) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f46,plain,
    ~ spl1_2,
    inference(avatar_split_clause,[],[f26,f42]) ).

fof(f42,plain,
    ( spl1_2
  <=> goal ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).

fof(f26,plain,
    ~ goal,
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ~ goal,
    inference(flattening,[],[f11]) ).

fof(f11,negated_conjecture,
    ~ goal,
    inference(negated_conjecture,[],[f10]) ).

fof(f10,conjecture,
    goal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_to_be_proved) ).

fof(f45,plain,
    ( spl1_1
    | spl1_2 ),
    inference(avatar_split_clause,[],[f30,f42,f39]) ).

fof(f30,plain,
    ! [X0] :
      ( goal
      | ~ reflexive_rewrite(c,X0)
      | ~ reflexive_rewrite(b,X0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0] :
      ( goal
      | ~ reflexive_rewrite(c,X0)
      | ~ reflexive_rewrite(b,X0) ),
    inference(flattening,[],[f13]) ).

fof(f13,plain,
    ! [X0] :
      ( goal
      | ~ reflexive_rewrite(c,X0)
      | ~ reflexive_rewrite(b,X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( ( reflexive_rewrite(c,X0)
        & reflexive_rewrite(b,X0) )
     => goal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_ax) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : COM007+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n017.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   : Sun May 19 10:35:53 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (19045)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (19047)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  TRYING [3]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [5]
% 0.14/0.38  TRYING [6]
% 0.14/0.38  % (19046)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.38  % (19049)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.38  % (19048)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)
% 0.14/0.38  % (19050)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.38  % (19052)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)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  % (19051)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [1]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [2]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [3]
% 0.14/0.38  TRYING [7]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [4]
% 0.14/0.38  TRYING [5]
% 0.14/0.39  TRYING [5]
% 0.14/0.39  TRYING [5]
% 0.14/0.39  % (19051)First to succeed.
% 0.14/0.39  TRYING [8]
% 0.14/0.39  TRYING [6]
% 0.14/0.39  % (19051)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-19045"
% 0.14/0.39  TRYING [6]
% 0.14/0.39  % (19051)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  % (19051)------------------------------
% 0.14/0.39  % (19051)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39  % (19051)Termination reason: Refutation
% 0.14/0.39  
% 0.14/0.39  % (19051)Memory used [KB]: 876
% 0.14/0.39  % (19051)Time elapsed: 0.009 s
% 0.14/0.39  % (19051)Instructions burned: 11 (million)
% 0.14/0.39  % (19045)Success in time 0.014 s
%------------------------------------------------------------------------------