TSTP Solution File: COM012+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : COM012+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n015.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 : Wed Aug 31 15:53:09 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   45 (  11 unt;   0 def)
%            Number of atoms       :  248 (  27 equ)
%            Maximal formula atoms :   21 (   5 avg)
%            Number of connectives :  276 (  73   ~;  88   |; 104   &)
%                                         (   4 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   5 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   41 (  24   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f168,plain,
    $false,
    inference(avatar_sat_refutation,[],[f95,f109,f134,f148,f167]) ).

fof(f167,plain,
    ( ~ spl3_4
    | ~ spl3_8 ),
    inference(avatar_contradiction_clause,[],[f166]) ).

fof(f166,plain,
    ( $false
    | ~ spl3_4
    | ~ spl3_8 ),
    inference(subsumption_resolution,[],[f163,f108]) ).

fof(f108,plain,
    ( sdtmndtplgtdt0(xx,xR,xy)
    | ~ spl3_8 ),
    inference(avatar_component_clause,[],[f106]) ).

fof(f106,plain,
    ( spl3_8
  <=> sdtmndtplgtdt0(xx,xR,xy) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).

fof(f163,plain,
    ( ~ sdtmndtplgtdt0(xx,xR,xy)
    | ~ spl3_4 ),
    inference(unit_resulting_resolution,[],[f69,f70,f71,f68,f49,f90,f43]) ).

fof(f43,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sdtmndtplgtdt0(X2,X3,X1)
      | ~ aElement0(X0)
      | sdtmndtplgtdt0(X0,X3,X1)
      | ~ aElement0(X2)
      | ~ aElement0(X1)
      | ~ sdtmndtplgtdt0(X0,X3,X2)
      | ~ aRewritingSystem0(X3) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1,X2,X3] :
      ( ~ aElement0(X1)
      | ~ sdtmndtplgtdt0(X2,X3,X1)
      | sdtmndtplgtdt0(X0,X3,X1)
      | ~ sdtmndtplgtdt0(X0,X3,X2)
      | ~ aRewritingSystem0(X3)
      | ~ aElement0(X0)
      | ~ aElement0(X2) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ! [X0,X3,X2,X1] :
      ( ~ aElement0(X3)
      | ~ sdtmndtplgtdt0(X2,X1,X3)
      | sdtmndtplgtdt0(X0,X1,X3)
      | ~ sdtmndtplgtdt0(X0,X1,X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0)
      | ~ aElement0(X2) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X0,X2,X3,X1] :
      ( sdtmndtplgtdt0(X0,X1,X3)
      | ~ sdtmndtplgtdt0(X2,X1,X3)
      | ~ sdtmndtplgtdt0(X0,X1,X2)
      | ~ aElement0(X3)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X0)
      | ~ aElement0(X2) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X2,X3,X1] :
      ( ( aElement0(X3)
        & aRewritingSystem0(X1)
        & aElement0(X0)
        & aElement0(X2) )
     => ( ( sdtmndtplgtdt0(X2,X1,X3)
          & sdtmndtplgtdt0(X0,X1,X2) )
       => sdtmndtplgtdt0(X0,X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCTrans) ).

fof(f90,plain,
    ( sdtmndtplgtdt0(xy,xR,xz)
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f88]) ).

fof(f88,plain,
    ( spl3_4
  <=> sdtmndtplgtdt0(xy,xR,xz) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

fof(f49,plain,
    ~ sdtmndtplgtdt0(xx,xR,xz),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ( sdtmndtasgtdt0(xx,xR,xy)
    & ~ aReductOfIn0(xz,xx,xR)
    & ! [X0] :
        ( ~ aElement0(X0)
        | ~ aReductOfIn0(X0,xx,xR)
        | ~ sdtmndtplgtdt0(X0,xR,xz) )
    & ( ( sdtmndtplgtdt0(xx,xR,xy)
        & ( ( sdtmndtplgtdt0(sK0,xR,xy)
            & aReductOfIn0(sK0,xx,xR)
            & aElement0(sK0) )
          | aReductOfIn0(xy,xx,xR) ) )
      | xx = xy )
    & sdtmndtasgtdt0(xy,xR,xz)
    & ~ sdtmndtasgtdt0(xx,xR,xz)
    & ( xy = xz
      | ( ( aReductOfIn0(xz,xy,xR)
          | ( sdtmndtplgtdt0(sK1,xR,xz)
            & aReductOfIn0(sK1,xy,xR)
            & aElement0(sK1) ) )
        & sdtmndtplgtdt0(xy,xR,xz) ) )
    & ~ sdtmndtplgtdt0(xx,xR,xz)
    & xx != xz ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f34,f36,f35]) ).

fof(f35,plain,
    ( ? [X1] :
        ( sdtmndtplgtdt0(X1,xR,xy)
        & aReductOfIn0(X1,xx,xR)
        & aElement0(X1) )
   => ( sdtmndtplgtdt0(sK0,xR,xy)
      & aReductOfIn0(sK0,xx,xR)
      & aElement0(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ( ? [X2] :
        ( sdtmndtplgtdt0(X2,xR,xz)
        & aReductOfIn0(X2,xy,xR)
        & aElement0(X2) )
   => ( sdtmndtplgtdt0(sK1,xR,xz)
      & aReductOfIn0(sK1,xy,xR)
      & aElement0(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ( sdtmndtasgtdt0(xx,xR,xy)
    & ~ aReductOfIn0(xz,xx,xR)
    & ! [X0] :
        ( ~ aElement0(X0)
        | ~ aReductOfIn0(X0,xx,xR)
        | ~ sdtmndtplgtdt0(X0,xR,xz) )
    & ( ( sdtmndtplgtdt0(xx,xR,xy)
        & ( ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,xy)
              & aReductOfIn0(X1,xx,xR)
              & aElement0(X1) )
          | aReductOfIn0(xy,xx,xR) ) )
      | xx = xy )
    & sdtmndtasgtdt0(xy,xR,xz)
    & ~ sdtmndtasgtdt0(xx,xR,xz)
    & ( xy = xz
      | ( ( aReductOfIn0(xz,xy,xR)
          | ? [X2] :
              ( sdtmndtplgtdt0(X2,xR,xz)
              & aReductOfIn0(X2,xy,xR)
              & aElement0(X2) ) )
        & sdtmndtplgtdt0(xy,xR,xz) ) )
    & ~ sdtmndtplgtdt0(xx,xR,xz)
    & xx != xz ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ( sdtmndtasgtdt0(xx,xR,xy)
    & ~ aReductOfIn0(xz,xx,xR)
    & ! [X2] :
        ( ~ aElement0(X2)
        | ~ aReductOfIn0(X2,xx,xR)
        | ~ sdtmndtplgtdt0(X2,xR,xz) )
    & ( ( sdtmndtplgtdt0(xx,xR,xy)
        & ( ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,xy)
              & aReductOfIn0(X1,xx,xR)
              & aElement0(X1) )
          | aReductOfIn0(xy,xx,xR) ) )
      | xx = xy )
    & sdtmndtasgtdt0(xy,xR,xz)
    & ~ sdtmndtasgtdt0(xx,xR,xz)
    & ( xy = xz
      | ( ( aReductOfIn0(xz,xy,xR)
          | ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xz)
              & aReductOfIn0(X0,xy,xR)
              & aElement0(X0) ) )
        & sdtmndtplgtdt0(xy,xR,xz) ) )
    & ~ sdtmndtplgtdt0(xx,xR,xz)
    & xx != xz ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ( ! [X2] :
        ( ~ aElement0(X2)
        | ~ aReductOfIn0(X2,xx,xR)
        | ~ sdtmndtplgtdt0(X2,xR,xz) )
    & ~ sdtmndtasgtdt0(xx,xR,xz)
    & ~ sdtmndtplgtdt0(xx,xR,xz)
    & ~ aReductOfIn0(xz,xx,xR)
    & xx != xz
    & ( ( sdtmndtplgtdt0(xx,xR,xy)
        & ( ? [X1] :
              ( sdtmndtplgtdt0(X1,xR,xy)
              & aReductOfIn0(X1,xx,xR)
              & aElement0(X1) )
          | aReductOfIn0(xy,xx,xR) ) )
      | xx = xy )
    & sdtmndtasgtdt0(xy,xR,xz)
    & ( xy = xz
      | ( ( aReductOfIn0(xz,xy,xR)
          | ? [X0] :
              ( sdtmndtplgtdt0(X0,xR,xz)
              & aReductOfIn0(X0,xy,xR)
              & aElement0(X0) ) )
        & sdtmndtplgtdt0(xy,xR,xz) ) )
    & sdtmndtasgtdt0(xx,xR,xy) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ~ ( ( ( ( sdtmndtplgtdt0(xx,xR,xy)
            & ( ? [X1] :
                  ( sdtmndtplgtdt0(X1,xR,xy)
                  & aReductOfIn0(X1,xx,xR)
                  & aElement0(X1) )
              | aReductOfIn0(xy,xx,xR) ) )
          | xx = xy )
        & sdtmndtasgtdt0(xy,xR,xz)
        & ( xy = xz
          | ( ( aReductOfIn0(xz,xy,xR)
              | ? [X0] :
                  ( sdtmndtplgtdt0(X0,xR,xz)
                  & aReductOfIn0(X0,xy,xR)
                  & aElement0(X0) ) )
            & sdtmndtplgtdt0(xy,xR,xz) ) )
        & sdtmndtasgtdt0(xx,xR,xy) )
     => ( ? [X2] :
            ( sdtmndtplgtdt0(X2,xR,xz)
            & aElement0(X2)
            & aReductOfIn0(X2,xx,xR) )
        | sdtmndtasgtdt0(xx,xR,xz)
        | sdtmndtplgtdt0(xx,xR,xz)
        | aReductOfIn0(xz,xx,xR)
        | xx = xz ) ),
    inference(rectify,[],[f11]) ).

fof(f11,negated_conjecture,
    ~ ( ( ( xy = xz
          | ( ( aReductOfIn0(xz,xy,xR)
              | ? [X0] :
                  ( sdtmndtplgtdt0(X0,xR,xz)
                  & aReductOfIn0(X0,xy,xR)
                  & aElement0(X0) ) )
            & sdtmndtplgtdt0(xy,xR,xz) ) )
        & sdtmndtasgtdt0(xy,xR,xz)
        & ( ( ( aReductOfIn0(xy,xx,xR)
              | ? [X0] :
                  ( sdtmndtplgtdt0(X0,xR,xy)
                  & aElement0(X0)
                  & aReductOfIn0(X0,xx,xR) ) )
            & sdtmndtplgtdt0(xx,xR,xy) )
          | xx = xy )
        & sdtmndtasgtdt0(xx,xR,xy) )
     => ( aReductOfIn0(xz,xx,xR)
        | ? [X0] :
            ( aElement0(X0)
            & sdtmndtplgtdt0(X0,xR,xz)
            & aReductOfIn0(X0,xx,xR) )
        | xx = xz
        | sdtmndtplgtdt0(xx,xR,xz)
        | sdtmndtasgtdt0(xx,xR,xz) ) ),
    inference(negated_conjecture,[],[f10]) ).

fof(f10,conjecture,
    ( ( ( xy = xz
        | ( ( aReductOfIn0(xz,xy,xR)
            | ? [X0] :
                ( sdtmndtplgtdt0(X0,xR,xz)
                & aReductOfIn0(X0,xy,xR)
                & aElement0(X0) ) )
          & sdtmndtplgtdt0(xy,xR,xz) ) )
      & sdtmndtasgtdt0(xy,xR,xz)
      & ( ( ( aReductOfIn0(xy,xx,xR)
            | ? [X0] :
                ( sdtmndtplgtdt0(X0,xR,xy)
                & aElement0(X0)
                & aReductOfIn0(X0,xx,xR) ) )
          & sdtmndtplgtdt0(xx,xR,xy) )
        | xx = xy )
      & sdtmndtasgtdt0(xx,xR,xy) )
   => ( aReductOfIn0(xz,xx,xR)
      | ? [X0] :
          ( aElement0(X0)
          & sdtmndtplgtdt0(X0,xR,xz)
          & aReductOfIn0(X0,xx,xR) )
      | xx = xz
      | sdtmndtplgtdt0(xx,xR,xz)
      | sdtmndtasgtdt0(xx,xR,xz) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f68,plain,
    aElement0(xy),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ( aElement0(xz)
    & aElement0(xx)
    & aRewritingSystem0(xR)
    & aElement0(xy) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__349) ).

fof(f71,plain,
    aElement0(xz),
    inference(cnf_transformation,[],[f9]) ).

fof(f70,plain,
    aElement0(xx),
    inference(cnf_transformation,[],[f9]) ).

fof(f69,plain,
    aRewritingSystem0(xR),
    inference(cnf_transformation,[],[f9]) ).

fof(f148,plain,
    ~ spl3_5,
    inference(avatar_contradiction_clause,[],[f147]) ).

fof(f147,plain,
    ( $false
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f139,f62]) ).

fof(f62,plain,
    sdtmndtasgtdt0(xx,xR,xy),
    inference(cnf_transformation,[],[f37]) ).

fof(f139,plain,
    ( ~ sdtmndtasgtdt0(xx,xR,xy)
    | ~ spl3_5 ),
    inference(backward_demodulation,[],[f54,f94]) ).

fof(f94,plain,
    ( xy = xz
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f92]) ).

fof(f92,plain,
    ( spl3_5
  <=> xy = xz ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

fof(f54,plain,
    ~ sdtmndtasgtdt0(xx,xR,xz),
    inference(cnf_transformation,[],[f37]) ).

fof(f134,plain,
    ~ spl3_3,
    inference(avatar_contradiction_clause,[],[f133]) ).

fof(f133,plain,
    ( $false
    | ~ spl3_3 ),
    inference(subsumption_resolution,[],[f131,f54]) ).

fof(f131,plain,
    ( sdtmndtasgtdt0(xx,xR,xz)
    | ~ spl3_3 ),
    inference(backward_demodulation,[],[f55,f85]) ).

fof(f85,plain,
    ( xx = xy
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f83]) ).

fof(f83,plain,
    ( spl3_3
  <=> xx = xy ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

fof(f55,plain,
    sdtmndtasgtdt0(xy,xR,xz),
    inference(cnf_transformation,[],[f37]) ).

fof(f109,plain,
    ( spl3_3
    | spl3_8 ),
    inference(avatar_split_clause,[],[f59,f106,f83]) ).

fof(f59,plain,
    ( sdtmndtplgtdt0(xx,xR,xy)
    | xx = xy ),
    inference(cnf_transformation,[],[f37]) ).

fof(f95,plain,
    ( spl3_4
    | spl3_5 ),
    inference(avatar_split_clause,[],[f50,f92,f88]) ).

fof(f50,plain,
    ( xy = xz
    | sdtmndtplgtdt0(xy,xR,xz) ),
    inference(cnf_transformation,[],[f37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : COM012+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.33  % Computer : n015.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon Aug 29 17:15:50 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.19/0.50  % (7932)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.50  % (7942)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.50  % (7950)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.50  % (7935)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.50  % (7953)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.50  % (7936)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.19/0.50  % (7929)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.51  % (7934)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51  % (7936)First to succeed.
% 0.19/0.51  % (7941)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.51  % (7940)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (7929)Instruction limit reached!
% 0.19/0.51  % (7929)------------------------------
% 0.19/0.51  % (7929)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (7929)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (7929)Termination reason: Unknown
% 0.19/0.51  % (7929)Termination phase: Saturation
% 0.19/0.51  
% 0.19/0.51  % (7929)Memory used [KB]: 5884
% 0.19/0.51  % (7929)Time elapsed: 0.099 s
% 0.19/0.51  % (7929)Instructions burned: 3 (million)
% 0.19/0.51  % (7929)------------------------------
% 0.19/0.51  % (7929)------------------------------
% 0.19/0.51  % (7928)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.51  % (7928)Also succeeded, but the first one will report.
% 0.19/0.51  % (7947)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.19/0.51  % (7936)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (7936)------------------------------
% 0.19/0.51  % (7936)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (7936)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (7936)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (7936)Memory used [KB]: 6012
% 0.19/0.51  % (7936)Time elapsed: 0.116 s
% 0.19/0.51  % (7936)Instructions burned: 5 (million)
% 0.19/0.51  % (7936)------------------------------
% 0.19/0.51  % (7936)------------------------------
% 0.19/0.51  % (7923)Success in time 0.171 s
%------------------------------------------------------------------------------