TSTP Solution File: ALG070+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : ALG070+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n022.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 15:42:29 EDT 2022

% Result   : Theorem 1.33s 0.53s
% Output   : Refutation 1.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   54 (  12 unt;   0 def)
%            Number of atoms       :  203 (  68 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  228 (  79   ~;  65   |;  46   &)
%                                         (   1 <=>;  37  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   89 (  81   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f234,plain,
    $false,
    inference(avatar_sat_refutation,[],[f197,f233]) ).

fof(f233,plain,
    ~ spl2_7,
    inference(avatar_contradiction_clause,[],[f232]) ).

fof(f232,plain,
    ( $false
    | ~ spl2_7 ),
    inference(subsumption_resolution,[],[f231,f31]) ).

fof(f31,plain,
    sK0 != op2(sK0,sK1),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ( sK0 != op2(sK0,sK1)
    & op2(sK0,sK0) = sK1
    & sorti2(sK1)
    & sorti2(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f18,f17]) ).

fof(f17,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( op2(X0,X1) != X0
            & op2(X0,X0) = X1
            & sorti2(X1) )
        & sorti2(X0) )
   => ( ? [X1] :
          ( op2(sK0,X1) != sK0
          & op2(sK0,sK0) = X1
          & sorti2(X1) )
      & sorti2(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ( ? [X1] :
        ( op2(sK0,X1) != sK0
        & op2(sK0,sK0) = X1
        & sorti2(X1) )
   => ( sK0 != op2(sK0,sK1)
      & op2(sK0,sK0) = sK1
      & sorti2(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f12,plain,
    ? [X0] :
      ( ? [X1] :
          ( op2(X0,X1) != X0
          & op2(X0,X0) = X1
          & sorti2(X1) )
      & sorti2(X0) ),
    inference(flattening,[],[f11]) ).

fof(f11,plain,
    ? [X0] :
      ( ? [X1] :
          ( op2(X0,X0) = X1
          & op2(X0,X1) != X0
          & sorti2(X1) )
      & sorti2(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ~ ! [X0] :
        ( sorti2(X0)
       => ! [X1] :
            ( sorti2(X1)
           => ( op2(X0,X0) != X1
              | op2(X0,X1) = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

fof(f231,plain,
    ( sK0 = op2(sK0,sK1)
    | ~ spl2_7 ),
    inference(forward_demodulation,[],[f229,f36]) ).

fof(f36,plain,
    h(j(sK0)) = sK0,
    inference(resolution,[],[f24,f28]) ).

fof(f28,plain,
    sorti2(sK0),
    inference(cnf_transformation,[],[f19]) ).

fof(f24,plain,
    ! [X1] :
      ( ~ sorti2(X1)
      | h(j(X1)) = X1 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( ! [X0] :
        ( ~ sorti2(X0)
        | sorti1(j(X0)) )
    & ! [X1] :
        ( h(j(X1)) = X1
        | ~ sorti2(X1) )
    & ! [X2] :
        ( ~ sorti2(X2)
        | ! [X3] :
            ( ~ sorti2(X3)
            | j(op2(X2,X3)) = op1(j(X2),j(X3)) ) )
    & ! [X4] :
        ( ~ sorti1(X4)
        | sorti2(h(X4)) )
    & ! [X5] :
        ( ~ sorti1(X5)
        | j(h(X5)) = X5 )
    & ! [X6] :
        ( ! [X7] :
            ( ~ sorti1(X7)
            | op2(h(X6),h(X7)) = h(op1(X6,X7)) )
        | ~ sorti1(X6) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,plain,
    ( ! [X0] :
        ( ~ sorti2(X0)
        | sorti1(j(X0)) )
    & ! [X7] :
        ( h(j(X7)) = X7
        | ~ sorti2(X7) )
    & ! [X5] :
        ( ~ sorti2(X5)
        | ! [X6] :
            ( ~ sorti2(X6)
            | j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
    & ! [X1] :
        ( ~ sorti1(X1)
        | sorti2(h(X1)) )
    & ! [X2] :
        ( ~ sorti1(X2)
        | j(h(X2)) = X2 )
    & ! [X3] :
        ( ! [X4] :
            ( ~ sorti1(X4)
            | h(op1(X3,X4)) = op2(h(X3),h(X4)) )
        | ~ sorti1(X3) ) ),
    inference(flattening,[],[f8]) ).

fof(f8,plain,
    ( ! [X7] :
        ( h(j(X7)) = X7
        | ~ sorti2(X7) )
    & ! [X3] :
        ( ! [X4] :
            ( ~ sorti1(X4)
            | h(op1(X3,X4)) = op2(h(X3),h(X4)) )
        | ~ sorti1(X3) )
    & ! [X5] :
        ( ~ sorti2(X5)
        | ! [X6] :
            ( ~ sorti2(X6)
            | j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
    & ! [X2] :
        ( ~ sorti1(X2)
        | j(h(X2)) = X2 )
    & ! [X0] :
        ( ~ sorti2(X0)
        | sorti1(j(X0)) )
    & ! [X1] :
        ( ~ sorti1(X1)
        | sorti2(h(X1)) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,plain,
    ~ ( ( ! [X0] :
            ( sorti2(X0)
           => sorti1(j(X0)) )
        & ! [X1] :
            ( sorti1(X1)
           => sorti2(h(X1)) ) )
     => ~ ( ! [X7] :
              ( sorti2(X7)
             => h(j(X7)) = X7 )
          & ! [X3] :
              ( sorti1(X3)
             => ! [X4] :
                  ( sorti1(X4)
                 => h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
          & ! [X5] :
              ( sorti2(X5)
             => ! [X6] :
                  ( sorti2(X6)
                 => j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
          & ! [X2] :
              ( sorti1(X2)
             => j(h(X2)) = X2 ) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,negated_conjecture,
    ~ ( ( ! [X1] :
            ( sorti2(X1)
           => sorti1(j(X1)) )
        & ! [X0] :
            ( sorti1(X0)
           => sorti2(h(X0)) ) )
     => ~ ( ! [X7] :
              ( sorti1(X7)
             => j(h(X7)) = X7 )
          & ! [X2] :
              ( sorti1(X2)
             => ! [X3] :
                  ( sorti1(X3)
                 => h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
          & ! [X4] :
              ( sorti2(X4)
             => ! [X5] :
                  ( sorti2(X5)
                 => j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
          & ! [X6] :
              ( sorti2(X6)
             => h(j(X6)) = X6 ) ) ),
    inference(negated_conjecture,[],[f5]) ).

fof(f5,conjecture,
    ( ( ! [X1] :
          ( sorti2(X1)
         => sorti1(j(X1)) )
      & ! [X0] :
          ( sorti1(X0)
         => sorti2(h(X0)) ) )
   => ~ ( ! [X7] :
            ( sorti1(X7)
           => j(h(X7)) = X7 )
        & ! [X2] :
            ( sorti1(X2)
           => ! [X3] :
                ( sorti1(X3)
               => h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
        & ! [X4] :
            ( sorti2(X4)
           => ! [X5] :
                ( sorti2(X5)
               => j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
        & ! [X6] :
            ( sorti2(X6)
           => h(j(X6)) = X6 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f229,plain,
    ( h(j(sK0)) = op2(sK0,sK1)
    | ~ spl2_7 ),
    inference(superposition,[],[f110,f225]) ).

fof(f225,plain,
    ( j(op2(sK0,sK1)) = j(sK0)
    | ~ spl2_7 ),
    inference(forward_demodulation,[],[f223,f204]) ).

fof(f204,plain,
    ( op1(j(sK0),j(sK1)) = j(sK0)
    | ~ spl2_7 ),
    inference(forward_demodulation,[],[f201,f183]) ).

fof(f183,plain,
    j(sK1) = op1(j(sK0),j(sK0)),
    inference(forward_demodulation,[],[f181,f30]) ).

fof(f30,plain,
    op2(sK0,sK0) = sK1,
    inference(cnf_transformation,[],[f19]) ).

fof(f181,plain,
    op1(j(sK0),j(sK0)) = j(op2(sK0,sK0)),
    inference(resolution,[],[f86,f28]) ).

fof(f86,plain,
    ! [X5] :
      ( ~ sorti2(X5)
      | op1(j(X5),j(sK0)) = j(op2(X5,sK0)) ),
    inference(resolution,[],[f23,f28]) ).

fof(f23,plain,
    ! [X2,X3] :
      ( ~ sorti2(X3)
      | ~ sorti2(X2)
      | j(op2(X2,X3)) = op1(j(X2),j(X3)) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f201,plain,
    ( j(sK0) = op1(j(sK0),op1(j(sK0),j(sK0)))
    | ~ spl2_7 ),
    inference(resolution,[],[f188,f34]) ).

fof(f34,plain,
    ! [X0] :
      ( ~ sorti1(X0)
      | op1(X0,op1(X0,X0)) = X0 ),
    inference(subsumption_resolution,[],[f33,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( sorti1(op1(X0,X1))
      | ~ sorti1(X0)
      | ~ sorti1(X1) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ sorti1(X1)
          | sorti1(op1(X0,X1)) )
      | ~ sorti1(X0) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] :
      ( sorti1(X0)
     => ! [X1] :
          ( sorti1(X1)
         => sorti1(op1(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

fof(f33,plain,
    ! [X0] :
      ( op1(X0,op1(X0,X0)) = X0
      | ~ sorti1(X0)
      | ~ sorti1(op1(X0,X0)) ),
    inference(equality_resolution,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ sorti1(X0)
      | ~ sorti1(X1)
      | op1(X0,X0) != X1
      | op1(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0] :
      ( ~ sorti1(X0)
      | ! [X1] :
          ( ~ sorti1(X1)
          | op1(X0,X0) != X1
          | op1(X0,X1) = X0 ) ),
    inference(flattening,[],[f13]) ).

fof(f13,plain,
    ! [X0] :
      ( ! [X1] :
          ( op1(X0,X1) = X0
          | op1(X0,X0) != X1
          | ~ sorti1(X1) )
      | ~ sorti1(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( sorti1(X0)
     => ! [X1] :
          ( sorti1(X1)
         => ( op1(X0,X1) = X0
            | op1(X0,X0) != X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

fof(f188,plain,
    ( sorti1(j(sK0))
    | ~ spl2_7 ),
    inference(avatar_component_clause,[],[f187]) ).

fof(f187,plain,
    ( spl2_7
  <=> sorti1(j(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).

fof(f223,plain,
    j(op2(sK0,sK1)) = op1(j(sK0),j(sK1)),
    inference(resolution,[],[f87,f28]) ).

fof(f87,plain,
    ! [X6] :
      ( ~ sorti2(X6)
      | j(op2(X6,sK1)) = op1(j(X6),j(sK1)) ),
    inference(resolution,[],[f23,f29]) ).

fof(f29,plain,
    sorti2(sK1),
    inference(cnf_transformation,[],[f19]) ).

fof(f110,plain,
    op2(sK0,sK1) = h(j(op2(sK0,sK1))),
    inference(resolution,[],[f66,f28]) ).

fof(f66,plain,
    ! [X6] :
      ( ~ sorti2(X6)
      | h(j(op2(X6,sK1))) = op2(X6,sK1) ),
    inference(resolution,[],[f41,f29]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ sorti2(X1)
      | ~ sorti2(X0)
      | op2(X0,X1) = h(j(op2(X0,X1))) ),
    inference(resolution,[],[f27,f24]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( sorti2(op2(X0,X1))
      | ~ sorti2(X0)
      | ~ sorti2(X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0] :
      ( ! [X1] :
          ( sorti2(op2(X0,X1))
          | ~ sorti2(X1) )
      | ~ sorti2(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( sorti2(X0)
     => ! [X1] :
          ( sorti2(X1)
         => sorti2(op2(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

fof(f197,plain,
    spl2_7,
    inference(avatar_contradiction_clause,[],[f196]) ).

fof(f196,plain,
    ( $false
    | spl2_7 ),
    inference(subsumption_resolution,[],[f195,f28]) ).

fof(f195,plain,
    ( ~ sorti2(sK0)
    | spl2_7 ),
    inference(resolution,[],[f189,f25]) ).

fof(f25,plain,
    ! [X0] :
      ( sorti1(j(X0))
      | ~ sorti2(X0) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f189,plain,
    ( ~ sorti1(j(sK0))
    | spl2_7 ),
    inference(avatar_component_clause,[],[f187]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : ALG070+1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n022.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon Aug 29 14:54:41 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.50  % (2763)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51  % (2768)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.51  % (2776)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.52  % (2763)Instruction limit reached!
% 0.19/0.52  % (2763)------------------------------
% 0.19/0.52  % (2763)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (2763)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (2763)Termination reason: Unknown
% 0.19/0.52  % (2763)Termination phase: Saturation
% 0.19/0.52  
% 0.19/0.52  % (2763)Memory used [KB]: 5500
% 0.19/0.52  % (2763)Time elapsed: 0.123 s
% 0.19/0.52  % (2763)Instructions burned: 9 (million)
% 0.19/0.52  % (2763)------------------------------
% 0.19/0.52  % (2763)------------------------------
% 0.19/0.52  % (2783)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.19/0.52  % (2756)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.52  % (2784)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.19/0.52  TRYING [1]
% 0.19/0.52  TRYING [2]
% 0.19/0.52  % (2764)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.52  % (2764)Instruction limit reached!
% 0.19/0.52  % (2764)------------------------------
% 0.19/0.52  % (2764)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (2764)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (2764)Termination reason: Unknown
% 0.19/0.52  % (2764)Termination phase: Preprocessing 3
% 0.19/0.52  
% 0.19/0.52  % (2764)Memory used [KB]: 895
% 0.19/0.52  % (2764)Time elapsed: 0.002 s
% 0.19/0.52  % (2764)Instructions burned: 2 (million)
% 0.19/0.52  % (2764)------------------------------
% 0.19/0.52  % (2764)------------------------------
% 0.19/0.52  % (2760)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  TRYING [3]
% 0.19/0.52  % (2770)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.53  TRYING [4]
% 0.19/0.53  % (2758)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.53  % (2761)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.53  % (2768)First to succeed.
% 0.19/0.53  % (2759)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.33/0.53  % (2768)Refutation found. Thanks to Tanya!
% 1.33/0.53  % SZS status Theorem for theBenchmark
% 1.33/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.33/0.53  % (2768)------------------------------
% 1.33/0.53  % (2768)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.53  % (2768)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.53  % (2768)Termination reason: Refutation
% 1.33/0.53  
% 1.33/0.53  % (2768)Memory used [KB]: 5628
% 1.33/0.53  % (2768)Time elapsed: 0.131 s
% 1.33/0.53  % (2768)Instructions burned: 9 (million)
% 1.33/0.53  % (2768)------------------------------
% 1.33/0.53  % (2768)------------------------------
% 1.33/0.53  % (2755)Success in time 0.186 s
%------------------------------------------------------------------------------