TSTP Solution File: ALG073+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : ALG073+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_uns --cores 0 -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 : Wed Aug 31 15:39:22 EDT 2022

% Result   : Theorem 0.18s 0.51s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   55 (  21 unt;   0 def)
%            Number of atoms       :  199 (  88 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  219 (  75   ~;  61   |;  53   &)
%                                         (   1 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   2 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   :   67 (  59   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f135,plain,
    $false,
    inference(avatar_sat_refutation,[],[f86,f134]) ).

fof(f134,plain,
    ~ spl2_1,
    inference(avatar_contradiction_clause,[],[f133]) ).

fof(f133,plain,
    ( $false
    | ~ spl2_1 ),
    inference(subsumption_resolution,[],[f132,f19]) ).

fof(f19,plain,
    op1(sK0,sK1) != sK0,
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ( sorti1(sK0)
    & sorti1(sK1)
    & op1(sK0,sK1) != sK0
    & sK0 = op1(sK1,sK1)
    & op1(sK0,sK0) = sK1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f3,f14,f13]) ).

fof(f13,plain,
    ( ? [X0] :
        ( sorti1(X0)
        & ? [X1] :
            ( sorti1(X1)
            & op1(X0,X1) != X0
            & op1(X1,X1) = X0
            & op1(X0,X0) = X1 ) )
   => ( sorti1(sK0)
      & ? [X1] :
          ( sorti1(X1)
          & op1(sK0,X1) != sK0
          & op1(X1,X1) = sK0
          & op1(sK0,sK0) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ( ? [X1] :
        ( sorti1(X1)
        & op1(sK0,X1) != sK0
        & op1(X1,X1) = sK0
        & op1(sK0,sK0) = X1 )
   => ( sorti1(sK1)
      & op1(sK0,sK1) != sK0
      & sK0 = op1(sK1,sK1)
      & op1(sK0,sK0) = sK1 ) ),
    introduced(choice_axiom,[]) ).

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

fof(f132,plain,
    ( op1(sK0,sK1) = sK0
    | ~ spl2_1 ),
    inference(forward_demodulation,[],[f130,f59]) ).

fof(f59,plain,
    j(h(sK0)) = sK0,
    inference(unit_resulting_resolution,[],[f21,f28]) ).

fof(f28,plain,
    ! [X3] :
      ( ~ sorti1(X3)
      | j(h(X3)) = X3 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( ! [X0] :
        ( ~ sorti1(X0)
        | sorti2(h(X0)) )
    & ! [X1] :
        ( ! [X2] :
            ( ~ sorti1(X2)
            | op2(h(X1),h(X2)) = h(op1(X1,X2)) )
        | ~ sorti1(X1) )
    & ! [X3] :
        ( ~ sorti1(X3)
        | j(h(X3)) = X3 )
    & ! [X4] :
        ( ~ sorti2(X4)
        | sorti1(j(X4)) )
    & ! [X5] :
        ( ! [X6] :
            ( ~ sorti2(X6)
            | j(op2(X5,X6)) = op1(j(X5),j(X6)) )
        | ~ sorti2(X5) )
    & ! [X7] :
        ( h(j(X7)) = X7
        | ~ sorti2(X7) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,plain,
    ( ! [X0] :
        ( ~ sorti1(X0)
        | sorti2(h(X0)) )
    & ! [X4] :
        ( ! [X5] :
            ( ~ sorti1(X5)
            | h(op1(X4,X5)) = op2(h(X4),h(X5)) )
        | ~ sorti1(X4) )
    & ! [X2] :
        ( ~ sorti1(X2)
        | j(h(X2)) = X2 )
    & ! [X1] :
        ( ~ sorti2(X1)
        | sorti1(j(X1)) )
    & ! [X6] :
        ( ! [X7] :
            ( ~ sorti2(X7)
            | j(op2(X6,X7)) = op1(j(X6),j(X7)) )
        | ~ sorti2(X6) )
    & ! [X3] :
        ( h(j(X3)) = X3
        | ~ sorti2(X3) ) ),
    inference(flattening,[],[f9]) ).

fof(f9,plain,
    ( ! [X4] :
        ( ! [X5] :
            ( ~ sorti1(X5)
            | h(op1(X4,X5)) = op2(h(X4),h(X5)) )
        | ~ sorti1(X4) )
    & ! [X3] :
        ( h(j(X3)) = X3
        | ~ sorti2(X3) )
    & ! [X2] :
        ( ~ sorti1(X2)
        | j(h(X2)) = X2 )
    & ! [X6] :
        ( ! [X7] :
            ( ~ sorti2(X7)
            | j(op2(X6,X7)) = op1(j(X6),j(X7)) )
        | ~ sorti2(X6) )
    & ! [X1] :
        ( ~ sorti2(X1)
        | sorti1(j(X1)) )
    & ! [X0] :
        ( ~ sorti1(X0)
        | sorti2(h(X0)) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,plain,
    ~ ( ( ! [X1] :
            ( sorti2(X1)
           => sorti1(j(X1)) )
        & ! [X0] :
            ( sorti1(X0)
           => sorti2(h(X0)) ) )
     => ~ ( ! [X4] :
              ( sorti1(X4)
             => ! [X5] :
                  ( sorti1(X5)
                 => h(op1(X4,X5)) = op2(h(X4),h(X5)) ) )
          & ! [X3] :
              ( sorti2(X3)
             => h(j(X3)) = X3 )
          & ! [X2] :
              ( sorti1(X2)
             => j(h(X2)) = X2 )
          & ! [X6] :
              ( sorti2(X6)
             => ! [X7] :
                  ( sorti2(X7)
                 => j(op2(X6,X7)) = op1(j(X6),j(X7)) ) ) ) ),
    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 )
          & ! [X6] :
              ( sorti2(X6)
             => h(j(X6)) = X6 )
          & ! [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)) ) ) ) ),
    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 )
        & ! [X6] :
            ( sorti2(X6)
           => h(j(X6)) = X6 )
        & ! [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)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f21,plain,
    sorti1(sK0),
    inference(cnf_transformation,[],[f15]) ).

fof(f130,plain,
    ( j(h(sK0)) = op1(sK0,sK1)
    | ~ spl2_1 ),
    inference(backward_demodulation,[],[f122,f129]) ).

fof(f129,plain,
    ( h(sK0) = h(op1(sK0,sK1))
    | ~ spl2_1 ),
    inference(backward_demodulation,[],[f74,f128]) ).

fof(f128,plain,
    ( h(sK0) = op2(h(sK0),h(sK1))
    | ~ spl2_1 ),
    inference(forward_demodulation,[],[f127,f87]) ).

fof(f87,plain,
    ( op2(h(sK0),h(sK0)) = h(sK1)
    | ~ spl2_1 ),
    inference(forward_demodulation,[],[f52,f80]) ).

fof(f80,plain,
    h(sK0) = op2(h(sK1),h(sK1)),
    inference(forward_demodulation,[],[f75,f18]) ).

fof(f18,plain,
    sK0 = op1(sK1,sK1),
    inference(cnf_transformation,[],[f15]) ).

fof(f75,plain,
    h(op1(sK1,sK1)) = op2(h(sK1),h(sK1)),
    inference(unit_resulting_resolution,[],[f20,f20,f29]) ).

fof(f29,plain,
    ! [X2,X1] :
      ( ~ sorti1(X2)
      | op2(h(X1),h(X2)) = h(op1(X1,X2))
      | ~ sorti1(X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f20,plain,
    sorti1(sK1),
    inference(cnf_transformation,[],[f15]) ).

fof(f52,plain,
    ( op2(op2(h(sK1),h(sK1)),op2(h(sK1),h(sK1))) = h(sK1)
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f51,plain,
    ( spl2_1
  <=> op2(op2(h(sK1),h(sK1)),op2(h(sK1),h(sK1))) = h(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f127,plain,
    ( h(sK0) = op2(h(sK0),op2(h(sK0),h(sK0)))
    | ~ spl2_1 ),
    inference(subsumption_resolution,[],[f126,f80]) ).

fof(f126,plain,
    ( h(sK0) = op2(h(sK0),op2(h(sK0),h(sK0)))
    | h(sK0) != op2(h(sK1),h(sK1))
    | ~ spl2_1 ),
    inference(forward_demodulation,[],[f125,f87]) ).

fof(f125,plain,
    ( h(sK0) != op2(op2(h(sK0),h(sK0)),op2(h(sK0),h(sK0)))
    | h(sK0) = op2(h(sK0),op2(h(sK0),h(sK0)))
    | ~ spl2_1 ),
    inference(subsumption_resolution,[],[f124,f35]) ).

fof(f35,plain,
    sorti2(h(sK1)),
    inference(unit_resulting_resolution,[],[f20,f30]) ).

fof(f30,plain,
    ! [X0] :
      ( ~ sorti1(X0)
      | sorti2(h(X0)) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f124,plain,
    ( ~ sorti2(h(sK1))
    | h(sK0) = op2(h(sK0),op2(h(sK0),h(sK0)))
    | h(sK0) != op2(op2(h(sK0),h(sK0)),op2(h(sK0),h(sK0)))
    | ~ spl2_1 ),
    inference(forward_demodulation,[],[f104,f87]) ).

fof(f104,plain,
    ( ~ sorti2(op2(h(sK0),h(sK0)))
    | h(sK0) != op2(op2(h(sK0),h(sK0)),op2(h(sK0),h(sK0)))
    | h(sK0) = op2(h(sK0),op2(h(sK0),h(sK0))) ),
    inference(resolution,[],[f38,f31]) ).

fof(f31,plain,
    ! [X0] :
      ( ~ sorti2(X0)
      | op2(X0,op2(X0,X0)) = X0
      | op2(op2(X0,X0),op2(X0,X0)) != X0
      | ~ sorti2(op2(X0,X0)) ),
    inference(equality_resolution,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ sorti2(X0)
      | ~ sorti2(X1)
      | op2(X0,X0) != X1
      | op2(X1,X1) != X0
      | op2(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f11]) ).

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

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

fof(f38,plain,
    sorti2(h(sK0)),
    inference(resolution,[],[f30,f21]) ).

fof(f74,plain,
    op2(h(sK0),h(sK1)) = h(op1(sK0,sK1)),
    inference(unit_resulting_resolution,[],[f21,f20,f29]) ).

fof(f122,plain,
    op1(sK0,sK1) = j(h(op1(sK0,sK1))),
    inference(forward_demodulation,[],[f121,f59]) ).

fof(f121,plain,
    op1(j(h(sK0)),sK1) = j(h(op1(sK0,sK1))),
    inference(forward_demodulation,[],[f120,f60]) ).

fof(f60,plain,
    sK1 = j(h(sK1)),
    inference(unit_resulting_resolution,[],[f20,f28]) ).

fof(f120,plain,
    j(h(op1(sK0,sK1))) = op1(j(h(sK0)),j(h(sK1))),
    inference(forward_demodulation,[],[f97,f74]) ).

fof(f97,plain,
    op1(j(h(sK0)),j(h(sK1))) = j(op2(h(sK0),h(sK1))),
    inference(unit_resulting_resolution,[],[f35,f38,f26]) ).

fof(f26,plain,
    ! [X6,X5] :
      ( ~ sorti2(X6)
      | ~ sorti2(X5)
      | j(op2(X5,X6)) = op1(j(X5),j(X6)) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f86,plain,
    spl2_1,
    inference(avatar_contradiction_clause,[],[f85]) ).

fof(f85,plain,
    ( $false
    | spl2_1 ),
    inference(subsumption_resolution,[],[f84,f82]) ).

fof(f82,plain,
    ( op2(h(sK0),h(sK0)) != h(sK1)
    | spl2_1 ),
    inference(backward_demodulation,[],[f53,f80]) ).

fof(f53,plain,
    ( op2(op2(h(sK1),h(sK1)),op2(h(sK1),h(sK1))) != h(sK1)
    | spl2_1 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f84,plain,
    op2(h(sK0),h(sK0)) = h(sK1),
    inference(forward_demodulation,[],[f72,f17]) ).

fof(f17,plain,
    op1(sK0,sK0) = sK1,
    inference(cnf_transformation,[],[f15]) ).

fof(f72,plain,
    op2(h(sK0),h(sK0)) = h(op1(sK0,sK0)),
    inference(unit_resulting_resolution,[],[f21,f21,f29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : ALG073+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Aug 29 15:02:29 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.18/0.48  % (6951)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)
% 0.18/0.48  % (6958)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.18/0.49  % (6950)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)
% 0.18/0.49  % (6943)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)
% 0.18/0.49  % (6950)Instruction limit reached!
% 0.18/0.49  % (6950)------------------------------
% 0.18/0.49  % (6950)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49  % (6950)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.49  % (6950)Termination reason: Unknown
% 0.18/0.49  % (6950)Termination phase: Saturation
% 0.18/0.49  
% 0.18/0.49  % (6950)Memory used [KB]: 5884
% 0.18/0.49  % (6950)Time elapsed: 0.063 s
% 0.18/0.49  % (6950)Instructions burned: 3 (million)
% 0.18/0.49  % (6950)------------------------------
% 0.18/0.49  % (6950)------------------------------
% 0.18/0.49  % (6951)Instruction limit reached!
% 0.18/0.49  % (6951)------------------------------
% 0.18/0.49  % (6951)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.49  % (6942)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.18/0.50  % (6949)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)
% 0.18/0.50  % (6940)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.18/0.50  % (6959)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)
% 0.18/0.50  % (6943)First to succeed.
% 0.18/0.50  % (6951)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (6951)Termination reason: Unknown
% 0.18/0.50  % (6951)Termination phase: Saturation
% 0.18/0.50  
% 0.18/0.50  % (6951)Memory used [KB]: 6012
% 0.18/0.50  % (6951)Time elapsed: 0.107 s
% 0.18/0.50  % (6951)Instructions burned: 7 (million)
% 0.18/0.50  % (6951)------------------------------
% 0.18/0.50  % (6951)------------------------------
% 0.18/0.51  % (6943)Refutation found. Thanks to Tanya!
% 0.18/0.51  % SZS status Theorem for theBenchmark
% 0.18/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.51  % (6943)------------------------------
% 0.18/0.51  % (6943)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51  % (6943)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51  % (6943)Termination reason: Refutation
% 0.18/0.51  
% 0.18/0.51  % (6943)Memory used [KB]: 6012
% 0.18/0.51  % (6943)Time elapsed: 0.116 s
% 0.18/0.51  % (6943)Instructions burned: 5 (million)
% 0.18/0.51  % (6943)------------------------------
% 0.18/0.51  % (6943)------------------------------
% 0.18/0.51  % (6935)Success in time 0.166 s
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