TSTP Solution File: ALG041+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : ALG041+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 : n006.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 15:39:08 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   37 (  14 unt;   0 def)
%            Number of atoms       :  147 (  49 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  164 (  54   ~;  40   |;  38   &)
%                                         (   0 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   75 (  68   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f135,plain,
    $false,
    inference(subsumption_resolution,[],[f134,f38]) ).

fof(f38,plain,
    j(sK0) != op1(sK1(j(sK0)),sK1(j(sK0))),
    inference(unit_resulting_resolution,[],[f32,f30]) ).

fof(f30,plain,
    ! [X0] :
      ( op1(sK1(X0),sK1(X0)) != X0
      | ~ sorti1(X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0] :
      ( ( sorti1(sK1(X0))
        & op1(sK1(X0),sK1(X0)) != X0 )
      | ~ sorti1(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f12,f18]) ).

fof(f18,plain,
    ! [X0] :
      ( ? [X1] :
          ( sorti1(X1)
          & op1(X1,X1) != X0 )
     => ( sorti1(sK1(X0))
        & op1(sK1(X0),sK1(X0)) != X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f12,plain,
    ! [X0] :
      ( ? [X1] :
          ( sorti1(X1)
          & op1(X1,X1) != X0 )
      | ~ sorti1(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ~ ? [X0] :
        ( ! [X1] :
            ( sorti1(X1)
           => op1(X1,X1) = X0 )
        & sorti1(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

fof(f32,plain,
    sorti1(j(sK0)),
    inference(unit_resulting_resolution,[],[f21,f23]) ).

fof(f23,plain,
    ! [X6] :
      ( sorti1(j(X6))
      | ~ sorti2(X6) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ( ! [X0] :
        ( ~ sorti1(X0)
        | j(h(X0)) = X0 )
    & ! [X1] :
        ( ! [X2] :
            ( ~ sorti1(X2)
            | op2(h(X1),h(X2)) = h(op1(X1,X2)) )
        | ~ sorti1(X1) )
    & ! [X3] :
        ( ~ sorti2(X3)
        | ! [X4] :
            ( ~ sorti2(X4)
            | op1(j(X3),j(X4)) = j(op2(X3,X4)) ) )
    & ! [X5] :
        ( ~ sorti2(X5)
        | h(j(X5)) = X5 )
    & ! [X6] :
        ( ~ sorti2(X6)
        | sorti1(j(X6)) )
    & ! [X7] :
        ( ~ sorti1(X7)
        | sorti2(h(X7)) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ( ! [X7] :
        ( ~ sorti1(X7)
        | j(h(X7)) = X7 )
    & ! [X5] :
        ( ! [X6] :
            ( ~ sorti1(X6)
            | op2(h(X5),h(X6)) = h(op1(X5,X6)) )
        | ~ sorti1(X5) )
    & ! [X3] :
        ( ~ sorti2(X3)
        | ! [X4] :
            ( ~ sorti2(X4)
            | op1(j(X3),j(X4)) = j(op2(X3,X4)) ) )
    & ! [X2] :
        ( ~ sorti2(X2)
        | h(j(X2)) = X2 )
    & ! [X1] :
        ( ~ sorti2(X1)
        | sorti1(j(X1)) )
    & ! [X0] :
        ( ~ sorti1(X0)
        | sorti2(h(X0)) ) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ( ! [X7] :
        ( ~ sorti1(X7)
        | j(h(X7)) = X7 )
    & ! [X3] :
        ( ~ sorti2(X3)
        | ! [X4] :
            ( ~ sorti2(X4)
            | op1(j(X3),j(X4)) = j(op2(X3,X4)) ) )
    & ! [X5] :
        ( ! [X6] :
            ( ~ sorti1(X6)
            | op2(h(X5),h(X6)) = h(op1(X5,X6)) )
        | ~ sorti1(X5) )
    & ! [X2] :
        ( ~ sorti2(X2)
        | h(j(X2)) = X2 )
    & ! [X0] :
        ( ~ sorti1(X0)
        | sorti2(h(X0)) )
    & ! [X1] :
        ( ~ sorti2(X1)
        | sorti1(j(X1)) ) ),
    inference(ennf_transformation,[],[f7]) ).

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

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

fof(f5,conjecture,
    ( ( ! [X0] :
          ( sorti1(X0)
         => sorti2(h(X0)) )
      & ! [X1] :
          ( sorti2(X1)
         => sorti1(j(X1)) ) )
   => ~ ( ! [X6] :
            ( sorti2(X6)
           => h(j(X6)) = X6 )
        & ! [X4] :
            ( sorti2(X4)
           => ! [X5] :
                ( sorti2(X5)
               => j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
        & ! [X2] :
            ( sorti1(X2)
           => ! [X3] :
                ( sorti1(X3)
               => h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
        & ! [X7] :
            ( sorti1(X7)
           => j(h(X7)) = X7 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

fof(f21,plain,
    sorti2(sK0),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( sorti2(sK0)
    & ! [X1] :
        ( op2(X1,X1) = sK0
        | ~ sorti2(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f15]) ).

fof(f15,plain,
    ( ? [X0] :
        ( sorti2(X0)
        & ! [X1] :
            ( op2(X1,X1) = X0
            | ~ sorti2(X1) ) )
   => ( sorti2(sK0)
      & ! [X1] :
          ( op2(X1,X1) = sK0
          | ~ sorti2(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0] :
      ( sorti2(X0)
      & ! [X1] :
          ( op2(X1,X1) = X0
          | ~ sorti2(X1) ) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,plain,
    ? [X0] :
      ( ! [X1] :
          ( sorti2(X1)
         => op2(X1,X1) = X0 )
      & sorti2(X0) ),
    inference(flattening,[],[f4]) ).

fof(f4,axiom,
    ~ ~ ? [X0] :
          ( ! [X1] :
              ( sorti2(X1)
             => op2(X1,X1) = X0 )
          & sorti2(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

fof(f134,plain,
    j(sK0) = op1(sK1(j(sK0)),sK1(j(sK0))),
    inference(backward_demodulation,[],[f127,f132]) ).

fof(f132,plain,
    sK0 = h(op1(sK1(j(sK0)),sK1(j(sK0)))),
    inference(backward_demodulation,[],[f54,f109]) ).

fof(f109,plain,
    sK0 = op2(h(sK1(j(sK0))),h(sK1(j(sK0)))),
    inference(unit_resulting_resolution,[],[f40,f20]) ).

fof(f20,plain,
    ! [X1] :
      ( ~ sorti2(X1)
      | op2(X1,X1) = sK0 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f40,plain,
    sorti2(h(sK1(j(sK0)))),
    inference(unit_resulting_resolution,[],[f35,f22]) ).

fof(f22,plain,
    ! [X7] :
      ( sorti2(h(X7))
      | ~ sorti1(X7) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f35,plain,
    sorti1(sK1(j(sK0))),
    inference(unit_resulting_resolution,[],[f32,f31]) ).

fof(f31,plain,
    ! [X0] :
      ( sorti1(sK1(X0))
      | ~ sorti1(X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f54,plain,
    h(op1(sK1(j(sK0)),sK1(j(sK0)))) = op2(h(sK1(j(sK0))),h(sK1(j(sK0)))),
    inference(unit_resulting_resolution,[],[f35,f35,f26]) ).

fof(f26,plain,
    ! [X2,X1] :
      ( ~ sorti1(X2)
      | op2(h(X1),h(X2)) = h(op1(X1,X2))
      | ~ sorti1(X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f127,plain,
    j(h(op1(sK1(j(sK0)),sK1(j(sK0))))) = op1(sK1(j(sK0)),sK1(j(sK0))),
    inference(forward_demodulation,[],[f126,f54]) ).

fof(f126,plain,
    j(op2(h(sK1(j(sK0))),h(sK1(j(sK0))))) = op1(sK1(j(sK0)),sK1(j(sK0))),
    inference(forward_demodulation,[],[f114,f48]) ).

fof(f48,plain,
    j(h(sK1(j(sK0)))) = sK1(j(sK0)),
    inference(unit_resulting_resolution,[],[f35,f27]) ).

fof(f27,plain,
    ! [X0] :
      ( ~ sorti1(X0)
      | j(h(X0)) = X0 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f114,plain,
    j(op2(h(sK1(j(sK0))),h(sK1(j(sK0))))) = op1(j(h(sK1(j(sK0)))),j(h(sK1(j(sK0))))),
    inference(unit_resulting_resolution,[],[f40,f40,f25]) ).

fof(f25,plain,
    ! [X3,X4] :
      ( ~ sorti2(X4)
      | op1(j(X3),j(X4)) = j(op2(X3,X4))
      | ~ sorti2(X3) ),
    inference(cnf_transformation,[],[f17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : ALG041+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12  % 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 : n006.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 14:50:55 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.48  % (6188)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)
% 0.19/0.49  % (6191)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)
% 0.19/0.49  % (6204)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)
% 0.19/0.49  % (6186)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)
% 0.19/0.49  % (6190)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)
% 0.19/0.49  % (6192)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.49  % (6183)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)
% 0.19/0.50  % (6196)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)
% 0.19/0.50  % (6194)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.50  % (6196)Instruction limit reached!
% 0.19/0.50  % (6196)------------------------------
% 0.19/0.50  % (6196)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (6185)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (6192)Instruction limit reached!
% 0.19/0.50  % (6192)------------------------------
% 0.19/0.50  % (6192)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (6182)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.50  % (6184)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)
% 0.19/0.50  % (6187)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)
% 0.19/0.51  % (6184)Instruction limit reached!
% 0.19/0.51  % (6184)------------------------------
% 0.19/0.51  % (6184)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (6186)Instruction limit reached!
% 0.19/0.51  % (6186)------------------------------
% 0.19/0.51  % (6186)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (6186)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (6186)Termination reason: Unknown
% 0.19/0.51  % (6186)Termination phase: Saturation
% 0.19/0.51  
% 0.19/0.51  % (6186)Memory used [KB]: 6140
% 0.19/0.51  % (6186)Time elapsed: 0.122 s
% 0.19/0.51  % (6186)Instructions burned: 15 (million)
% 0.19/0.51  % (6186)------------------------------
% 0.19/0.51  % (6186)------------------------------
% 0.19/0.51  % (6207)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.19/0.51  % (6184)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (6184)Termination reason: Unknown
% 0.19/0.51  % (6184)Termination phase: Saturation
% 0.19/0.51  
% 0.19/0.51  % (6184)Memory used [KB]: 5884
% 0.19/0.51  % (6184)Time elapsed: 0.119 s
% 0.19/0.51  % (6184)Instructions burned: 3 (million)
% 0.19/0.51  % (6184)------------------------------
% 0.19/0.51  % (6184)------------------------------
% 0.19/0.51  % (6191)First to succeed.
% 0.19/0.51  % (6192)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (6192)Termination reason: Unknown
% 0.19/0.51  % (6192)Termination phase: Saturation
% 0.19/0.51  
% 0.19/0.51  % (6192)Memory used [KB]: 6140
% 0.19/0.51  % (6192)Time elapsed: 0.121 s
% 0.19/0.51  % (6192)Instructions burned: 12 (million)
% 0.19/0.51  % (6192)------------------------------
% 0.19/0.51  % (6192)------------------------------
% 0.19/0.51  % (6197)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)
% 0.19/0.51  % (6191)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  % (6191)------------------------------
% 0.19/0.51  % (6191)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (6191)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (6191)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (6191)Memory used [KB]: 6012
% 0.19/0.51  % (6191)Time elapsed: 0.126 s
% 0.19/0.51  % (6191)Instructions burned: 4 (million)
% 0.19/0.51  % (6191)------------------------------
% 0.19/0.51  % (6191)------------------------------
% 0.19/0.51  % (6181)Success in time 0.171 s
%------------------------------------------------------------------------------