TSTP Solution File: ALG177+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : ALG177+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 : n010.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 15:40:21 EDT 2022

% Result   : Theorem 0.15s 0.48s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   32 (  11 unt;   0 def)
%            Number of atoms       :  138 (  44 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  158 (  52   ~;  38   |;  37   &)
%                                         (   0 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    5 (   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   :   71 (  65   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f132,plain,
    $false,
    inference(subsumption_resolution,[],[f131,f105]) ).

fof(f105,plain,
    op1(sK0,j(sK1(h(sK0)))) != j(sK1(h(sK0))),
    inference(resolution,[],[f52,f19]) ).

fof(f19,plain,
    ! [X1] :
      ( op1(sK0,X1) != X1
      | ~ sorti1(X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ( sorti1(sK0)
    & ! [X1] :
        ( ~ sorti1(X1)
        | op1(sK0,X1) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f14]) ).

fof(f14,plain,
    ( ? [X0] :
        ( sorti1(X0)
        & ! [X1] :
            ( ~ sorti1(X1)
            | op1(X0,X1) != X1 ) )
   => ( sorti1(sK0)
      & ! [X1] :
          ( ~ sorti1(X1)
          | op1(sK0,X1) != X1 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0] :
      ( sorti1(X0)
      & ! [X1] :
          ( ~ sorti1(X1)
          | op1(X0,X1) != X1 ) ),
    inference(ennf_transformation,[],[f3]) ).

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

fof(f52,plain,
    sorti1(j(sK1(h(sK0)))),
    inference(unit_resulting_resolution,[],[f39,f24]) ).

fof(f24,plain,
    ! [X2] :
      ( sorti1(j(X2))
      | ~ sorti2(X2) ),
    inference(cnf_transformation,[],[f16]) ).

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

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

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

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

fof(f6,negated_conjecture,
    ~ ( ( ! [X1] :
            ( sorti2(X1)
           => sorti1(j(X1)) )
        & ! [X0] :
            ( sorti1(X0)
           => sorti2(h(X0)) ) )
     => ~ ( ! [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,
    ( ( ! [X1] :
          ( sorti2(X1)
         => sorti1(j(X1)) )
      & ! [X0] :
          ( sorti1(X0)
         => sorti2(h(X0)) ) )
   => ~ ( ! [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/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f39,plain,
    sorti2(sK1(h(sK0))),
    inference(unit_resulting_resolution,[],[f33,f28]) ).

fof(f28,plain,
    ! [X0] :
      ( sorti2(sK1(X0))
      | ~ sorti2(X0) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0] :
      ( ( sK1(X0) = op2(X0,sK1(X0))
        & sorti2(sK1(X0)) )
      | ~ sorti2(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f13,f17]) ).

fof(f17,plain,
    ! [X0] :
      ( ? [X1] :
          ( op2(X0,X1) = X1
          & sorti2(X1) )
     => ( sK1(X0) = op2(X0,sK1(X0))
        & sorti2(sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ! [X0] :
      ( ? [X1] :
          ( op2(X0,X1) = X1
          & sorti2(X1) )
      | ~ sorti2(X0) ),
    inference(ennf_transformation,[],[f4]) ).

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

fof(f33,plain,
    sorti2(h(sK0)),
    inference(resolution,[],[f23,f20]) ).

fof(f20,plain,
    sorti1(sK0),
    inference(cnf_transformation,[],[f15]) ).

fof(f23,plain,
    ! [X3] :
      ( ~ sorti1(X3)
      | sorti2(h(X3)) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f131,plain,
    op1(sK0,j(sK1(h(sK0)))) = j(sK1(h(sK0))),
    inference(forward_demodulation,[],[f130,f44]) ).

fof(f44,plain,
    op2(h(sK0),sK1(h(sK0))) = sK1(h(sK0)),
    inference(resolution,[],[f33,f29]) ).

fof(f29,plain,
    ! [X0] :
      ( sK1(X0) = op2(X0,sK1(X0))
      | ~ sorti2(X0) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f130,plain,
    j(op2(h(sK0),sK1(h(sK0)))) = op1(sK0,j(sK1(h(sK0)))),
    inference(forward_demodulation,[],[f118,f47]) ).

fof(f47,plain,
    j(h(sK0)) = sK0,
    inference(unit_resulting_resolution,[],[f20,f25]) ).

fof(f25,plain,
    ! [X1] :
      ( ~ sorti1(X1)
      | j(h(X1)) = X1 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f118,plain,
    j(op2(h(sK0),sK1(h(sK0)))) = op1(j(h(sK0)),j(sK1(h(sK0)))),
    inference(unit_resulting_resolution,[],[f39,f33,f22]) ).

fof(f22,plain,
    ! [X4,X5] :
      ( ~ sorti2(X5)
      | ~ sorti2(X4)
      | j(op2(X4,X5)) = op1(j(X4),j(X5)) ),
    inference(cnf_transformation,[],[f16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem    : ALG177+1 : TPTP v8.1.0. Released v2.7.0.
% 0.00/0.10  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.09/0.29  % Computer : n010.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit   : 300
% 0.09/0.30  % WCLimit    : 300
% 0.09/0.30  % DateTime   : Mon Aug 29 14:50:14 EDT 2022
% 0.09/0.30  % CPUTime    : 
% 0.15/0.45  % (5856)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)
% 0.15/0.45  % (5865)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)
% 0.15/0.46  % (5856)Instruction limit reached!
% 0.15/0.46  % (5856)------------------------------
% 0.15/0.46  % (5856)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.46  % (5857)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)
% 0.15/0.46  % (5856)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.46  % (5856)Termination reason: Unknown
% 0.15/0.46  % (5856)Termination phase: Saturation
% 0.15/0.46  
% 0.15/0.46  % (5856)Memory used [KB]: 6012
% 0.15/0.46  % (5856)Time elapsed: 0.094 s
% 0.15/0.46  % (5856)Instructions burned: 4 (million)
% 0.15/0.46  % (5856)------------------------------
% 0.15/0.46  % (5856)------------------------------
% 0.15/0.47  % (5857)Instruction limit reached!
% 0.15/0.47  % (5857)------------------------------
% 0.15/0.47  % (5857)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.47  % (5848)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)
% 0.15/0.47  % (5849)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)
% 0.15/0.48  % (5857)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.48  % (5857)Termination reason: Unknown
% 0.15/0.48  % (5857)Termination phase: Saturation
% 0.15/0.48  
% 0.15/0.48  % (5857)Memory used [KB]: 6012
% 0.15/0.48  % (5857)Time elapsed: 0.067 s
% 0.15/0.48  % (5857)Instructions burned: 7 (million)
% 0.15/0.48  % (5857)------------------------------
% 0.15/0.48  % (5857)------------------------------
% 0.15/0.48  % (5864)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)
% 0.15/0.48  % (5849)First to succeed.
% 0.15/0.48  % (5849)Refutation found. Thanks to Tanya!
% 0.15/0.48  % SZS status Theorem for theBenchmark
% 0.15/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.48  % (5849)------------------------------
% 0.15/0.48  % (5849)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.48  % (5849)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.48  % (5849)Termination reason: Refutation
% 0.15/0.48  
% 0.15/0.48  % (5849)Memory used [KB]: 6012
% 0.15/0.48  % (5849)Time elapsed: 0.082 s
% 0.15/0.48  % (5849)Instructions burned: 3 (million)
% 0.15/0.48  % (5849)------------------------------
% 0.15/0.48  % (5849)------------------------------
% 0.15/0.48  % (5841)Success in time 0.179 s
%------------------------------------------------------------------------------