TSTP Solution File: ALG176+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : ALG176+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 15:40:20 EDT 2022

% Result   : Theorem 0.21s 0.54s
% Output   : Refutation 0.21s
% 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(f509,plain,
    $false,
    inference(subsumption_resolution,[],[f508,f80]) ).

fof(f80,plain,
    op1(j(sK0(h(sK1))),sK1) != j(sK0(h(sK1))),
    inference(resolution,[],[f52,f22]) ).

fof(f22,plain,
    ! [X1] :
      ( ~ sorti1(X1)
      | op1(X1,sK1) != X1 ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ( sorti1(sK1)
    & ! [X1] :
        ( op1(X1,sK1) != X1
        | ~ sorti1(X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f8,f16]) ).

fof(f16,plain,
    ( ? [X0] :
        ( sorti1(X0)
        & ! [X1] :
            ( op1(X1,X0) != X1
            | ~ sorti1(X1) ) )
   => ( sorti1(sK1)
      & ! [X1] :
          ( op1(X1,sK1) != X1
          | ~ sorti1(X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f8,plain,
    ? [X0] :
      ( sorti1(X0)
      & ! [X1] :
          ( op1(X1,X0) != X1
          | ~ sorti1(X1) ) ),
    inference(ennf_transformation,[],[f3]) ).

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

fof(f52,plain,
    sorti1(j(sK0(h(sK1)))),
    inference(unit_resulting_resolution,[],[f39,f25]) ).

fof(f25,plain,
    ! [X6] :
      ( sorti1(j(X6))
      | ~ sorti2(X6) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( ! [X0] :
        ( ~ sorti1(X0)
        | sorti2(h(X0)) )
    & ! [X1] :
        ( ~ sorti2(X1)
        | h(j(X1)) = X1 )
    & ! [X2] :
        ( ~ sorti2(X2)
        | ! [X3] :
            ( ~ sorti2(X3)
            | j(op2(X2,X3)) = op1(j(X2),j(X3)) ) )
    & ! [X4] :
        ( ~ sorti1(X4)
        | ! [X5] :
            ( ~ sorti1(X5)
            | op2(h(X4),h(X5)) = h(op1(X4,X5)) ) )
    & ! [X6] :
        ( sorti1(j(X6))
        | ~ sorti2(X6) )
    & ! [X7] :
        ( j(h(X7)) = X7
        | ~ sorti1(X7) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,plain,
    ( ! [X1] :
        ( ~ sorti1(X1)
        | sorti2(h(X1)) )
    & ! [X5] :
        ( ~ sorti2(X5)
        | h(j(X5)) = X5 )
    & ! [X6] :
        ( ~ sorti2(X6)
        | ! [X7] :
            ( ~ sorti2(X7)
            | op1(j(X6),j(X7)) = j(op2(X6,X7)) ) )
    & ! [X3] :
        ( ~ sorti1(X3)
        | ! [X4] :
            ( ~ sorti1(X4)
            | op2(h(X3),h(X4)) = h(op1(X3,X4)) ) )
    & ! [X0] :
        ( sorti1(j(X0))
        | ~ sorti2(X0) )
    & ! [X2] :
        ( j(h(X2)) = X2
        | ~ sorti1(X2) ) ),
    inference(flattening,[],[f11]) ).

fof(f11,plain,
    ( ! [X3] :
        ( ~ sorti1(X3)
        | ! [X4] :
            ( ~ sorti1(X4)
            | op2(h(X3),h(X4)) = h(op1(X3,X4)) ) )
    & ! [X5] :
        ( ~ sorti2(X5)
        | h(j(X5)) = X5 )
    & ! [X2] :
        ( j(h(X2)) = X2
        | ~ sorti1(X2) )
    & ! [X6] :
        ( ~ sorti2(X6)
        | ! [X7] :
            ( ~ sorti2(X7)
            | op1(j(X6),j(X7)) = j(op2(X6,X7)) ) )
    & ! [X0] :
        ( sorti1(j(X0))
        | ~ sorti2(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)) ) )
     => ~ ( ! [X3] :
              ( sorti1(X3)
             => ! [X4] :
                  ( sorti1(X4)
                 => op2(h(X3),h(X4)) = h(op1(X3,X4)) ) )
          & ! [X5] :
              ( sorti2(X5)
             => h(j(X5)) = X5 )
          & ! [X2] :
              ( sorti1(X2)
             => j(h(X2)) = X2 )
          & ! [X6] :
              ( sorti2(X6)
             => ! [X7] :
                  ( sorti2(X7)
                 => op1(j(X6),j(X7)) = j(op2(X6,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 )
          & ! [X2] :
              ( sorti1(X2)
             => ! [X3] :
                  ( sorti1(X3)
                 => h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
          & ! [X6] :
              ( sorti2(X6)
             => h(j(X6)) = X6 )
          & ! [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 )
        & ! [X2] :
            ( sorti1(X2)
           => ! [X3] :
                ( sorti1(X3)
               => h(op1(X2,X3)) = op2(h(X2),h(X3)) ) )
        & ! [X6] :
            ( sorti2(X6)
           => h(j(X6)) = X6 )
        & ! [X4] :
            ( sorti2(X4)
           => ! [X5] :
                ( sorti2(X5)
               => j(op2(X4,X5)) = op1(j(X4),j(X5)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f39,plain,
    sorti2(sK0(h(sK1))),
    inference(unit_resulting_resolution,[],[f36,f21]) ).

fof(f21,plain,
    ! [X0] :
      ( sorti2(sK0(X0))
      | ~ sorti2(X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0] :
      ( ~ sorti2(X0)
      | ( sorti2(sK0(X0))
        & op2(sK0(X0),X0) = sK0(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).

fof(f14,plain,
    ! [X0] :
      ( ? [X1] :
          ( sorti2(X1)
          & op2(X1,X0) = X1 )
     => ( sorti2(sK0(X0))
        & op2(sK0(X0),X0) = sK0(X0) ) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f36,plain,
    sorti2(h(sK1)),
    inference(resolution,[],[f29,f23]) ).

fof(f23,plain,
    sorti1(sK1),
    inference(cnf_transformation,[],[f17]) ).

fof(f29,plain,
    ! [X0] :
      ( ~ sorti1(X0)
      | sorti2(h(X0)) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f508,plain,
    op1(j(sK0(h(sK1))),sK1) = j(sK0(h(sK1))),
    inference(forward_demodulation,[],[f507,f40]) ).

fof(f40,plain,
    sK0(h(sK1)) = op2(sK0(h(sK1)),h(sK1)),
    inference(unit_resulting_resolution,[],[f36,f20]) ).

fof(f20,plain,
    ! [X0] :
      ( op2(sK0(X0),X0) = sK0(X0)
      | ~ sorti2(X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f507,plain,
    j(op2(sK0(h(sK1)),h(sK1))) = op1(j(sK0(h(sK1))),sK1),
    inference(forward_demodulation,[],[f386,f49]) ).

fof(f49,plain,
    j(h(sK1)) = sK1,
    inference(resolution,[],[f24,f23]) ).

fof(f24,plain,
    ! [X7] :
      ( ~ sorti1(X7)
      | j(h(X7)) = X7 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f386,plain,
    j(op2(sK0(h(sK1)),h(sK1))) = op1(j(sK0(h(sK1))),j(h(sK1))),
    inference(unit_resulting_resolution,[],[f36,f39,f27]) ).

fof(f27,plain,
    ! [X2,X3] :
      ( ~ sorti2(X3)
      | ~ sorti2(X2)
      | j(op2(X2,X3)) = op1(j(X2),j(X3)) ),
    inference(cnf_transformation,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : ALG176+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_uns --cores 0 -t %d %s
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Aug 29 14:56:25 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.50  % (29776)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)
% 0.21/0.50  % (29760)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)
% 0.21/0.51  % (29768)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)
% 0.21/0.52  % (29759)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)
% 0.21/0.52  % (29768)Instruction limit reached!
% 0.21/0.52  % (29768)------------------------------
% 0.21/0.52  % (29768)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.53  % (29775)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)
% 0.21/0.53  % (29767)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)
% 0.21/0.53  % (29760)First to succeed.
% 0.21/0.53  % (29768)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.53  % (29768)Termination reason: Unknown
% 0.21/0.53  % (29768)Termination phase: Saturation
% 0.21/0.53  
% 0.21/0.53  % (29768)Memory used [KB]: 6012
% 0.21/0.53  % (29768)Time elapsed: 0.119 s
% 0.21/0.53  % (29768)Instructions burned: 7 (million)
% 0.21/0.53  % (29768)------------------------------
% 0.21/0.53  % (29768)------------------------------
% 0.21/0.53  % (29767)Instruction limit reached!
% 0.21/0.53  % (29767)------------------------------
% 0.21/0.53  % (29767)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54  % (29760)Refutation found. Thanks to Tanya!
% 0.21/0.54  % SZS status Theorem for theBenchmark
% 0.21/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.54  % (29760)------------------------------
% 0.21/0.54  % (29760)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54  % (29760)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54  % (29760)Termination reason: Refutation
% 0.21/0.54  
% 0.21/0.54  % (29760)Memory used [KB]: 6268
% 0.21/0.54  % (29760)Time elapsed: 0.110 s
% 0.21/0.54  % (29760)Instructions burned: 20 (million)
% 0.21/0.54  % (29760)------------------------------
% 0.21/0.54  % (29760)------------------------------
% 0.21/0.54  % (29752)Success in time 0.179 s
%------------------------------------------------------------------------------