TSTP Solution File: ALG176+1 by Vampire-SAT---4.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.9
% Problem  : ALG176+1 : TPTP v8.2.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire %s %d SAT

% Computer : n004.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 : Mon Jun 24 04:11:45 EDT 2024

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   60 (   4 unt;   0 def)
%            Number of atoms       :  198 (  46 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  229 (  91   ~;  78   |;  26   &)
%                                         (   5 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    9 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   64 (  60   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1759,plain,
    $false,
    inference(avatar_sat_refutation,[],[f43,f47,f136,f387,f466,f1753]) ).

fof(f1753,plain,
    ( ~ spl2_6
    | ~ spl2_1
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(avatar_split_clause,[],[f1752,f86,f36,f32,f120]) ).

fof(f120,plain,
    ( spl2_6
  <=> sorti2(sK0(h(sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).

fof(f32,plain,
    ( spl2_1
  <=> sorti2(h(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f36,plain,
    ( spl2_2
  <=> sorti1(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

fof(f86,plain,
    ( spl2_3
  <=> sorti1(j(h(sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

fof(f1752,plain,
    ( ~ sorti2(sK0(h(sK1)))
    | ~ spl2_1
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(trivial_inequality_removal,[],[f1749]) ).

fof(f1749,plain,
    ( j(sK0(h(sK1))) != j(sK0(h(sK1)))
    | ~ sorti2(sK0(h(sK1)))
    | ~ spl2_1
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(superposition,[],[f41,f845]) ).

fof(f845,plain,
    ( j(sK0(h(sK1))) = op1(j(sK0(h(sK1))),sK1)
    | ~ spl2_1
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(backward_demodulation,[],[f804,f812]) ).

fof(f812,plain,
    ( sK0(h(sK1)) = op2(sK0(h(sK1)),h(sK1))
    | ~ spl2_1
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(backward_demodulation,[],[f694,f737]) ).

fof(f737,plain,
    ( sK1 = j(h(sK1))
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(superposition,[],[f475,f350]) ).

fof(f350,plain,
    ( sK1 = j(h(sK1))
    | ~ spl2_2 ),
    inference(superposition,[],[f326,f26]) ).

fof(f26,plain,
    sK1 = j(h(sK1)),
    inference(resolution,[],[f16,f25]) ).

fof(f25,plain,
    sorti1(sK1),
    inference(cnf_transformation,[],[f13]) ).

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

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

fof(f16,plain,
    ! [X2] :
      ( ~ sorti1(X2)
      | j(h(X2)) = X2 ),
    inference(cnf_transformation,[],[f9]) ).

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

fof(f8,plain,
    ( ! [X2] :
        ( j(h(X2)) = X2
        | ~ sorti1(X2) )
    & ! [X3] :
        ( h(j(X3)) = X3
        | ~ sorti2(X3) )
    & ! [X4] :
        ( ! [X5] :
            ( j(op2(X4,X5)) = op1(j(X4),j(X5))
            | ~ sorti2(X5) )
        | ~ sorti2(X4) )
    & ! [X6] :
        ( ! [X7] :
            ( h(op1(X6,X7)) = op2(h(X6),h(X7))
            | ~ sorti1(X7) )
        | ~ sorti1(X6) )
    & ! [X0] :
        ( sorti1(j(X0))
        | ~ sorti2(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)) ) )
     => ~ ( ! [X2] :
              ( sorti1(X2)
             => j(h(X2)) = X2 )
          & ! [X3] :
              ( sorti2(X3)
             => h(j(X3)) = X3 )
          & ! [X4] :
              ( sorti2(X4)
             => ! [X5] :
                  ( sorti2(X5)
                 => j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
          & ! [X6] :
              ( sorti1(X6)
             => ! [X7] :
                  ( sorti1(X7)
                 => h(op1(X6,X7)) = op2(h(X6),h(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 )
          & ! [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)) ) ) ) ),
    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 )
        & ! [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)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).

fof(f326,plain,
    ( j(h(sK1)) = j(h(j(h(sK1))))
    | ~ spl2_2 ),
    inference(resolution,[],[f74,f38]) ).

fof(f38,plain,
    ( sorti1(sK1)
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f36]) ).

fof(f74,plain,
    ! [X0] :
      ( ~ sorti1(X0)
      | j(h(X0)) = j(h(j(h(X0)))) ),
    inference(resolution,[],[f27,f19]) ).

fof(f19,plain,
    ! [X1] :
      ( sorti2(h(X1))
      | ~ sorti1(X1) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f27,plain,
    ! [X0] :
      ( ~ sorti2(X0)
      | j(X0) = j(h(j(X0))) ),
    inference(resolution,[],[f16,f18]) ).

fof(f18,plain,
    ! [X0] :
      ( sorti1(j(X0))
      | ~ sorti2(X0) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f475,plain,
    ( j(h(sK1)) = j(h(j(h(sK1))))
    | ~ spl2_3 ),
    inference(resolution,[],[f87,f16]) ).

fof(f87,plain,
    ( sorti1(j(h(sK1)))
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f86]) ).

fof(f694,plain,
    ( sK0(h(j(h(sK1)))) = op2(sK0(h(j(h(sK1)))),h(j(h(sK1))))
    | ~ spl2_1 ),
    inference(resolution,[],[f106,f33]) ).

fof(f33,plain,
    ( sorti2(h(sK1))
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f32]) ).

fof(f106,plain,
    ! [X0] :
      ( ~ sorti2(X0)
      | sK0(h(j(X0))) = op2(sK0(h(j(X0))),h(j(X0))) ),
    inference(resolution,[],[f51,f18]) ).

fof(f51,plain,
    ! [X0] :
      ( ~ sorti1(X0)
      | sK0(h(X0)) = op2(sK0(h(X0)),h(X0)) ),
    inference(resolution,[],[f21,f19]) ).

fof(f21,plain,
    ! [X0] :
      ( ~ sorti2(X0)
      | sK0(X0) = op2(sK0(X0),X0) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X0] :
      ( ? [X1] :
          ( op2(X1,X0) = X1
          & sorti2(X1) )
      | ~ sorti2(X0) ),
    inference(ennf_transformation,[],[f4]) ).

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

fof(f804,plain,
    ( op1(j(sK0(h(sK1))),sK1) = j(op2(sK0(h(sK1)),h(sK1)))
    | ~ spl2_1
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(backward_demodulation,[],[f626,f737]) ).

fof(f626,plain,
    ( j(op2(sK0(h(sK1)),h(sK1))) = op1(j(sK0(h(sK1))),j(h(sK1)))
    | ~ spl2_1 ),
    inference(resolution,[],[f247,f33]) ).

fof(f247,plain,
    ! [X0] :
      ( ~ sorti2(X0)
      | j(op2(sK0(X0),X0)) = op1(j(sK0(X0)),j(X0)) ),
    inference(factoring,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ~ sorti2(X1)
      | ~ sorti2(X0)
      | j(op2(sK0(X1),X0)) = op1(j(sK0(X1)),j(X0)) ),
    inference(resolution,[],[f14,f20]) ).

fof(f20,plain,
    ! [X0] :
      ( sorti2(sK0(X0))
      | ~ sorti2(X0) ),
    inference(cnf_transformation,[],[f10]) ).

fof(f14,plain,
    ! [X4,X5] :
      ( ~ sorti2(X5)
      | ~ sorti2(X4)
      | j(op2(X4,X5)) = op1(j(X4),j(X5)) ),
    inference(cnf_transformation,[],[f9]) ).

fof(f41,plain,
    ! [X0] :
      ( j(X0) != op1(j(X0),sK1)
      | ~ sorti2(X0) ),
    inference(resolution,[],[f24,f18]) ).

fof(f24,plain,
    ! [X1] :
      ( ~ sorti1(X1)
      | op1(X1,sK1) != X1 ),
    inference(cnf_transformation,[],[f13]) ).

fof(f466,plain,
    ( ~ spl2_1
    | spl2_8 ),
    inference(avatar_split_clause,[],[f463,f379,f32]) ).

fof(f379,plain,
    ( spl2_8
  <=> sorti2(h(j(h(sK1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).

fof(f463,plain,
    ( ~ sorti2(h(sK1))
    | spl2_8 ),
    inference(superposition,[],[f381,f26]) ).

fof(f381,plain,
    ( ~ sorti2(h(j(h(sK1))))
    | spl2_8 ),
    inference(avatar_component_clause,[],[f379]) ).

fof(f387,plain,
    ( ~ spl2_8
    | spl2_3
    | ~ spl2_2 ),
    inference(avatar_split_clause,[],[f352,f36,f86,f379]) ).

fof(f352,plain,
    ( sorti1(j(h(sK1)))
    | ~ sorti2(h(j(h(sK1))))
    | ~ spl2_2 ),
    inference(superposition,[],[f18,f326]) ).

fof(f136,plain,
    ( ~ spl2_1
    | spl2_6 ),
    inference(avatar_split_clause,[],[f135,f120,f32]) ).

fof(f135,plain,
    ( ~ sorti2(h(sK1))
    | spl2_6 ),
    inference(resolution,[],[f121,f20]) ).

fof(f121,plain,
    ( ~ sorti2(sK0(h(sK1)))
    | spl2_6 ),
    inference(avatar_component_clause,[],[f120]) ).

fof(f47,plain,
    spl2_2,
    inference(avatar_contradiction_clause,[],[f46]) ).

fof(f46,plain,
    ( $false
    | spl2_2 ),
    inference(resolution,[],[f37,f25]) ).

fof(f37,plain,
    ( ~ sorti1(sK1)
    | spl2_2 ),
    inference(avatar_component_clause,[],[f36]) ).

fof(f43,plain,
    ( ~ spl2_2
    | spl2_1 ),
    inference(avatar_split_clause,[],[f42,f32,f36]) ).

fof(f42,plain,
    ( ~ sorti1(sK1)
    | spl2_1 ),
    inference(resolution,[],[f34,f19]) ).

fof(f34,plain,
    ( ~ sorti2(h(sK1))
    | spl2_1 ),
    inference(avatar_component_clause,[],[f32]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : ALG176+1 : TPTP v8.2.0. Released v2.7.0.
% 0.07/0.14  % Command    : run_vampire %s %d SAT
% 0.12/0.35  % Computer : n004.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit   : 300
% 0.12/0.35  % WCLimit    : 300
% 0.12/0.35  % DateTime   : Wed Jun 19 15:39:39 EDT 2024
% 0.12/0.35  % CPUTime    : 
% 0.12/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.12/0.37  Running first-order model finding
% 0.12/0.37  Running /export/starexec/sandbox/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.43  % (14155)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (14158)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (3000ds/214858Mi)
% 0.20/0.43  % (14155)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (14160)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (3000ds/104Mi)
% 0.20/0.43  % (14155)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (14162)ott-4_1:1_sil=4000:sp=reverse_arity:lcm=predicate:newcnf=on:i=115:bce=on:fd=off:fs=off:fsr=off_0 on theBenchmark for (3000ds/115Mi)
% 0.20/0.43  % (14155)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (14159)fmb+10_1:1_sil=256000:fmbss=23:fmbes=contour:newcnf=on:fmbsr=1.14:i=152523:nm=2:gsp=on:rp=on_0 on theBenchmark for (3000ds/152523Mi)
% 0.20/0.43  % (14155)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (14157)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency:i=99418_0 on theBenchmark for (3000ds/99418Mi)
% 0.20/0.43  % (14155)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43  % (14161)ott+11_8:59_sil=16000:sp=occurrence:lsd=20:abs=on:i=146:aac=none:nm=16:fdi=10:rawr=on:nicw=on_0 on theBenchmark for (3000ds/146Mi)
% 0.20/0.44  TRYING [1]
% 0.20/0.44  % (14155)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.44  % (14156)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (3000ds/98885Mi)
% 0.20/0.44  TRYING [2]
% 0.20/0.44  TRYING [3]
% 0.20/0.44  TRYING [4]
% 0.20/0.44  TRYING [10]
% 0.20/0.45  TRYING [5]
% 0.20/0.47  TRYING [23]
% 0.20/0.49  % (14162)First to succeed.
% 0.20/0.49  % (14160)Instruction limit reached!
% 0.20/0.49  % (14160)------------------------------
% 0.20/0.49  % (14160)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.49  % (14160)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.49  % (14160)Termination reason: Time limit
% 0.20/0.49  % (14160)Termination phase: Saturation
% 0.20/0.49  
% 0.20/0.49  % (14160)Memory used [KB]: 1182
% 0.20/0.49  % (14160)Time elapsed: 0.056 s
% 0.20/0.49  % (14160)Instructions burned: 104 (million)
% 0.20/0.49  % (14162)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14155"
% 0.20/0.49  % (14155)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.49  % (14162)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Theorem for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (14162)------------------------------
% 0.20/0.49  % (14162)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.49  % (14162)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.49  % (14162)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (14162)Memory used [KB]: 2049
% 0.20/0.49  % (14162)Time elapsed: 0.056 s
% 0.20/0.49  % (14162)Instructions burned: 88 (million)
% 0.20/0.49  % (14162)------------------------------
% 0.20/0.49  % (14162)------------------------------
% 0.20/0.49  % (14155)Success in time 0.113 s
%------------------------------------------------------------------------------