TSTP Solution File: SYN075+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYN075+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n019.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 : Tue Apr 30 18:02:06 EDT 2024

% Result   : Theorem 0.22s 0.38s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   43 (   5 unt;   0 def)
%            Number of atoms       :  172 ( 108 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  207 (  78   ~;  86   |;  30   &)
%                                         (   8 <=>;   4  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   97 (  68   !;  29   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f86,plain,
    $false,
    inference(resolution,[],[f85,f25]) ).

fof(f25,plain,
    big_f(sK3,sK4),
    inference(equality_resolution,[],[f24]) ).

fof(f24,plain,
    ! [X2] :
      ( big_f(X2,sK4)
      | sK3 != X2 ),
    inference(equality_resolution,[],[f22]) ).

fof(f22,plain,
    ! [X2,X3] :
      ( big_f(X2,X3)
      | sK4 != X3
      | sK3 != X2 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X2,X3] :
      ( ( big_f(X2,X3)
        | sK4 != X3
        | sK3 != X2 )
      & ( ( sK4 = X3
          & sK3 = X2 )
        | ~ big_f(X2,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f13,f14]) ).

fof(f14,plain,
    ( ? [X0,X1] :
      ! [X2,X3] :
        ( ( big_f(X2,X3)
          | X1 != X3
          | X0 != X2 )
        & ( ( X1 = X3
            & X0 = X2 )
          | ~ big_f(X2,X3) ) )
   => ! [X3,X2] :
        ( ( big_f(X2,X3)
          | sK4 != X3
          | sK3 != X2 )
        & ( ( sK4 = X3
            & sK3 = X2 )
          | ~ big_f(X2,X3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0,X1] :
    ! [X2,X3] :
      ( ( big_f(X2,X3)
        | X1 != X3
        | X0 != X2 )
      & ( ( X1 = X3
          & X0 = X2 )
        | ~ big_f(X2,X3) ) ),
    inference(flattening,[],[f12]) ).

fof(f12,plain,
    ? [X0,X1] :
    ! [X2,X3] :
      ( ( big_f(X2,X3)
        | X1 != X3
        | X0 != X2 )
      & ( ( X1 = X3
          & X0 = X2 )
        | ~ big_f(X2,X3) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ? [X0,X1] :
    ! [X2,X3] :
      ( big_f(X2,X3)
    <=> ( X1 = X3
        & X0 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel52_1) ).

fof(f85,plain,
    ~ big_f(sK3,sK4),
    inference(trivial_inequality_removal,[],[f84]) ).

fof(f84,plain,
    ( sK4 != sK4
    | ~ big_f(sK3,sK4) ),
    inference(forward_demodulation,[],[f83,f45]) ).

fof(f45,plain,
    sK4 = sK0(sK4),
    inference(equality_resolution,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( sK4 != X0
      | sK0(X0) = X0 ),
    inference(equality_factoring,[],[f35]) ).

fof(f35,plain,
    ! [X0] :
      ( sK0(X0) = sK4
      | sK0(X0) = X0 ),
    inference(resolution,[],[f21,f32]) ).

fof(f32,plain,
    ! [X0] :
      ( big_f(sK3,sK0(X0))
      | sK0(X0) = X0 ),
    inference(duplicate_literal_removal,[],[f31]) ).

fof(f31,plain,
    ! [X0] :
      ( big_f(sK3,sK0(X0))
      | sK0(X0) = X0
      | sK0(X0) = X0 ),
    inference(superposition,[],[f23,f30]) ).

fof(f30,plain,
    ! [X0] :
      ( sK2(X0) = sK3
      | sK0(X0) = X0 ),
    inference(resolution,[],[f20,f23]) ).

fof(f20,plain,
    ! [X2,X3] :
      ( ~ big_f(X2,X3)
      | sK3 = X2 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f23,plain,
    ! [X0] :
      ( big_f(sK2(X0),sK0(X0))
      | sK0(X0) = X0 ),
    inference(equality_resolution,[],[f17]) ).

fof(f17,plain,
    ! [X0,X5] :
      ( sK0(X0) = X0
      | big_f(X5,sK0(X0))
      | sK2(X0) != X5 ),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0] :
      ( ( sK0(X0) != X0
        | ! [X2] :
            ( ( sK1(X0,X2) != X2
              | ~ big_f(sK1(X0,X2),sK0(X0)) )
            & ( sK1(X0,X2) = X2
              | big_f(sK1(X0,X2),sK0(X0)) ) ) )
      & ( sK0(X0) = X0
        | ! [X5] :
            ( ( big_f(X5,sK0(X0))
              | sK2(X0) != X5 )
            & ( sK2(X0) = X5
              | ~ big_f(X5,sK0(X0)) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f10,f9,f8]) ).

fof(f8,plain,
    ! [X0] :
      ( ? [X1] :
          ( ( X0 != X1
            | ! [X2] :
              ? [X3] :
                ( ( X2 != X3
                  | ~ big_f(X3,X1) )
                & ( X2 = X3
                  | big_f(X3,X1) ) ) )
          & ( X0 = X1
            | ? [X4] :
              ! [X5] :
                ( ( big_f(X5,X1)
                  | X4 != X5 )
                & ( X4 = X5
                  | ~ big_f(X5,X1) ) ) ) )
     => ( ( sK0(X0) != X0
          | ! [X2] :
            ? [X3] :
              ( ( X2 != X3
                | ~ big_f(X3,sK0(X0)) )
              & ( X2 = X3
                | big_f(X3,sK0(X0)) ) ) )
        & ( sK0(X0) = X0
          | ? [X4] :
            ! [X5] :
              ( ( big_f(X5,sK0(X0))
                | X4 != X5 )
              & ( X4 = X5
                | ~ big_f(X5,sK0(X0)) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ! [X0,X2] :
      ( ? [X3] :
          ( ( X2 != X3
            | ~ big_f(X3,sK0(X0)) )
          & ( X2 = X3
            | big_f(X3,sK0(X0)) ) )
     => ( ( sK1(X0,X2) != X2
          | ~ big_f(sK1(X0,X2),sK0(X0)) )
        & ( sK1(X0,X2) = X2
          | big_f(sK1(X0,X2),sK0(X0)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ! [X0] :
      ( ? [X4] :
        ! [X5] :
          ( ( big_f(X5,sK0(X0))
            | X4 != X5 )
          & ( X4 = X5
            | ~ big_f(X5,sK0(X0)) ) )
     => ! [X5] :
          ( ( big_f(X5,sK0(X0))
            | sK2(X0) != X5 )
          & ( sK2(X0) = X5
            | ~ big_f(X5,sK0(X0)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f7,plain,
    ! [X0] :
    ? [X1] :
      ( ( X0 != X1
        | ! [X2] :
          ? [X3] :
            ( ( X2 != X3
              | ~ big_f(X3,X1) )
            & ( X2 = X3
              | big_f(X3,X1) ) ) )
      & ( X0 = X1
        | ? [X4] :
          ! [X5] :
            ( ( big_f(X5,X1)
              | X4 != X5 )
            & ( X4 = X5
              | ~ big_f(X5,X1) ) ) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,plain,
    ! [X0] :
    ? [X1] :
      ( ( X0 != X1
        | ! [X2] :
          ? [X3] :
            ( ( X2 != X3
              | ~ big_f(X3,X1) )
            & ( X2 = X3
              | big_f(X3,X1) ) ) )
      & ( X0 = X1
        | ? [X2] :
          ! [X3] :
            ( ( big_f(X3,X1)
              | X2 != X3 )
            & ( X2 = X3
              | ~ big_f(X3,X1) ) ) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,plain,
    ! [X0] :
    ? [X1] :
      ( ? [X2] :
        ! [X3] :
          ( big_f(X3,X1)
        <=> X2 = X3 )
    <~> X0 = X1 ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,plain,
    ~ ? [X0] :
      ! [X1] :
        ( ? [X2] :
          ! [X3] :
            ( big_f(X3,X1)
          <=> X2 = X3 )
      <=> X0 = X1 ),
    inference(rectify,[],[f3]) ).

fof(f3,negated_conjecture,
    ~ ? [X1] :
      ! [X3] :
        ( ? [X0] :
          ! [X2] :
            ( big_f(X2,X3)
          <=> X0 = X2 )
      <=> X1 = X3 ),
    inference(negated_conjecture,[],[f2]) ).

fof(f2,conjecture,
    ? [X1] :
    ! [X3] :
      ( ? [X0] :
        ! [X2] :
          ( big_f(X2,X3)
        <=> X0 = X2 )
    <=> X1 = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel52) ).

fof(f21,plain,
    ! [X2,X3] :
      ( ~ big_f(X2,X3)
      | sK4 = X3 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f83,plain,
    ( sK4 != sK0(sK4)
    | ~ big_f(sK3,sK4) ),
    inference(trivial_inequality_removal,[],[f82]) ).

fof(f82,plain,
    ( sK3 != sK3
    | sK4 != sK0(sK4)
    | ~ big_f(sK3,sK4) ),
    inference(superposition,[],[f27,f80]) ).

fof(f80,plain,
    sK3 = sK1(sK4,sK3),
    inference(equality_resolution,[],[f73]) ).

fof(f73,plain,
    ! [X0] :
      ( sK3 != X0
      | sK3 = sK1(sK4,X0) ),
    inference(equality_factoring,[],[f66]) ).

fof(f66,plain,
    ! [X0] :
      ( sK1(sK4,X0) = X0
      | sK3 = sK1(sK4,X0) ),
    inference(resolution,[],[f63,f20]) ).

fof(f63,plain,
    ! [X0] :
      ( big_f(sK1(sK4,X0),sK4)
      | sK1(sK4,X0) = X0 ),
    inference(trivial_inequality_removal,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( sK4 != sK4
      | sK1(sK4,X0) = X0
      | big_f(sK1(sK4,X0),sK4) ),
    inference(superposition,[],[f28,f45]) ).

fof(f28,plain,
    ! [X2,X0] :
      ( sK0(X0) != X0
      | sK1(X0,X2) = X2
      | big_f(sK1(X0,X2),X0) ),
    inference(inner_rewriting,[],[f18]) ).

fof(f18,plain,
    ! [X2,X0] :
      ( sK0(X0) != X0
      | sK1(X0,X2) = X2
      | big_f(sK1(X0,X2),sK0(X0)) ),
    inference(cnf_transformation,[],[f11]) ).

fof(f27,plain,
    ! [X2,X0] :
      ( sK1(X0,X2) != X2
      | sK0(X0) != X0
      | ~ big_f(X2,X0) ),
    inference(inner_rewriting,[],[f26]) ).

fof(f26,plain,
    ! [X2,X0] :
      ( sK0(X0) != X0
      | sK1(X0,X2) != X2
      | ~ big_f(sK1(X0,X2),X0) ),
    inference(inner_rewriting,[],[f19]) ).

fof(f19,plain,
    ! [X2,X0] :
      ( sK0(X0) != X0
      | sK1(X0,X2) != X2
      | ~ big_f(sK1(X0,X2),sK0(X0)) ),
    inference(cnf_transformation,[],[f11]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYN075+1 : TPTP v8.1.2. Released v2.0.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n019.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   : Tue Apr 30 01:56:14 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (18990)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (18995)WARNING: value z3 for option sas not known
% 0.22/0.37  % (18996)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.37  % (18994)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.37  % (18995)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.37  % (18997)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_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.37  % (18993)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.37  % (18998)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.37  % (18999)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.38  TRYING [1]
% 0.22/0.38  TRYING [2]
% 0.22/0.38  TRYING [3]
% 0.22/0.38  TRYING [4]
% 0.22/0.38  % (18998)First to succeed.
% 0.22/0.38  TRYING [1]
% 0.22/0.38  % (18999)Also succeeded, but the first one will report.
% 0.22/0.38  TRYING [5]
% 0.22/0.38  TRYING [2]
% 0.22/0.38  TRYING [1]
% 0.22/0.38  TRYING [2]
% 0.22/0.38  TRYING [3]
% 0.22/0.38  % (18998)Refutation found. Thanks to Tanya!
% 0.22/0.38  % SZS status Theorem for theBenchmark
% 0.22/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.38  % (18998)------------------------------
% 0.22/0.38  % (18998)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.38  % (18998)Termination reason: Refutation
% 0.22/0.38  
% 0.22/0.38  % (18998)Memory used [KB]: 769
% 0.22/0.38  % (18998)Time elapsed: 0.005 s
% 0.22/0.38  % (18998)Instructions burned: 6 (million)
% 0.22/0.38  % (18998)------------------------------
% 0.22/0.38  % (18998)------------------------------
% 0.22/0.38  % (18990)Success in time 0.01 s
%------------------------------------------------------------------------------