TSTP Solution File: SYN084+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% 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 : Wed Aug 31 19:36:51 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   34
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   59 (   5 unt;   0 def)
%            Number of atoms       :  267 (   0 equ)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  362 ( 154   ~; 142   |;  50   &)
%                                         (   5 <=>;   8  =>;   0  <=;   3 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   2 prp; 0-1 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-1 aty)
%            Number of variables   :   35 (  29   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f97,plain,
    $false,
    inference(resolution,[],[f95,f66]) ).

fof(f66,plain,
    ~ sP1,
    inference(duplicate_literal_removal,[],[f65]) ).

fof(f65,plain,
    ( ~ sP1
    | ~ sP1 ),
    inference(resolution,[],[f59,f53]) ).

fof(f53,plain,
    ( ~ big_p(a)
    | ~ sP1 ),
    inference(duplicate_literal_removal,[],[f52]) ).

fof(f52,plain,
    ( ~ sP1
    | ~ big_p(a)
    | ~ sP1
    | ~ big_p(a) ),
    inference(resolution,[],[f50,f41]) ).

fof(f41,plain,
    ( ~ big_p(sK3)
    | ~ big_p(a)
    | ~ sP1 ),
    inference(resolution,[],[f39,f27]) ).

fof(f27,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ big_p(X0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ( ~ big_p(X0)
          & big_p(a)
          & ~ big_p(f(f(X0))) ) )
      & ( big_p(X0)
        | ~ big_p(a)
        | big_p(f(f(X0)))
        | ~ sP0(X0) ) ),
    inference(flattening,[],[f13]) ).

fof(f13,plain,
    ! [X0] :
      ( ( sP0(X0)
        | ( ~ big_p(X0)
          & big_p(a)
          & ~ big_p(f(f(X0))) ) )
      & ( big_p(X0)
        | ~ big_p(a)
        | big_p(f(f(X0)))
        | ~ sP0(X0) ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,plain,
    ! [X0] :
      ( sP0(X0)
    <=> ( big_p(X0)
        | ~ big_p(a)
        | big_p(f(f(X0))) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f39,plain,
    ( ~ sP0(sK3)
    | ~ big_p(a)
    | ~ sP1 ),
    inference(duplicate_literal_removal,[],[f38]) ).

fof(f38,plain,
    ( ~ sP0(sK3)
    | ~ sP1
    | ~ sP0(sK3)
    | ~ sP1
    | ~ big_p(a) ),
    inference(resolution,[],[f37,f30]) ).

fof(f30,plain,
    ( big_p(f(sK3))
    | ~ sP0(sK3)
    | ~ sP1 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( ( ( big_p(a)
        & ~ big_p(f(f(sK3)))
        & big_p(f(sK3)) )
      | ~ sP0(sK3)
      | ~ sP1 )
    & ( ! [X1] :
          ( ( ~ big_p(a)
            | big_p(f(f(X1)))
            | ~ big_p(f(X1)) )
          & sP0(X1) )
      | sP1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f16,f17]) ).

fof(f17,plain,
    ( ? [X0] :
        ( ( big_p(a)
          & ~ big_p(f(f(X0)))
          & big_p(f(X0)) )
        | ~ sP0(X0) )
   => ( ( big_p(a)
        & ~ big_p(f(f(sK3)))
        & big_p(f(sK3)) )
      | ~ sP0(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ( ( ? [X0] :
          ( ( big_p(a)
            & ~ big_p(f(f(X0)))
            & big_p(f(X0)) )
          | ~ sP0(X0) )
      | ~ sP1 )
    & ( ! [X1] :
          ( ( ~ big_p(a)
            | big_p(f(f(X1)))
            | ~ big_p(f(X1)) )
          & sP0(X1) )
      | sP1 ) ),
    inference(rectify,[],[f15]) ).

fof(f15,plain,
    ( ( ? [X0] :
          ( ( big_p(a)
            & ~ big_p(f(f(X0)))
            & big_p(f(X0)) )
          | ~ sP0(X0) )
      | ~ sP1 )
    & ( ! [X0] :
          ( ( ~ big_p(a)
            | big_p(f(f(X0)))
            | ~ big_p(f(X0)) )
          & sP0(X0) )
      | sP1 ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,plain,
    ( sP1
  <~> ! [X0] :
        ( ( ~ big_p(a)
          | big_p(f(f(X0)))
          | ~ big_p(f(X0)) )
        & sP0(X0) ) ),
    inference(definition_folding,[],[f5,f7,f6]) ).

fof(f7,plain,
    ( sP1
  <=> ! [X1] :
        ( ( ~ big_p(f(X1))
          & big_p(X1) )
        | ~ big_p(a)
        | big_p(f(f(X1))) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f5,plain,
    ( ! [X1] :
        ( ( ~ big_p(f(X1))
          & big_p(X1) )
        | ~ big_p(a)
        | big_p(f(f(X1))) )
  <~> ! [X0] :
        ( ( ~ big_p(a)
          | big_p(f(f(X0)))
          | ~ big_p(f(X0)) )
        & ( big_p(X0)
          | ~ big_p(a)
          | big_p(f(f(X0))) ) ) ),
    inference(flattening,[],[f4]) ).

fof(f4,plain,
    ( ! [X0] :
        ( ( ~ big_p(a)
          | big_p(f(f(X0)))
          | ~ big_p(f(X0)) )
        & ( big_p(X0)
          | ~ big_p(a)
          | big_p(f(f(X0))) ) )
  <~> ! [X1] :
        ( big_p(f(f(X1)))
        | ~ big_p(a)
        | ( ~ big_p(f(X1))
          & big_p(X1) ) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,plain,
    ~ ( ! [X0] :
          ( ( ~ big_p(a)
            | big_p(f(f(X0)))
            | ~ big_p(f(X0)) )
          & ( big_p(X0)
            | ~ big_p(a)
            | big_p(f(f(X0))) ) )
    <=> ! [X1] :
          ( ( big_p(a)
            & ( big_p(X1)
             => big_p(f(X1)) ) )
         => big_p(f(f(X1))) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,negated_conjecture,
    ~ ( ! [X1] :
          ( ( big_p(X1)
            | ~ big_p(a)
            | big_p(f(f(X1))) )
          & ( ~ big_p(a)
            | big_p(f(f(X1)))
            | ~ big_p(f(X1)) ) )
    <=> ! [X0] :
          ( ( ( big_p(X0)
             => big_p(f(X0)) )
            & big_p(a) )
         => big_p(f(f(X0))) ) ),
    inference(negated_conjecture,[],[f1]) ).

fof(f1,conjecture,
    ( ! [X1] :
        ( ( big_p(X1)
          | ~ big_p(a)
          | big_p(f(f(X1))) )
        & ( ~ big_p(a)
          | big_p(f(f(X1)))
          | ~ big_p(f(X1)) ) )
  <=> ! [X0] :
        ( ( ( big_p(X0)
           => big_p(f(X0)) )
          & big_p(a) )
       => big_p(f(f(X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel62) ).

fof(f37,plain,
    ( ~ big_p(f(sK3))
    | ~ sP0(sK3)
    | ~ sP1
    | ~ big_p(a) ),
    inference(duplicate_literal_removal,[],[f36]) ).

fof(f36,plain,
    ( ~ sP0(sK3)
    | ~ big_p(f(sK3))
    | ~ big_p(a)
    | ~ sP1
    | ~ sP1 ),
    inference(resolution,[],[f20,f31]) ).

fof(f31,plain,
    ( ~ big_p(f(f(sK3)))
    | ~ sP0(sK3)
    | ~ sP1 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f20,plain,
    ! [X1] :
      ( big_p(f(f(X1)))
      | ~ big_p(a)
      | ~ sP1
      | ~ big_p(f(X1)) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ( ( sP1
      | ( ( big_p(f(sK2))
          | ~ big_p(sK2) )
        & big_p(a)
        & ~ big_p(f(f(sK2))) ) )
    & ( ! [X1] :
          ( ( ~ big_p(f(X1))
            & big_p(X1) )
          | ~ big_p(a)
          | big_p(f(f(X1))) )
      | ~ sP1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f10,f11]) ).

fof(f11,plain,
    ( ? [X0] :
        ( ( big_p(f(X0))
          | ~ big_p(X0) )
        & big_p(a)
        & ~ big_p(f(f(X0))) )
   => ( ( big_p(f(sK2))
        | ~ big_p(sK2) )
      & big_p(a)
      & ~ big_p(f(f(sK2))) ) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ( ( sP1
      | ? [X0] :
          ( ( big_p(f(X0))
            | ~ big_p(X0) )
          & big_p(a)
          & ~ big_p(f(f(X0))) ) )
    & ( ! [X1] :
          ( ( ~ big_p(f(X1))
            & big_p(X1) )
          | ~ big_p(a)
          | big_p(f(f(X1))) )
      | ~ sP1 ) ),
    inference(rectify,[],[f9]) ).

fof(f9,plain,
    ( ( sP1
      | ? [X1] :
          ( ( big_p(f(X1))
            | ~ big_p(X1) )
          & big_p(a)
          & ~ big_p(f(f(X1))) ) )
    & ( ! [X1] :
          ( ( ~ big_p(f(X1))
            & big_p(X1) )
          | ~ big_p(a)
          | big_p(f(f(X1))) )
      | ~ sP1 ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f50,plain,
    ( big_p(sK3)
    | ~ big_p(a)
    | ~ sP1 ),
    inference(duplicate_literal_removal,[],[f47]) ).

fof(f47,plain,
    ( big_p(sK3)
    | ~ big_p(a)
    | ~ sP1
    | ~ big_p(a)
    | ~ sP1 ),
    inference(resolution,[],[f40,f19]) ).

fof(f19,plain,
    ! [X1] :
      ( big_p(f(f(X1)))
      | ~ sP1
      | big_p(X1)
      | ~ big_p(a) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f40,plain,
    ( ~ big_p(f(f(sK3)))
    | ~ sP1
    | ~ big_p(a) ),
    inference(resolution,[],[f39,f25]) ).

fof(f25,plain,
    ! [X0] :
      ( sP0(X0)
      | ~ big_p(f(f(X0))) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f59,plain,
    ( big_p(a)
    | ~ sP1 ),
    inference(resolution,[],[f56,f26]) ).

fof(f26,plain,
    ! [X0] :
      ( sP0(X0)
      | big_p(a) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f56,plain,
    ( ~ sP0(sK3)
    | ~ sP1 ),
    inference(duplicate_literal_removal,[],[f55]) ).

fof(f55,plain,
    ( ~ sP0(sK3)
    | ~ sP1
    | ~ sP1 ),
    inference(resolution,[],[f53,f32]) ).

fof(f32,plain,
    ( big_p(a)
    | ~ sP1
    | ~ sP0(sK3) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f95,plain,
    sP1,
    inference(resolution,[],[f93,f22]) ).

fof(f22,plain,
    ( big_p(a)
    | sP1 ),
    inference(cnf_transformation,[],[f12]) ).

fof(f93,plain,
    ~ big_p(a),
    inference(resolution,[],[f92,f66]) ).

fof(f92,plain,
    ( sP1
    | ~ big_p(a) ),
    inference(resolution,[],[f88,f28]) ).

fof(f28,plain,
    ! [X1] :
      ( sP0(X1)
      | sP1 ),
    inference(cnf_transformation,[],[f18]) ).

fof(f88,plain,
    ( ~ sP0(sK2)
    | ~ big_p(a) ),
    inference(duplicate_literal_removal,[],[f87]) ).

fof(f87,plain,
    ( ~ big_p(a)
    | ~ big_p(a)
    | ~ sP0(sK2) ),
    inference(resolution,[],[f86,f73]) ).

fof(f73,plain,
    ( big_p(sK2)
    | ~ big_p(a)
    | ~ sP0(sK2) ),
    inference(resolution,[],[f24,f67]) ).

fof(f67,plain,
    ~ big_p(f(f(sK2))),
    inference(resolution,[],[f66,f21]) ).

fof(f21,plain,
    ( sP1
    | ~ big_p(f(f(sK2))) ),
    inference(cnf_transformation,[],[f12]) ).

fof(f24,plain,
    ! [X0] :
      ( big_p(f(f(X0)))
      | ~ big_p(a)
      | big_p(X0)
      | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f86,plain,
    ( ~ big_p(sK2)
    | ~ big_p(a) ),
    inference(resolution,[],[f85,f66]) ).

fof(f85,plain,
    ( sP1
    | ~ big_p(sK2)
    | ~ big_p(a) ),
    inference(resolution,[],[f84,f23]) ).

fof(f23,plain,
    ( big_p(f(sK2))
    | ~ big_p(sK2)
    | sP1 ),
    inference(cnf_transformation,[],[f12]) ).

fof(f84,plain,
    ( ~ big_p(f(sK2))
    | ~ big_p(a) ),
    inference(resolution,[],[f70,f66]) ).

fof(f70,plain,
    ( sP1
    | ~ big_p(f(sK2))
    | ~ big_p(a) ),
    inference(resolution,[],[f67,f29]) ).

fof(f29,plain,
    ! [X1] :
      ( big_p(f(f(X1)))
      | sP1
      | ~ big_p(f(X1))
      | ~ big_p(a) ),
    inference(cnf_transformation,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33  % Computer : n004.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 30 21:26:19 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (12772)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.19/0.50  % (12780)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.19/0.50  % (12775)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.19/0.50  % (12772)Refutation not found, incomplete strategy% (12772)------------------------------
% 0.19/0.50  % (12772)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (12793)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/498Mi)
% 0.19/0.50  % (12772)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (12772)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.50  
% 0.19/0.50  % (12772)Memory used [KB]: 5373
% 0.19/0.50  % (12772)Time elapsed: 0.101 s
% 0.19/0.50  % (12772)Instructions burned: 2 (million)
% 0.19/0.50  % (12772)------------------------------
% 0.19/0.50  % (12772)------------------------------
% 0.19/0.51  % (12780)First to succeed.
% 0.19/0.51  % (12790)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.19/0.51  % (12771)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/191324Mi)
% 0.19/0.51  % (12780)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  % (12780)------------------------------
% 0.19/0.51  % (12780)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (12780)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (12780)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (12780)Memory used [KB]: 895
% 0.19/0.51  % (12780)Time elapsed: 0.115 s
% 0.19/0.51  % (12780)Instructions burned: 2 (million)
% 0.19/0.51  % (12780)------------------------------
% 0.19/0.51  % (12780)------------------------------
% 0.19/0.51  % (12770)Success in time 0.166 s
%------------------------------------------------------------------------------