%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : NUM016-2 : TPTP v8.1.0. Released v1.0.0.
% 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 : n022.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 18:03:16 EDT 2022

% Result   : Unsatisfiable 1.25s 0.51s
% Output   : Refutation 1.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   36 (   6 unt;   0 def)
%            Number of atoms       :   72 (   1 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   62 (  26   ~;  32   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-1 aty)
%            Number of variables   :   13 (  13   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f54,plain,
    $false,
    inference(avatar_sat_refutation,[],[f27,f40,f46,f49,f53]) ).

fof(f53,plain,
    ( spl1_1
    | ~ spl1_4 ),
    inference(avatar_contradiction_clause,[],[f52]) ).

fof(f52,plain,
    ( $false
    | spl1_1
    | ~ spl1_4 ),
    inference(subsumption_resolution,[],[f50,f21]) ).

fof(f21,plain,
    ( ~ prime(sF0)
    | spl1_1 ),
    inference(avatar_component_clause,[],[f20]) ).

fof(f20,plain,
    ( spl1_1
  <=> prime(sF0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).

fof(f50,plain,
    ( prime(sF0)
    | ~ spl1_4 ),
    inference(resolution,[],[f39,f15]) ).

fof(f15,plain,
    ! [X0] :
      ( ~ less(X0,prime_divisor(X0))
      | prime(X0) ),
    inference(resolution,[],[f7,f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ~ less(X1,X0)
      | ~ less(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',numbers_are_different) ).

fof(f7,axiom,
    ! [X0] :
      ( less(prime_divisor(X0),X0)
      | prime(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_prime_divisors) ).

fof(f39,plain,
    ( less(sF0,prime_divisor(sF0))
    | ~ spl1_4 ),
    inference(avatar_component_clause,[],[f37]) ).

fof(f37,plain,
    ( spl1_4
  <=> less(sF0,prime_divisor(sF0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).

fof(f49,plain,
    ( spl1_1
    | spl1_3 ),
    inference(avatar_contradiction_clause,[],[f48]) ).

fof(f48,plain,
    ( $false
    | spl1_1
    | spl1_3 ),
    inference(subsumption_resolution,[],[f47,f21]) ).

fof(f47,plain,
    ( prime(sF0)
    | spl1_3 ),
    inference(resolution,[],[f35,f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( prime(prime_divisor(X0))
      | prime(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prime_divsiors) ).

fof(f35,plain,
    ( ~ prime(prime_divisor(sF0))
    | spl1_3 ),
    inference(avatar_component_clause,[],[f33]) ).

fof(f33,plain,
    ( spl1_3
  <=> prime(prime_divisor(sF0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

fof(f46,plain,
    ~ spl1_1,
    inference(avatar_split_clause,[],[f45,f20]) ).

fof(f45,plain,
    ~ prime(sF0),
    inference(subsumption_resolution,[],[f44,f1]) ).

fof(f1,axiom,
    ! [X0] : ~ less(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',nothing_is_less_than_itself) ).

fof(f44,plain,
    ( ~ prime(sF0)
    | less(sF0,sF0) ),
    inference(forward_demodulation,[],[f43,f9]) ).

fof(f9,plain,
    factorial_plus_one(a) = sF0,
    introduced(function_definition,[]) ).

fof(f43,plain,
    ( ~ prime(sF0)
    | less(sF0,factorial_plus_one(a)) ),
    inference(forward_demodulation,[],[f31,f9]) ).

fof(f31,plain,
    ( ~ prime(factorial_plus_one(a))
    | less(sF0,factorial_plus_one(a)) ),
    inference(resolution,[],[f10,f3]) ).

fof(f3,axiom,
    ! [X0] : less(X0,factorial_plus_one(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_prime_is_less_than_the_next_one) ).

fof(f10,plain,
    ! [X0] :
      ( ~ less(a,X0)
      | less(sF0,X0)
      | ~ prime(X0) ),
    inference(definition_folding,[],[f8,f9]) ).

fof(f8,axiom,
    ! [X0] :
      ( less(factorial_plus_one(a),X0)
      | ~ less(a,X0)
      | ~ prime(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_another_prime) ).

fof(f40,plain,
    ( ~ spl1_3
    | spl1_4
    | ~ spl1_2 ),
    inference(avatar_split_clause,[],[f30,f24,f37,f33]) ).

fof(f24,plain,
    ( spl1_2
  <=> less(a,prime_divisor(sF0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).

fof(f30,plain,
    ( less(sF0,prime_divisor(sF0))
    | ~ prime(prime_divisor(sF0))
    | ~ spl1_2 ),
    inference(resolution,[],[f10,f26]) ).

fof(f26,plain,
    ( less(a,prime_divisor(sF0))
    | ~ spl1_2 ),
    inference(avatar_component_clause,[],[f24]) ).

fof(f27,plain,
    ( spl1_1
    | spl1_2 ),
    inference(avatar_split_clause,[],[f18,f24,f20]) ).

fof(f18,plain,
    ( less(a,prime_divisor(sF0))
    | prime(sF0) ),
    inference(resolution,[],[f17,f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( divides(prime_divisor(X0),X0)
      | prime(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',division_by_prime_divisor) ).

fof(f17,plain,
    ! [X0] :
      ( ~ divides(X0,sF0)
      | less(a,X0) ),
    inference(superposition,[],[f4,f9]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( ~ divides(X0,factorial_plus_one(X1))
      | less(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_is_smaller) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM016-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 05:49:41 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.50  % (23695)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/101Mi)
% 0.20/0.51  % (23711)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/439Mi)
% 1.25/0.51  % (23695)First to succeed.
% 1.25/0.51  % (23688)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/48Mi)
% 1.25/0.51  % (23695)Refutation found. Thanks to Tanya!
% 1.25/0.51  % SZS status Unsatisfiable for theBenchmark
% 1.25/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 1.25/0.51  % (23695)------------------------------
% 1.25/0.51  % (23695)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.25/0.51  % (23695)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.25/0.51  % (23695)Termination reason: Refutation
% 1.25/0.51  
% 1.25/0.51  % (23695)Memory used [KB]: 5373
% 1.25/0.51  % (23695)Time elapsed: 0.114 s
% 1.25/0.51  % (23695)Instructions burned: 2 (million)
% 1.25/0.51  % (23695)------------------------------
% 1.25/0.51  % (23695)------------------------------
% 1.25/0.51  % (23682)Success in time 0.159 s
%------------------------------------------------------------------------------