TSTP Solution File: NUM016-2 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM016-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n029.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 : Sun May  5 08:17:14 EDT 2024

% Result   : Unsatisfiable 0.13s 0.34s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   18 (   6 unt;   0 def)
%            Number of atoms       :   32 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   25 (  11   ~;  14   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   12 (  12   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f21,plain,
    $false,
    inference(subsumption_resolution,[],[f19,f10]) ).

fof(f10,plain,
    ~ prime(factorial_plus_one(a)),
    inference(subsumption_resolution,[],[f9,f1]) ).

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

fof(f9,plain,
    ( ~ prime(factorial_plus_one(a))
    | less(factorial_plus_one(a),factorial_plus_one(a)) ),
    inference(resolution,[],[f8,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(f8,axiom,
    ! [X0] :
      ( ~ less(a,X0)
      | ~ prime(X0)
      | less(factorial_plus_one(a),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_another_prime) ).

fof(f19,plain,
    prime(factorial_plus_one(a)),
    inference(resolution,[],[f18,f12]) ).

fof(f12,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(f18,plain,
    less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))),
    inference(subsumption_resolution,[],[f17,f10]) ).

fof(f17,plain,
    ( less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
    | prime(factorial_plus_one(a)) ),
    inference(resolution,[],[f16,f6]) ).

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

fof(f16,plain,
    ( ~ prime(prime_divisor(factorial_plus_one(a)))
    | less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
    inference(subsumption_resolution,[],[f14,f10]) ).

fof(f14,plain,
    ( prime(factorial_plus_one(a))
    | ~ prime(prime_divisor(factorial_plus_one(a)))
    | less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
    inference(resolution,[],[f13,f8]) ).

fof(f13,plain,
    ! [X0] :
      ( less(X0,prime_divisor(factorial_plus_one(X0)))
      | prime(factorial_plus_one(X0)) ),
    inference(resolution,[],[f4,f5]) ).

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

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
% 0.07/0.11  % Problem    : NUM016-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.32  % Computer : n029.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit   : 300
% 0.13/0.32  % WCLimit    : 300
% 0.13/0.32  % DateTime   : Fri May  3 14:50:22 EDT 2024
% 0.13/0.32  % CPUTime    : 
% 0.13/0.33  % (8132)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.34  % (8137)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.34  % (8137)First to succeed.
% 0.13/0.34  % (8137)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8132"
% 0.13/0.34  % (8137)Refutation found. Thanks to Tanya!
% 0.13/0.34  % SZS status Unsatisfiable for theBenchmark
% 0.13/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.34  % (8137)------------------------------
% 0.13/0.34  % (8137)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.34  % (8137)Termination reason: Refutation
% 0.13/0.34  
% 0.13/0.34  % (8137)Memory used [KB]: 745
% 0.13/0.34  % (8137)Time elapsed: 0.002 s
% 0.13/0.34  % (8137)Instructions burned: 2 (million)
% 0.13/0.34  % (8132)Success in time 0.003 s
%------------------------------------------------------------------------------