%------------------------------------------------------------------------------
% File     : PyRes---1.3
% Problem  : NUM016-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %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  : 600s
% DateTime : Mon Jul 18 13:33:56 EDT 2022

% Result   : Unsatisfiable 0.17s 0.48s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named input)

% Comments : 
%------------------------------------------------------------------------------
cnf(nothing_is_less_than_itself,axiom,
    ~ less(X2,X2),
    input ).

cnf(a_prime_is_less_than_the_next_one,axiom,
    less(X3,factorial_plus_one(X3)),
    input ).

cnf(prove_there_is_another_prime,negated_conjecture,
    ( ~ prime(X15)
    | ~ less(a,X15)
    | less(factorial_plus_one(a),X15) ),
    input ).

cnf(c4,plain,
    ( ~ prime(factorial_plus_one(a))
    | less(factorial_plus_one(a),factorial_plus_one(a)) ),
    inference(resolution,status(thm),[prove_there_is_another_prime,a_prime_is_less_than_the_next_one]) ).

cnf(numbers_are_different,axiom,
    ( ~ less(X5,X4)
    | ~ less(X4,X5) ),
    input ).

cnf(smaller_prime_divisors,axiom,
    ( prime(X11)
    | less(prime_divisor(X11),X11) ),
    input ).

cnf(c2,plain,
    ( prime(X12)
    | ~ less(X12,prime_divisor(X12)) ),
    inference(resolution,status(thm),[smaller_prime_divisors,numbers_are_different]) ).

cnf(prime_divsiors,axiom,
    ( prime(X7)
    | prime(prime_divisor(X7)) ),
    input ).

cnf(divisor_is_smaller,axiom,
    ( ~ divides(X9,factorial_plus_one(X8))
    | less(X8,X9) ),
    input ).

cnf(division_by_prime_divisor,axiom,
    ( prime(X10)
    | divides(prime_divisor(X10),X10) ),
    input ).

cnf(c1,plain,
    ( prime(factorial_plus_one(X13))
    | less(X13,prime_divisor(factorial_plus_one(X13))) ),
    inference(resolution,status(thm),[division_by_prime_divisor,divisor_is_smaller]) ).

cnf(c5,plain,
    ( ~ prime(prime_divisor(factorial_plus_one(a)))
    | less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
    | prime(factorial_plus_one(a)) ),
    inference(resolution,status(thm),[prove_there_is_another_prime,c1]) ).

cnf(c17,plain,
    ( less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
    | prime(factorial_plus_one(a)) ),
    inference(resolution,status(thm),[c5,prime_divsiors]) ).

cnf(c23,plain,
    prime(factorial_plus_one(a)),
    inference(resolution,status(thm),[c17,c2]) ).

cnf(c26,plain,
    less(factorial_plus_one(a),factorial_plus_one(a)),
    inference(resolution,status(thm),[c23,c4]) ).

cnf(c28,plain,
    $false,
    inference(resolution,status(thm),[c26,nothing_is_less_than_itself]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : NUM016-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.11  % Command  : pyres-fof.py -tifbsVp -nlargest -HPickGiven5 %s
% 0.11/0.32  % Computer : n029.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Wed Jul  6 16:35:58 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.17/0.48  # Version:  1.3
% 0.17/0.48  # SZS status Unsatisfiable
% 0.17/0.48  # SZS output start CNFRefutation
% See solution above
% 0.17/0.48  
% 0.17/0.48  # Initial clauses    : 8
% 0.17/0.48  # Processed clauses  : 22
% 0.17/0.48  # Factors computed   : 0
% 0.17/0.48  # Resolvents computed: 29
% 0.17/0.48  # Tautologies deleted: 0
% 0.17/0.48  # Forward subsumed   : 2
% 0.17/0.48  # Backward subsumed  : 5
% 0.17/0.48  # -------- CPU Time ---------
% 0.17/0.48  # User time          : 0.136 s
% 0.17/0.48  # System time        : 0.014 s
% 0.17/0.48  # Total time         : 0.150 s
%------------------------------------------------------------------------------