%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:38:32 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 7 unt; 4 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 26 ~; 31 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ less(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( ~ less(Y,X)
| ~ divides(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : less(X,factorial_plus_one(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( less(Y,X)
| ~ divides(X,factorial_plus_one(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( divides(prime_divisor(X),X)
| prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( prime(prime_divisor(X))
| prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
! [X] :
( less(factorial_plus_one(a),X)
| ~ less(a,X)
| ~ prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0] : ~ less(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1] :
( ~ less(X1,X0)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
! [X0] : less(X0,factorial_plus_one(X0)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
! [X0,X1] :
( less(X1,X0)
| ~ divides(X0,factorial_plus_one(X1)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,plain,
! [X0] :
( divides(prime_divisor(X0),X0)
| prime(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
! [X0] :
( prime(prime_divisor(X0))
| prime(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0] :
( less(factorial_plus_one(a),X0)
| ~ less(a,X0)
| ~ prime(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f37,plain,
! [X0] :
( less(factorial_plus_one(a),prime_divisor(X0))
| ~ less(a,prime_divisor(X0))
| prime(X0) ),
inference(resolution,[status(thm)],[f22,f25]) ).
fof(f39,plain,
! [X0] :
( less(X0,prime_divisor(factorial_plus_one(X0)))
| prime(factorial_plus_one(X0)) ),
inference(resolution,[status(thm)],[f21,f20]) ).
fof(f41,plain,
! [X0] :
( ~ less(X0,prime_divisor(X0))
| prime(X0) ),
inference(resolution,[status(thm)],[f21,f18]) ).
fof(f43,plain,
( less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| prime(factorial_plus_one(a))
| prime(factorial_plus_one(a)) ),
inference(resolution,[status(thm)],[f39,f37]) ).
fof(f45,definition,
( sQ2_spl
<=> prime(factorial_plus_one(a)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( ~ sQ2_spl
| prime(factorial_plus_one(a)) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,definition,
( sQ3_spl
<=> less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( ~ sQ3_spl
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f43,f45,f48]) ).
fof(f52,plain,
( ~ sQ2_spl
| less(factorial_plus_one(a),factorial_plus_one(a))
| ~ less(a,factorial_plus_one(a)) ),
inference(resolution,[status(thm)],[f46,f25]) ).
fof(f53,definition,
( sQ4_spl
<=> less(a,factorial_plus_one(a)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ4_spl
| ~ less(a,factorial_plus_one(a)) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ5_spl
<=> less(factorial_plus_one(a),factorial_plus_one(a)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ5_spl
| less(factorial_plus_one(a),factorial_plus_one(a)) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( ~ sQ2_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f52,f53,f56,f45]) ).
fof(f60,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f57,f13]) ).
fof(f61,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f62,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f19]) ).
fof(f63,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f62]) ).
fof(f64,plain,
( ~ sQ3_spl
| prime(factorial_plus_one(a)) ),
inference(resolution,[status(thm)],[f49,f41]) ).
fof(f66,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f64,f45,f48]) ).
fof(f67,plain,
$false,
inference(sat_refutation,[status(thm)],[f51,f59,f61,f63,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n007.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 01:56:35 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.046604 seconds
% 0.13/0.40 % CPU time: 0.124224 seconds
% 0.13/0.40 % Total memory used: 16.646 MB
% 0.13/0.40 % Net memory used: 16.165 MB
%------------------------------------------------------------------------------