%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 01:42:09 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 01:59:32 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.47 fof(f1,axiom,(
% 0.18/0.47 (![X]: (~ less(X,X) ))),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f5,axiom,(
% 0.18/0.47 (![X,Y]: (( ~ divides(X,Y)| ~ less(Y,X) ) ))),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f6,axiom,(
% 0.18/0.47 (![X]: (less(X,factorial_plus_one(X)) ))),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f7,axiom,(
% 0.18/0.47 (![X,Y]: (( ~ divides(X,factorial_plus_one(Y))| less(Y,X) ) ))),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f8,axiom,(
% 0.18/0.47 (![X]: (( prime(X)| divides(prime_divisor(X),X) ) ))),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f9,axiom,(
% 0.18/0.47 (![X]: (( prime(X)| prime(prime_divisor(X)) ) ))),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f12,negated_conjecture,(
% 0.18/0.47 (![X]: (( ~ prime(X)| ~ less(a,X)| less(factorial_plus_one(a),X) ) ))),
% 0.18/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.18/0.47 fof(f13,plain,(
% 0.18/0.47 ![X0]: (~less(X0,X0))),
% 0.18/0.47 inference(cnf_transformation,[status(thm)],[f1])).
% 0.18/0.47 fof(f18,plain,(
% 0.18/0.47 ![X0,X1]: (~divides(X0,X1)|~less(X1,X0))),
% 0.18/0.47 inference(cnf_transformation,[status(thm)],[f5])).
% 0.18/0.47 fof(f19,plain,(
% 0.18/0.47 ![X0]: (less(X0,factorial_plus_one(X0)))),
% 0.18/0.47 inference(cnf_transformation,[status(thm)],[f6])).
% 0.18/0.47 fof(f20,plain,(
% 0.18/0.47 ![X0,X1]: (~divides(X0,factorial_plus_one(X1))|less(X1,X0))),
% 0.18/0.47 inference(cnf_transformation,[status(thm)],[f7])).
% 0.18/0.47 fof(f21,plain,(
% 0.18/0.47 ![X0]: (prime(X0)|divides(prime_divisor(X0),X0))),
% 0.18/0.47 inference(cnf_transformation,[status(thm)],[f8])).
% 0.18/0.47 fof(f22,plain,(
% 0.18/0.47 ![X0]: (prime(X0)|prime(prime_divisor(X0)))),
% 0.18/0.47 inference(cnf_transformation,[status(thm)],[f9])).
% 0.18/0.47 fof(f25,plain,(
% 0.18/0.47 ![X0]: (~prime(X0)|~less(a,X0)|less(factorial_plus_one(a),X0))),
% 0.18/0.47 inference(cnf_transformation,[status(thm)],[f12])).
% 0.18/0.47 fof(f26,plain,(
% 0.18/0.47 ~prime(factorial_plus_one(a))|less(factorial_plus_one(a),factorial_plus_one(a))),
% 0.18/0.47 inference(resolution,[status(thm)],[f19,f25])).
% 0.18/0.47 fof(f28,definition,(
% 0.18/0.47 sQ0_spl <=> (prime(factorial_plus_one(a)))),
% 0.18/0.47 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.18/0.47 fof(f30,plain,(
% 0.18/0.47 ~prime(factorial_plus_one(a))|sQ0_spl),
% 0.18/0.47 inference(component_clause,[status(thm)],[f28])).
% 0.18/0.47 fof(f31,definition,(
% 0.18/0.47 sQ1_spl <=> (less(factorial_plus_one(a),factorial_plus_one(a)))),
% 0.18/0.47 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.18/0.47 fof(f32,plain,(
% 0.18/0.47 less(factorial_plus_one(a),factorial_plus_one(a))|~sQ1_spl),
% 0.18/0.47 inference(component_clause,[status(thm)],[f31])).
% 0.18/0.47 fof(f34,plain,(
% 0.18/0.47 ~sQ0_spl|sQ1_spl),
% 0.18/0.47 inference(split_clause,[status(thm)],[f26,f28,f31])).
% 0.18/0.47 fof(f38,plain,(
% 0.18/0.47 ![X0]: (prime(factorial_plus_one(X0))|less(X0,prime_divisor(factorial_plus_one(X0))))),
% 0.18/0.47 inference(resolution,[status(thm)],[f21,f20])).
% 0.18/0.47 fof(f40,plain,(
% 0.18/0.47 ![X0]: (prime(X0)|~less(X0,prime_divisor(X0)))),
% 0.18/0.47 inference(resolution,[status(thm)],[f21,f18])).
% 0.18/0.47 fof(f41,plain,(
% 0.18/0.47 prime(factorial_plus_one(a))|~prime(prime_divisor(factorial_plus_one(a)))|less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))),
% 0.18/0.47 inference(resolution,[status(thm)],[f38,f25])).
% 0.18/0.47 fof(f43,definition,(
% 0.18/0.47 sQ2_spl <=> (prime(prime_divisor(factorial_plus_one(a))))),
% 0.18/0.47 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.18/0.47 fof(f45,plain,(
% 0.18/0.47 ~prime(prime_divisor(factorial_plus_one(a)))|sQ2_spl),
% 0.18/0.47 inference(component_clause,[status(thm)],[f43])).
% 0.18/0.47 fof(f46,definition,(
% 0.18/0.47 sQ3_spl <=> (less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))))),
% 0.18/0.47 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.18/0.47 fof(f47,plain,(
% 0.18/0.47 less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))|~sQ3_spl),
% 0.18/0.47 inference(component_clause,[status(thm)],[f46])).
% 0.18/0.47 fof(f49,plain,(
% 0.18/0.47 sQ0_spl|~sQ2_spl|sQ3_spl),
% 0.18/0.47 inference(split_clause,[status(thm)],[f41,f28,f43,f46])).
% 0.18/0.47 fof(f50,plain,(
% 0.18/0.47 $false|~sQ1_spl),
% 0.18/0.47 inference(forward_subsumption_resolution,[status(thm)],[f32,f13])).
% 0.18/0.47 fof(f51,plain,(
% 0.18/0.47 ~sQ1_spl),
% 0.18/0.47 inference(contradiction_clause,[status(thm)],[f50])).
% 0.18/0.47 fof(f52,plain,(
% 0.18/0.47 prime(factorial_plus_one(a))|sQ2_spl),
% 0.18/0.47 inference(resolution,[status(thm)],[f45,f22])).
% 0.18/0.47 fof(f53,plain,(
% 0.18/0.47 $false|sQ0_spl|sQ2_spl),
% 0.18/0.47 inference(forward_subsumption_resolution,[status(thm)],[f52,f30])).
% 0.18/0.47 fof(f54,plain,(
% 0.18/0.47 sQ0_spl|sQ2_spl),
% 0.18/0.47 inference(contradiction_clause,[status(thm)],[f53])).
% 0.18/0.47 fof(f58,plain,(
% 0.18/0.47 prime(factorial_plus_one(a))|~sQ3_spl),
% 0.18/0.47 inference(resolution,[status(thm)],[f47,f40])).
% 0.18/0.47 fof(f60,plain,(
% 0.18/0.47 $false|sQ0_spl|~sQ3_spl),
% 0.18/0.47 inference(forward_subsumption_resolution,[status(thm)],[f58,f30])).
% 0.18/0.47 fof(f61,plain,(
% 0.18/0.47 sQ0_spl|~sQ3_spl),
% 0.18/0.47 inference(contradiction_clause,[status(thm)],[f60])).
% 0.18/0.47 fof(f62,plain,(
% 0.18/0.47 $false),
% 0.18/0.47 inference(sat_refutation,[status(thm)],[f34,f49,f51,f54,f61])).
% 0.18/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.18/0.50 % Elapsed time: 0.054125 seconds
% 0.18/0.50 % CPU time: 0.136323 seconds
% 0.18/0.50 % Total memory used: 16.647 MB
% 0.18/0.50 % Net memory used: 16.201 MB
%------------------------------------------------------------------------------