%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM016-2 : 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 : n017.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 0.12s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 01:53:56 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.37 fof(f1,axiom,(
% 0.12/0.37 (![X]: (~ less(X,X) ))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.37 fof(f2,axiom,(
% 0.12/0.37 (![X,Y]: (( ~ less(X,Y)| ~ less(Y,X) ) ))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.37 fof(f3,axiom,(
% 0.12/0.37 (![X]: (less(X,factorial_plus_one(X)) ))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.37 fof(f4,axiom,(
% 0.12/0.37 (![X,Y]: (( ~ divides(X,factorial_plus_one(Y))| less(Y,X) ) ))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.37 fof(f5,axiom,(
% 0.12/0.37 (![X]: (( prime(X)| divides(prime_divisor(X),X) ) ))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.37 fof(f6,axiom,(
% 0.12/0.37 (![X]: (( prime(X)| prime(prime_divisor(X)) ) ))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.37 fof(f7,axiom,(
% 0.12/0.37 (![X]: (( prime(X)| less(prime_divisor(X),X) ) ))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.37 fof(f8,negated_conjecture,(
% 0.12/0.37 (![X]: (( ~ prime(X)| ~ less(a,X)| less(factorial_plus_one(a),X) ) ))),
% 0.12/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.37 fof(f9,plain,(
% 0.12/0.37 ![X0]: (~less(X0,X0))),
% 0.12/0.37 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.37 fof(f10,plain,(
% 0.12/0.37 ![X0,X1]: (~less(X0,X1)|~less(X1,X0))),
% 0.12/0.37 inference(cnf_transformation,[status(thm)],[f2])).
% 0.12/0.37 fof(f11,plain,(
% 0.12/0.37 ![X0]: (less(X0,factorial_plus_one(X0)))),
% 0.12/0.37 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.37 fof(f12,plain,(
% 0.12/0.37 ![X0,X1]: (~divides(X0,factorial_plus_one(X1))|less(X1,X0))),
% 0.12/0.37 inference(cnf_transformation,[status(thm)],[f4])).
% 0.12/0.37 fof(f13,plain,(
% 0.12/0.37 ![X0]: (prime(X0)|divides(prime_divisor(X0),X0))),
% 0.12/0.37 inference(cnf_transformation,[status(thm)],[f5])).
% 0.12/0.37 fof(f14,plain,(
% 0.12/0.37 ![X0]: (prime(X0)|prime(prime_divisor(X0)))),
% 0.12/0.37 inference(cnf_transformation,[status(thm)],[f6])).
% 0.12/0.37 fof(f15,plain,(
% 0.12/0.37 ![X0]: (prime(X0)|less(prime_divisor(X0),X0))),
% 0.12/0.37 inference(cnf_transformation,[status(thm)],[f7])).
% 0.12/0.37 fof(f16,plain,(
% 0.12/0.37 ![X0]: (~prime(X0)|~less(a,X0)|less(factorial_plus_one(a),X0))),
% 0.12/0.37 inference(cnf_transformation,[status(thm)],[f8])).
% 0.12/0.37 fof(f18,plain,(
% 0.12/0.37 ![X0]: (prime(X0)|~less(a,prime_divisor(X0))|less(factorial_plus_one(a),prime_divisor(X0)))),
% 0.12/0.37 inference(resolution,[status(thm)],[f14,f16])).
% 0.12/0.37 fof(f19,plain,(
% 0.12/0.37 ![X0]: (prime(X0)|~less(X0,prime_divisor(X0)))),
% 0.12/0.37 inference(resolution,[status(thm)],[f15,f10])).
% 0.12/0.37 fof(f20,plain,(
% 0.12/0.37 ![X0]: (less(X0,prime_divisor(factorial_plus_one(X0)))|prime(factorial_plus_one(X0)))),
% 0.12/0.37 inference(resolution,[status(thm)],[f12,f13])).
% 0.12/0.37 fof(f21,plain,(
% 0.12/0.37 prime(factorial_plus_one(a))|prime(factorial_plus_one(a))|less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))),
% 0.12/0.37 inference(resolution,[status(thm)],[f20,f18])).
% 0.12/0.37 fof(f23,definition,(
% 0.12/0.37 sQ0_spl <=> (prime(factorial_plus_one(a)))),
% 0.12/0.37 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.37 fof(f24,plain,(
% 0.12/0.37 prime(factorial_plus_one(a))|~sQ0_spl),
% 0.12/0.37 inference(component_clause,[status(thm)],[f23])).
% 0.12/0.37 fof(f26,definition,(
% 0.12/0.37 sQ1_spl <=> (less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))))),
% 0.12/0.37 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.37 fof(f27,plain,(
% 0.12/0.37 less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))|~sQ1_spl),
% 0.12/0.37 inference(component_clause,[status(thm)],[f26])).
% 0.12/0.37 fof(f29,plain,(
% 0.12/0.37 sQ0_spl|sQ1_spl),
% 0.12/0.37 inference(split_clause,[status(thm)],[f21,f23,f26])).
% 0.12/0.37 fof(f30,plain,(
% 0.12/0.37 ~less(a,factorial_plus_one(a))|less(factorial_plus_one(a),factorial_plus_one(a))|~sQ0_spl),
% 0.12/0.37 inference(resolution,[status(thm)],[f24,f16])).
% 0.12/0.37 fof(f31,definition,(
% 0.12/0.37 sQ2_spl <=> (less(a,factorial_plus_one(a)))),
% 0.12/0.37 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.37 fof(f33,plain,(
% 0.12/0.37 ~less(a,factorial_plus_one(a))|sQ2_spl),
% 0.12/0.37 inference(component_clause,[status(thm)],[f31])).
% 0.12/0.37 fof(f34,definition,(
% 0.12/0.37 sQ3_spl <=> (less(factorial_plus_one(a),factorial_plus_one(a)))),
% 0.12/0.37 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.12/0.37 fof(f35,plain,(
% 0.12/0.37 less(factorial_plus_one(a),factorial_plus_one(a))|~sQ3_spl),
% 0.12/0.37 inference(component_clause,[status(thm)],[f34])).
% 0.12/0.37 fof(f37,plain,(
% 0.12/0.37 ~sQ2_spl|sQ3_spl|~sQ0_spl),
% 0.12/0.37 inference(split_clause,[status(thm)],[f30,f31,f34,f23])).
% 0.12/0.37 fof(f38,plain,(
% 0.12/0.37 $false|~sQ3_spl),
% 0.12/0.37 inference(forward_subsumption_resolution,[status(thm)],[f35,f9])).
% 0.12/0.37 fof(f39,plain,(
% 0.12/0.37 ~sQ3_spl),
% 0.12/0.37 inference(contradiction_clause,[status(thm)],[f38])).
% 0.12/0.37 fof(f40,plain,(
% 0.12/0.37 $false|sQ2_spl),
% 0.12/0.37 inference(forward_subsumption_resolution,[status(thm)],[f33,f11])).
% 0.12/0.37 fof(f41,plain,(
% 0.12/0.37 sQ2_spl),
% 0.12/0.37 inference(contradiction_clause,[status(thm)],[f40])).
% 0.12/0.37 fof(f42,plain,(
% 0.12/0.37 prime(factorial_plus_one(a))|~sQ1_spl),
% 0.12/0.37 inference(resolution,[status(thm)],[f27,f19])).
% 0.12/0.37 fof(f44,plain,(
% 0.12/0.37 sQ0_spl|~sQ1_spl),
% 0.12/0.37 inference(split_clause,[status(thm)],[f42,f23,f26])).
% 0.12/0.37 fof(f45,plain,(
% 0.12/0.37 $false),
% 0.12/0.37 inference(sat_refutation,[status(thm)],[f29,f37,f39,f41,f44])).
% 0.12/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.39 % Elapsed time: 0.036690 seconds
% 0.12/0.39 % CPU time: 0.101455 seconds
% 0.12/0.39 % Total memory used: 14.487 MB
% 0.12/0.39 % Net memory used: 14.028 MB
%------------------------------------------------------------------------------