%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 7 unt; 4 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 63 ( 26 ~; 33 |; 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 : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ less(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( ~ less(Y,X)
| ~ less(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : less(X,factorial_plus_one(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( less(Y,X)
| ~ divides(X,factorial_plus_one(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( divides(prime_divisor(X),X)
| prime(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( prime(prime_divisor(X))
| prime(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( less(prime_divisor(X),X)
| prime(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
! [X] :
( less(factorial_plus_one(a),X)
| ~ less(a,X)
| ~ prime(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] : ~ less(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1] :
( ~ less(X1,X0)
| ~ less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0] : less(X0,factorial_plus_one(X0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] :
( less(X1,X0)
| ~ divides(X0,factorial_plus_one(X1)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0] :
( divides(prime_divisor(X0),X0)
| prime(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0] :
( prime(prime_divisor(X0))
| prime(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
! [X0] :
( less(prime_divisor(X0),X0)
| prime(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
! [X0] :
( less(factorial_plus_one(a),X0)
| ~ less(a,X0)
| ~ prime(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f18,plain,
! [X0] :
( less(factorial_plus_one(a),prime_divisor(X0))
| ~ less(a,prime_divisor(X0))
| prime(X0) ),
inference(resolution,[status(thm)],[f14,f16]) ).
fof(f19,plain,
! [X0] :
( ~ less(X0,prime_divisor(X0))
| prime(X0) ),
inference(resolution,[status(thm)],[f15,f10]) ).
fof(f20,plain,
! [X0] :
( prime(factorial_plus_one(X0))
| less(X0,prime_divisor(factorial_plus_one(X0))) ),
inference(resolution,[status(thm)],[f12,f13]) ).
fof(f21,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)],[f20,f18]) ).
fof(f23,definition,
( sQ0_spl
<=> prime(factorial_plus_one(a)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f24,plain,
( ~ sQ0_spl
| prime(factorial_plus_one(a)) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f26,definition,
( sQ1_spl
<=> less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( ~ sQ1_spl
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
inference(component_clause,[status(thm)],[f26]) ).
fof(f29,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f21,f23,f26]) ).
fof(f30,plain,
( ~ sQ0_spl
| less(factorial_plus_one(a),factorial_plus_one(a))
| ~ less(a,factorial_plus_one(a)) ),
inference(resolution,[status(thm)],[f24,f16]) ).
fof(f31,definition,
( sQ2_spl
<=> less(a,factorial_plus_one(a)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( sQ2_spl
| ~ less(a,factorial_plus_one(a)) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,definition,
( sQ3_spl
<=> less(factorial_plus_one(a),factorial_plus_one(a)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( ~ sQ3_spl
| less(factorial_plus_one(a),factorial_plus_one(a)) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,plain,
( ~ sQ0_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f30,f31,f34,f23]) ).
fof(f38,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f35,f9]) ).
fof(f39,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f38]) ).
fof(f40,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f11]) ).
fof(f41,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f40]) ).
fof(f42,plain,
( ~ sQ1_spl
| prime(factorial_plus_one(a)) ),
inference(resolution,[status(thm)],[f27,f19]) ).
fof(f44,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f23,f26]) ).
fof(f45,plain,
$false,
inference(sat_refutation,[status(thm)],[f29,f37,f39,f41,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM016-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n008.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 01:59:24 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.08/0.37 % Refutation found
% 0.08/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.042431 seconds
% 0.12/0.41 % CPU time: 0.117627 seconds
% 0.12/0.41 % Total memory used: 16.560 MB
% 0.12/0.41 % Net memory used: 16.006 MB
%------------------------------------------------------------------------------