%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM015-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 01:38:31 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 46 ( 5 unt; 5 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 120 ( 57 ~; 58 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : divides(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] :
( divides(X,Z)
| ~ divides(Y,Z)
| ~ divides(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( divides(divisor(X),X)
| prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( less(n1,divisor(X))
| prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( less(divisor(X),X)
| prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( prime(factor_of(X))
| ~ less(X,a)
| ~ less(n1,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( divides(factor_of(X),X)
| ~ less(X,a)
| ~ less(n1,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [X] :
( ~ divides(X,a)
| ~ prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0] : divides(X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X,Z] :
( divides(X,Z)
| ! [Y] :
( ~ divides(Y,Z)
| ~ divides(X,Y) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1,X2] :
( divides(X0,X2)
| ~ divides(X1,X2)
| ~ divides(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0] :
( divides(divisor(X0),X0)
| prime(X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0] :
( less(n1,divisor(X0))
| prime(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
! [X0] :
( less(divisor(X0),X0)
| prime(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0] :
( prime(factor_of(X0))
| ~ less(X0,a)
| ~ less(n1,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
! [X0] :
( divides(factor_of(X0),X0)
| ~ less(X0,a)
| ~ less(n1,X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0] :
( ~ divides(X0,a)
| ~ prime(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
! [X0] :
( ~ divides(factor_of(X0),a)
| ~ less(X0,a)
| ~ less(n1,X0) ),
inference(resolution,[status(thm)],[f16,f19]) ).
fof(f21,plain,
! [X0,X1] :
( ~ divides(X1,a)
| ~ divides(factor_of(X0),X1)
| ~ less(X0,a)
| ~ less(n1,X0) ),
inference(resolution,[status(thm)],[f20,f12]) ).
fof(f35,plain,
! [X0] :
( ~ divides(X0,a)
| less(n1,divisor(X0)) ),
inference(resolution,[status(thm)],[f14,f19]) ).
fof(f36,plain,
! [X0] :
( divides(factor_of(divisor(X0)),divisor(X0))
| ~ less(divisor(X0),a)
| ~ divides(X0,a) ),
inference(resolution,[status(thm)],[f35,f17]) ).
fof(f37,plain,
! [X0,X1] :
( ~ divides(X1,a)
| ~ divides(factor_of(divisor(X0)),X1)
| ~ less(divisor(X0),a)
| ~ divides(X0,a) ),
inference(resolution,[status(thm)],[f35,f21]) ).
fof(f38,plain,
! [X0] :
( prime(a)
| ~ divides(X0,a)
| ~ divides(factor_of(divisor(a)),X0)
| ~ divides(a,a) ),
inference(resolution,[status(thm)],[f37,f15]) ).
fof(f39,definition,
( sQ3_spl
<=> divides(a,a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f41,plain,
( sQ3_spl
| ~ divides(a,a) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,definition,
! [X0] :
( sQ4_spl
<=> ( ~ divides(X0,a)
| ~ divides(factor_of(divisor(a)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f43,plain,
! [X0] :
( ~ sQ4_spl
| ~ divides(X0,a)
| ~ divides(factor_of(divisor(a)),X0) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,definition,
( sQ5_spl
<=> prime(a) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( ~ sQ5_spl
| prime(a) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( sQ5_spl
| sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f38,f39,f42,f45]) ).
fof(f49,plain,
( ~ sQ5_spl
| ~ divides(a,a) ),
inference(resolution,[status(thm)],[f46,f19]) ).
fof(f50,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f10]) ).
fof(f51,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f50]) ).
fof(f52,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f10]) ).
fof(f53,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f52]) ).
fof(f57,definition,
( sQ6_spl
<=> less(divisor(a),a) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ6_spl
| ~ less(divisor(a),a) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f65,plain,
( sQ6_spl
| prime(a) ),
inference(resolution,[status(thm)],[f59,f15]) ).
fof(f66,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f65,f45,f57]) ).
fof(f67,plain,
( ~ sQ4_spl
| ~ less(divisor(a),a)
| ~ divides(a,a)
| ~ divides(divisor(a),a) ),
inference(resolution,[status(thm)],[f43,f36]) ).
fof(f70,definition,
( sQ8_spl
<=> divides(divisor(a),a) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( sQ8_spl
| ~ divides(divisor(a),a) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f67,f70,f39,f57,f42]) ).
fof(f83,plain,
( sQ8_spl
| prime(a) ),
inference(resolution,[status(thm)],[f72,f13]) ).
fof(f85,plain,
( sQ8_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f83,f45,f70]) ).
fof(f86,plain,
$false,
inference(sat_refutation,[status(thm)],[f48,f51,f53,f66,f73,f85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM015-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 02:01:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.043942 seconds
% 0.10/0.43 % CPU time: 0.099903 seconds
% 0.10/0.43 % Total memory used: 12.019 MB
% 0.10/0.43 % Net memory used: 11.664 MB
%------------------------------------------------------------------------------