%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 01:38:31 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 12 unt; 1 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 44 ( 20 ~; 23 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(X,X,square(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( divides(X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z,U] :
( divides(X,Z)
| divides(X,Y)
| ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,hypothesis,
prime(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,hypothesis,
product(a,square(c),square(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ divides(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [X0] : product(X0,X0,square(X0)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X,Z] :
( divides(X,Z)
| ! [Y] : ~ product(X,Y,Z) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1,X2] :
( divides(X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X,Z] :
( divides(X,Z)
| ! [Y] :
( divides(X,Y)
| ! [U] :
( ~ divides(X,U)
| ~ product(Y,Z,U)
| ~ prime(X) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( divides(X0,X2)
| divides(X0,X1)
| ~ divides(X0,X3)
| ~ product(X1,X2,X3)
| ~ prime(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
prime(a),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
product(a,square(c),square(b)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
~ divides(a,b),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f22,plain,
divides(a,square(b)),
inference(resolution,[status(thm)],[f15,f11]) ).
fof(f23,plain,
! [X0,X1,X2] :
( divides(a,X1)
| divides(a,X0)
| ~ divides(a,X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f13,f14]) ).
fof(f24,plain,
! [X0,X1] :
( divides(a,X1)
| divides(a,X0)
| ~ product(X0,X1,square(b)) ),
inference(resolution,[status(thm)],[f23,f22]) ).
fof(f27,plain,
( divides(a,b)
| divides(a,b) ),
inference(resolution,[status(thm)],[f24,f8]) ).
fof(f36,definition,
( sQ2_spl
<=> divides(a,b) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( ~ sQ2_spl
| divides(a,b) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f27,f36]) ).
fof(f40,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f37,f16]) ).
fof(f41,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f40]) ).
fof(f42,plain,
$false,
inference(sat_refutation,[status(thm)],[f39,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 01:59:18 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.042059 seconds
% 0.13/0.40 % CPU time: 0.108354 seconds
% 0.13/0.40 % Total memory used: 16.584 MB
% 0.13/0.40 % Net memory used: 16.034 MB
%------------------------------------------------------------------------------