%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN069+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 01:57:12 PM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 4 unt; 0 def)
% Number of atoms : 36 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 33 ( 10 ~; 5 |; 18 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 0 con; 1-2 aty)
% Number of variables : 28 ( 17 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
? [Y1] :
( ? [Y2] :
( r2(Y2,Y1)
& r1(Y2) )
& Y1 = Y1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1] :
( ? [Y2] :
( r2(Y2,Y1)
& r1(Y2) )
& Y1 = Y1 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f34,plain,
! [X1,X8] :
( r3(X1,X8,sK7_skl(X8,X1))
& r2(sK7_skl(X8,X1),sK4_skl(X8,X1))
& sK5_skl(X8,X1) = sK4_skl(X8,X1)
& r3(X1,sK6_skl(X8,X1),sK5_skl(X8,X1))
& r2(X8,sK6_skl(X8,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(Y4,sK4_skl(X8,X1)),skolemize(Y5,sK5_skl(X8,X1)),skolemize(Y15,sK6_skl(X8,X1)),skolemize(Y7,sK7_skl(X8,X1))],[f5]) ).
fof(f35,plain,
! [X0,X1] : r2(X0,sK6_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f51,plain,
! [X5] :
( sK14_skl(X5) = sK16_skl(X5)
& r1(sK16_skl(X5))
& r4(X5,sK15_skl(X5),sK14_skl(X5))
& r1(sK15_skl(X5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl]),skolemize(Y8,sK14_skl(X5)),skolemize(Y17,sK15_skl(X5)),skolemize(Y18,sK16_skl(X5))],[f9]) ).
fof(f54,plain,
! [X0] : r1(sK16_skl(X0)),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f64,plain,
! [Y1] :
( ! [Y2] :
( ~ r2(Y2,Y1)
| ~ r1(Y2) )
| Y1 != Y1 ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f65,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| ~ r1(X1)
| X0 != X0 ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f93,plain,
! [X0,X1] :
( ~ r2(X0,X1)
| ~ r1(X0) ),
inference(trivial_equality_resolution,[status(thm)],[f65]) ).
fof(f107,plain,
! [X0,X1] : ~ r2(sK16_skl(X0),X1),
inference(resolution,[status(thm)],[f54,f93]) ).
fof(f108,plain,
$false,
inference(resolution,[status(thm)],[f35,f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN069+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n010.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 03:24:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.045469 seconds
% 0.13/0.40 % CPU time: 0.123900 seconds
% 0.13/0.40 % Total memory used: 63.924 MB
% 0.13/0.40 % Net memory used: 63.858 MB
%------------------------------------------------------------------------------