%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN067+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 01:57:11 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 35 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 36 ( 17 ~; 9 |; 10 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% Number of variables : 33 ( 26 !; 7 ?)
% 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
? [Y1] :
! [Y2] :
( Y1 != Y2
| ~ r1(Y2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ? [Y1] :
! [Y2] :
( Y1 != Y2
| ~ r1(Y2) ),
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(f38,plain,
! [X0,X1] : r2(sK7_skl(X0,X1),sK4_skl(X0,X1)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f62,plain,
! [Y10] :
( ! [X7] : ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ r2(X2,X1)
| X0 != X1
| ~ r1(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [Y1] :
? [Y2] :
( Y1 = Y2
& r1(Y2) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f65,plain,
! [Y1] :
( Y1 = sK20_skl(Y1)
& r1(sK20_skl(Y1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl]),skolemize(Y2,sK20_skl(Y1))],[f64]) ).
fof(f66,plain,
! [X0] : r1(sK20_skl(X0)),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0] : X0 = sK20_skl(X0),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f98,plain,
! [X0,X1] :
( ~ r2(X1,X0)
| ~ r1(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f99,plain,
! [X0] : r1(X0),
inference(backward_demodulation,[status(thm)],[f67,f66]) ).
fof(f107,plain,
! [X0,X1] : ~ r2(X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[f98,f99]) ).
fof(f111,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f38,f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN067+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n013.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 03:23:36 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.044854 seconds
% 0.12/0.40 % CPU time: 0.131885 seconds
% 0.12/0.40 % Total memory used: 86.301 MB
% 0.12/0.40 % Net memory used: 86.216 MB
%------------------------------------------------------------------------------