%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUN073+1 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.19s 0.45s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 9 unt; 2 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 43 ~; 35 |; 10 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 39 ( 34 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X21,X22] :
( id(X22,X21)
| ~ id(X21,X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X3,X10] :
( id(X3,X10)
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( ~ r2(X3,Y13)
| ~ id(Y13,Y12) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [Y1] :
( ! [Y3] :
( ~ r2(Y3,Y1)
| ! [Y5] :
( ~ r2(Y5,Y3)
| ~ r1(Y5) ) )
| ! [Y2] :
( ~ id(Y2,Y1)
| ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [Y1] :
( ! [Y3] :
( ~ r2(Y3,Y1)
| ! [Y5] :
( ~ r2(Y5,Y3)
| ~ r1(Y5) ) )
| ! [Y2] :
( ~ id(Y2,Y1)
| ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f42,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( id(X2,X3)
| ~ r2(X3,X1)
| ~ r2(X2,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f89,plain,
! [Y10] :
( ! [X7] : ~ r2(X7,Y10)
| ! [Y20] :
( ~ r1(Y20)
| ~ id(Y20,Y10) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ r2(X2,X1)
| ~ r1(X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
? [Y1] :
( ? [Y3] :
( r2(Y3,Y1)
& ? [Y5] :
( r2(Y5,Y3)
& r1(Y5) ) )
& ? [Y2] :
( id(Y2,Y1)
& ? [Y4] :
( r2(Y4,Y2)
& r1(Y4) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f92,plain,
( r2(sK23_skl,sK20_skl)
& r2(sK24_skl,sK23_skl)
& r1(sK24_skl)
& id(sK21_skl,sK20_skl)
& r2(sK22_skl,sK21_skl)
& r1(sK22_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl,sK24_skl]),skolemize(Y1,sK20_skl),skolemize(Y2,sK21_skl),skolemize(Y4,sK22_skl),skolemize(Y3,sK23_skl),skolemize(Y5,sK24_skl)],[f91]) ).
fof(f93,plain,
r1(sK22_skl),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,plain,
r2(sK22_skl,sK21_skl),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f95,plain,
id(sK21_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f97,plain,
r2(sK24_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f98,plain,
r2(sK23_skl,sK20_skl),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f144,plain,
id(sK20_skl,sK21_skl),
inference(resolution,[status(thm)],[f42,f95]) ).
fof(f148,plain,
! [X0] :
( ~ r1(X0)
| ~ id(X0,sK23_skl) ),
inference(resolution,[status(thm)],[f90,f97]) ).
fof(f163,plain,
! [X0,X1] :
( id(sK23_skl,X1)
| ~ r2(X1,X0)
| ~ id(sK20_skl,X0) ),
inference(resolution,[status(thm)],[f73,f98]) ).
fof(f195,plain,
( id(sK23_skl,sK22_skl)
| ~ id(sK20_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f163,f94]) ).
fof(f204,definition,
( sQ7_spl
<=> id(sK20_skl,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( sQ7_spl
| ~ id(sK20_skl,sK21_skl) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,definition,
( sQ8_spl
<=> id(sK23_skl,sK22_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( ~ sQ8_spl
| id(sK23_skl,sK22_skl) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f195,f204,f207]) ).
fof(f211,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f144]) ).
fof(f212,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f221,plain,
( ~ sQ8_spl
| id(sK22_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f208,f42]) ).
fof(f224,plain,
( ~ sQ8_spl
| ~ r1(sK22_skl) ),
inference(resolution,[status(thm)],[f221,f148]) ).
fof(f227,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f224,f93]) ).
fof(f228,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f229,plain,
$false,
inference(sat_refutation,[status(thm)],[f210,f212,f228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN073+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n014.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Mon Sep 21 03:24:49 UTC 2026
% 0.19/0.41 % CPUTime :
% 0.19/0.42 % Drodi V4.1.1
% 0.19/0.45 % Refutation found
% 0.19/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.48 % Elapsed time: 0.059801 seconds
% 0.19/0.48 % CPU time: 0.223364 seconds
% 0.19/0.48 % Total memory used: 14.404 MB
% 0.19/0.48 % Net memory used: 14.232 MB
%------------------------------------------------------------------------------