%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM295+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 01:38:54 PM UTC 2026
% Result : Theorem 0.19s 0.45s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 14 unt; 2 def)
% Number of atoms : 64 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 63 ( 31 ~; 22 |; 6 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 57 ( 53 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
rdn_translate(n0,rdn_pos(rdnn(n0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
rdn_translate(n1,rdn_pos(rdnn(n1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f282,axiom,
! [X,Y,RDN_X,RDN_Y] :
( ( rdn_translate(Y,rdn_pos(RDN_Y))
& rdn_translate(X,rdn_neg(RDN_X)) )
=> less(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f284,axiom,
! [X,Y] :
( less(X,Y)
<=> ( Y != X
& ~ less(Y,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f402,conjecture,
? [X,Y] : less(X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f403,negated_conjecture,
~ ? [X,Y] : less(X,Y),
inference(negated_conjecture,[status(cth)],[f402]) ).
fof(f404,plain,
rdn_translate(n0,rdn_pos(rdnn(n0))),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f405,plain,
rdn_translate(n1,rdn_pos(rdnn(n1))),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f697,plain,
! [X,Y,RDN_X,RDN_Y] :
( less(X,Y)
| ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(pre_NNF_transformation,[status(thm)],[f282]) ).
fof(f698,plain,
! [X,Y] :
( less(X,Y)
| ! [RDN_Y] : ~ rdn_translate(Y,rdn_pos(RDN_Y))
| ! [RDN_X] : ~ rdn_translate(X,rdn_neg(RDN_X)) ),
inference(miniscoping,[status(thm)],[f697]) ).
fof(f699,plain,
! [X0,X1,X2,X3] :
( less(X0,X2)
| ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(cnf_transformation,[status(thm)],[f698]) ).
fof(f703,plain,
! [X,Y] :
( ( Y = X
| less(Y,X)
| less(X,Y) )
& ( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f284]) ).
fof(f704,plain,
( ! [X,Y] :
( Y = X
| less(Y,X)
| less(X,Y) )
& ! [X,Y] :
( ( Y != X
& ~ less(Y,X) )
| ~ less(X,Y) ) ),
inference(miniscoping,[status(thm)],[f703]) ).
fof(f707,plain,
! [X0,X1] :
( X1 = X0
| less(X1,X0)
| less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f704]) ).
fof(f861,plain,
! [X,Y] : ~ less(X,Y),
inference(pre_NNF_transformation,[status(thm)],[f403]) ).
fof(f862,plain,
! [X0,X1] : ~ less(X0,X1),
inference(cnf_transformation,[status(thm)],[f861]) ).
fof(f866,plain,
! [X0,X1] :
( X0 = X1
| less(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f707,f862]) ).
fof(f867,plain,
! [X0,X1] : X0 = X1,
inference(resolution,[status(thm)],[f866,f862]) ).
fof(f868,plain,
! [X0,X1,X2,X3] :
( ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,rdn_neg(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f699,f862]) ).
fof(f869,plain,
! [X0,X1,X2,X3] :
( ~ rdn_translate(X2,rdn_pos(X3))
| ~ rdn_translate(X0,X1) ),
inference(paramodulation,[status(thm)],[f867,f868]) ).
fof(f871,definition,
! [X0,X1] :
( sQ0_spl
<=> ~ rdn_translate(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f872,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ rdn_translate(X0,X1) ),
inference(component_clause,[status(thm)],[f871]) ).
fof(f874,definition,
! [X2,X3] :
( sQ1_spl
<=> ~ rdn_translate(X2,rdn_pos(X3)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f875,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ rdn_translate(X0,rdn_pos(X1)) ),
inference(component_clause,[status(thm)],[f874]) ).
fof(f877,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f869,f871,f874]) ).
fof(f879,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f872]) ).
fof(f880,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f879]) ).
fof(f892,plain,
! [X0] : rdn_translate(n1,X0),
inference(paramodulation,[status(thm)],[f867,f405]) ).
fof(f914,plain,
! [X0,X1] : rdn_translate(X0,X1),
inference(paramodulation,[status(thm)],[f867,f892]) ).
fof(f919,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f875,f914]) ).
fof(f920,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f919]) ).
fof(f921,plain,
$false,
inference(sat_refutation,[status(thm)],[f877,f880,f920]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM295+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.39 % Computer : n016.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Mon Sep 21 02:25:38 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.19/0.44 % 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
% 0.19/0.51 % Elapsed time: 0.087534 seconds
% 0.19/0.51 % CPU time: 0.112419 seconds
% 0.19/0.51 % Total memory used: 6.068 MB
% 0.19/0.51 % Net memory used: 6.061 MB
%------------------------------------------------------------------------------