%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV205+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 02:46:53 PM UTC 2026
% Result : Theorem 1.00s 0.63s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 17 unt; 7 def)
% Number of atoms : 269 ( 169 equ)
% Maximal formula atoms : 40 ( 5 avg)
% Number of connectives : 267 ( 51 ~; 67 |; 133 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 16 con; 0-3 aty)
% Number of variables : 22 ( 21 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( ! [C,D] :
( ( leq(D,n998)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(z_defuse,C,D) = use )
& ! [A,B] :
( ( leq(B,n998)
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(u_defuse,A,B) = use )
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use )
=> ! [E] :
( ( leq(E,n5)
& leq(n0,E) )
=> a_select2(sigma_defuse,E) = use ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( ! [C,D] :
( ( leq(D,n998)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(z_defuse,C,D) = use )
& ! [A,B] :
( ( leq(B,n998)
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(u_defuse,A,B) = use )
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use )
=> ! [E] :
( ( leq(E,n5)
& leq(n0,E) )
=> a_select2(sigma_defuse,E) = use ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f84,axiom,
! [X] :
( ( leq(X,n5)
& leq(n0,X) )
=> ( X = n5
| X = n4
| X = n3
| X = n2
| X = n1
| X = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f251,plain,
( ? [E] :
( a_select2(sigma_defuse,E) != use
& leq(E,n5)
& leq(n0,E) )
& ! [C,D] :
( a_select3(z_defuse,C,D) = use
| ~ leq(D,n998)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(u_defuse,A,B) = use
| ~ leq(B,n998)
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f252,plain,
( a_select2(sigma_defuse,sK23_skl) != use
& leq(sK23_skl,n5)
& leq(n0,sK23_skl)
& ! [C,D] :
( a_select3(z_defuse,C,D) = use
| ~ leq(D,n998)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(u_defuse,A,B) = use
| ~ leq(B,n998)
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& a_select2(xinit_noise_defuse,n5) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n3) = use
& a_select3(u_defuse,n2,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n0,n0) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(rho_defuse,n2) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n0) = use ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl]),skolemize(E,sK23_skl)],[f251]) ).
fof(f256,plain,
a_select2(sigma_defuse,n0) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f257,plain,
a_select2(sigma_defuse,n1) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f258,plain,
a_select2(sigma_defuse,n2) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f259,plain,
a_select2(sigma_defuse,n3) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f260,plain,
a_select2(sigma_defuse,n4) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f261,plain,
a_select2(sigma_defuse,n5) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f282,plain,
leq(n0,sK23_skl),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f283,plain,
leq(sK23_skl,n5),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f284,plain,
a_select2(sigma_defuse,sK23_skl) != use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f315,plain,
! [X] :
( X = n5
| X = n4
| X = n3
| X = n2
| X = n1
| X = n0
| ~ leq(X,n5)
| ~ leq(n0,X) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f316,plain,
! [X0] :
( X0 = n5
| X0 = n4
| X0 = n3
| X0 = n2
| X0 = n1
| X0 = n0
| ~ leq(X0,n5)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f315]) ).
fof(f613,plain,
( sK23_skl = n5
| sK23_skl = n4
| sK23_skl = n3
| sK23_skl = n2
| sK23_skl = n1
| sK23_skl = n0
| ~ leq(sK23_skl,n5) ),
inference(resolution,[status(thm)],[f316,f282]) ).
fof(f620,definition,
( sQ17_spl
<=> leq(sK23_skl,n5) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f622,plain,
( sQ17_spl
| ~ leq(sK23_skl,n5) ),
inference(component_clause,[status(thm)],[f620]) ).
fof(f623,definition,
( sQ18_spl
<=> sK23_skl = n0 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f624,plain,
( ~ sQ18_spl
| sK23_skl = n0 ),
inference(component_clause,[status(thm)],[f623]) ).
fof(f626,definition,
( sQ19_spl
<=> sK23_skl = n1 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f627,plain,
( ~ sQ19_spl
| sK23_skl = n1 ),
inference(component_clause,[status(thm)],[f626]) ).
fof(f629,definition,
( sQ20_spl
<=> sK23_skl = n2 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f630,plain,
( ~ sQ20_spl
| sK23_skl = n2 ),
inference(component_clause,[status(thm)],[f629]) ).
fof(f632,definition,
( sQ21_spl
<=> sK23_skl = n3 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f633,plain,
( ~ sQ21_spl
| sK23_skl = n3 ),
inference(component_clause,[status(thm)],[f632]) ).
fof(f635,definition,
( sQ22_spl
<=> sK23_skl = n4 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( ~ sQ22_spl
| sK23_skl = n4 ),
inference(component_clause,[status(thm)],[f635]) ).
fof(f638,definition,
( sQ23_spl
<=> sK23_skl = n5 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f639,plain,
( ~ sQ23_spl
| sK23_skl = n5 ),
inference(component_clause,[status(thm)],[f638]) ).
fof(f641,plain,
( sQ23_spl
| sQ22_spl
| sQ21_spl
| sQ20_spl
| sQ19_spl
| sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f613,f620,f623,f626,f629,f632,f635,f638]) ).
fof(f983,plain,
( ~ sQ18_spl
| a_select2(sigma_defuse,sK23_skl) = use ),
inference(backward_demodulation,[status(thm)],[f624,f256]) ).
fof(f1024,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f983,f284]) ).
fof(f1025,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f1024]) ).
fof(f1026,plain,
( ~ sQ22_spl
| a_select2(sigma_defuse,sK23_skl) = use ),
inference(backward_demodulation,[status(thm)],[f636,f260]) ).
fof(f1030,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1026,f284]) ).
fof(f1031,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f1030]) ).
fof(f1182,plain,
( ~ sQ21_spl
| a_select2(sigma_defuse,sK23_skl) = use ),
inference(backward_demodulation,[status(thm)],[f633,f259]) ).
fof(f1192,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1182,f284]) ).
fof(f1193,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f1192]) ).
fof(f1197,plain,
( ~ sQ20_spl
| a_select2(sigma_defuse,sK23_skl) = use ),
inference(backward_demodulation,[status(thm)],[f630,f258]) ).
fof(f1210,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1197,f284]) ).
fof(f1211,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f1210]) ).
fof(f1212,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f622,f283]) ).
fof(f1213,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f1212]) ).
fof(f1218,plain,
( ~ sQ23_spl
| a_select2(sigma_defuse,sK23_skl) = use ),
inference(backward_demodulation,[status(thm)],[f639,f261]) ).
fof(f1225,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1218,f284]) ).
fof(f1226,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f1225]) ).
fof(f1242,plain,
( ~ sQ19_spl
| a_select2(sigma_defuse,sK23_skl) = use ),
inference(forward_demodulation,[status(thm)],[f627,f257]) ).
fof(f1243,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1242,f284]) ).
fof(f1244,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f1243]) ).
fof(f1245,plain,
$false,
inference(sat_refutation,[status(thm)],[f641,f1025,f1031,f1193,f1211,f1213,f1226,f1244]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV205+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 08:37:51 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.15/0.39 % Drodi V4.1.1
% 1.00/0.63 % Refutation found
% 1.00/0.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.00/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.00/0.68 % Elapsed time: 0.288348 seconds
% 1.00/0.68 % CPU time: 1.887033 seconds
% 1.00/0.68 % Total memory used: 130.184 MB
% 1.00/0.68 % Net memory used: 127.066 MB
%------------------------------------------------------------------------------