%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV204+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 02:46:52 PM UTC 2026
% Result : Theorem 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 11 unt; 4 def)
% Number of atoms : 230 ( 148 equ)
% Maximal formula atoms : 40 ( 6 avg)
% Number of connectives : 240 ( 48 ~; 46 |; 133 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 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,n2)
& leq(n0,E) )
=> a_select2(rho_defuse,E) = use ) ),
file('/export/starexec/sandbox2/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,n2)
& leq(n0,E) )
=> a_select2(rho_defuse,E) = use ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f87,axiom,
! [X] :
( ( leq(X,n2)
& leq(n0,X) )
=> ( X = n2
| X = n1
| X = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f251,plain,
( ? [E] :
( a_select2(rho_defuse,E) != use
& leq(E,n2)
& 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(rho_defuse,sK23_skl) != use
& leq(sK23_skl,n2)
& 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(f253,plain,
a_select2(rho_defuse,n0) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f254,plain,
a_select2(rho_defuse,n1) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f255,plain,
a_select2(rho_defuse,n2) = 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,n2),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f284,plain,
a_select2(rho_defuse,sK23_skl) != use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f321,plain,
! [X] :
( X = n2
| X = n1
| X = n0
| ~ leq(X,n2)
| ~ leq(n0,X) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f322,plain,
! [X0] :
( X0 = n2
| X0 = n1
| X0 = n0
| ~ leq(X0,n2)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f321]) ).
fof(f427,plain,
( sK23_skl = n2
| sK23_skl = n1
| sK23_skl = n0
| ~ leq(sK23_skl,n2) ),
inference(resolution,[status(thm)],[f322,f282]) ).
fof(f431,definition,
( sQ3_spl
<=> leq(sK23_skl,n2) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( sQ3_spl
| ~ leq(sK23_skl,n2) ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f434,definition,
( sQ4_spl
<=> sK23_skl = n0 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ4_spl
| sK23_skl = n0 ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,definition,
( sQ5_spl
<=> sK23_skl = n1 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( ~ sQ5_spl
| sK23_skl = n1 ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,definition,
( sQ6_spl
<=> sK23_skl = n2 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( ~ sQ6_spl
| sK23_skl = n2 ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( sQ6_spl
| sQ5_spl
| sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f427,f431,f434,f437,f440]) ).
fof(f501,plain,
( ~ sQ6_spl
| a_select2(rho_defuse,n2) != use ),
inference(backward_demodulation,[status(thm)],[f441,f284]) ).
fof(f517,plain,
( ~ sQ6_spl
| use != use ),
inference(forward_demodulation,[status(thm)],[f255,f501]) ).
fof(f518,plain,
( ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f517]) ).
fof(f519,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f525,plain,
( ~ sQ4_spl
| a_select2(rho_defuse,n0) != use ),
inference(backward_demodulation,[status(thm)],[f435,f284]) ).
fof(f528,plain,
( ~ sQ4_spl
| use != use ),
inference(forward_demodulation,[status(thm)],[f253,f525]) ).
fof(f529,plain,
( ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f528]) ).
fof(f530,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f531,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f433]) ).
fof(f532,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f536,plain,
( ~ sQ5_spl
| a_select2(rho_defuse,n1) != use ),
inference(backward_demodulation,[status(thm)],[f438,f284]) ).
fof(f538,plain,
( ~ sQ5_spl
| use != use ),
inference(forward_demodulation,[status(thm)],[f254,f536]) ).
fof(f539,plain,
( ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f538]) ).
fof(f540,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f541,plain,
$false,
inference(sat_refutation,[status(thm)],[f443,f519,f530,f532,f540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV204+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:35:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.43 % Refutation found
% 0.09/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.45 % Elapsed time: 0.082038 seconds
% 0.09/0.45 % CPU time: 0.463840 seconds
% 0.09/0.45 % Total memory used: 91.779 MB
% 0.09/0.45 % Net memory used: 90.893 MB
%------------------------------------------------------------------------------