%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV209+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 : n003.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 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 17 unt; 7 def)
% Number of atoms : 281 ( 175 equ)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 291 ( 69 ~; 73 |; 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(xinit_noise_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,n5)
& leq(n0,E) )
=> a_select2(xinit_noise_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/sandbox2/benchmark/theBenchmark.p') ).
fof(f251,plain,
( ? [E] :
( a_select2(xinit_noise_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(xinit_noise_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(f274,plain,
a_select2(xinit_noise_defuse,n0) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f275,plain,
a_select2(xinit_noise_defuse,n1) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f276,plain,
a_select2(xinit_noise_defuse,n2) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f277,plain,
a_select2(xinit_noise_defuse,n3) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f278,plain,
a_select2(xinit_noise_defuse,n4) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f279,plain,
a_select2(xinit_noise_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(xinit_noise_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(f598,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(f602,definition,
( sQ12_spl
<=> leq(sK23_skl,n5) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f604,plain,
( sQ12_spl
| ~ leq(sK23_skl,n5) ),
inference(component_clause,[status(thm)],[f602]) ).
fof(f605,definition,
( sQ13_spl
<=> sK23_skl = n0 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f606,plain,
( ~ sQ13_spl
| sK23_skl = n0 ),
inference(component_clause,[status(thm)],[f605]) ).
fof(f608,definition,
( sQ14_spl
<=> sK23_skl = n1 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f609,plain,
( ~ sQ14_spl
| sK23_skl = n1 ),
inference(component_clause,[status(thm)],[f608]) ).
fof(f611,definition,
( sQ15_spl
<=> sK23_skl = n2 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( ~ sQ15_spl
| sK23_skl = n2 ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f614,definition,
( sQ16_spl
<=> sK23_skl = n3 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( ~ sQ16_spl
| sK23_skl = n3 ),
inference(component_clause,[status(thm)],[f614]) ).
fof(f617,definition,
( sQ17_spl
<=> sK23_skl = n4 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( ~ sQ17_spl
| sK23_skl = n4 ),
inference(component_clause,[status(thm)],[f617]) ).
fof(f620,definition,
( sQ18_spl
<=> sK23_skl = n5 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f621,plain,
( ~ sQ18_spl
| sK23_skl = n5 ),
inference(component_clause,[status(thm)],[f620]) ).
fof(f623,plain,
( sQ18_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f598,f602,f605,f608,f611,f614,f617,f620]) ).
fof(f673,plain,
( ~ sQ18_spl
| a_select2(xinit_noise_defuse,n5) != use ),
inference(backward_demodulation,[status(thm)],[f621,f284]) ).
fof(f732,plain,
( ~ sQ18_spl
| use != use ),
inference(forward_demodulation,[status(thm)],[f279,f673]) ).
fof(f733,plain,
( ~ sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f732]) ).
fof(f734,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f733]) ).
fof(f761,plain,
( ~ sQ15_spl
| a_select2(xinit_noise_defuse,n2) != use ),
inference(backward_demodulation,[status(thm)],[f612,f284]) ).
fof(f788,plain,
( ~ sQ16_spl
| a_select2(xinit_noise_defuse,n3) != use ),
inference(backward_demodulation,[status(thm)],[f615,f284]) ).
fof(f792,plain,
( ~ sQ15_spl
| use != use ),
inference(forward_demodulation,[status(thm)],[f276,f761]) ).
fof(f793,plain,
( ~ sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f792]) ).
fof(f794,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f793]) ).
fof(f834,plain,
( ~ sQ13_spl
| a_select2(xinit_noise_defuse,n0) != use ),
inference(backward_demodulation,[status(thm)],[f606,f284]) ).
fof(f839,plain,
( ~ sQ13_spl
| use != use ),
inference(forward_demodulation,[status(thm)],[f274,f834]) ).
fof(f840,plain,
( ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f839]) ).
fof(f841,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f840]) ).
fof(f847,plain,
( ~ sQ14_spl
| a_select2(xinit_noise_defuse,n1) != use ),
inference(backward_demodulation,[status(thm)],[f609,f284]) ).
fof(f849,plain,
( ~ sQ14_spl
| use != use ),
inference(forward_demodulation,[status(thm)],[f275,f847]) ).
fof(f850,plain,
( ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f849]) ).
fof(f851,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f850]) ).
fof(f852,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f283]) ).
fof(f853,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f852]) ).
fof(f854,plain,
( ~ sQ16_spl
| use != use ),
inference(forward_demodulation,[status(thm)],[f277,f788]) ).
fof(f855,plain,
( ~ sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f854]) ).
fof(f856,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f855]) ).
fof(f860,plain,
( ~ sQ17_spl
| a_select2(xinit_noise_defuse,n4) != use ),
inference(backward_demodulation,[status(thm)],[f618,f284]) ).
fof(f865,plain,
( ~ sQ17_spl
| use != use ),
inference(forward_demodulation,[status(thm)],[f278,f860]) ).
fof(f866,plain,
( ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f865]) ).
fof(f867,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f866]) ).
fof(f868,plain,
$false,
inference(sat_refutation,[status(thm)],[f623,f734,f794,f841,f851,f853,f856,f867]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV209+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:36:01 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.092329 seconds
% 0.14/0.45 % CPU time: 0.485580 seconds
% 0.14/0.45 % Total memory used: 115.963 MB
% 0.14/0.45 % Net memory used: 115.000 MB
%------------------------------------------------------------------------------