%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV198+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 : 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 02:46:52 PM UTC 2026
% Result : Theorem 4.22s 1.09s
% Output : CNFRefutation 4.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 13 unt; 8 def)
% Number of atoms : 315 ( 160 equ)
% Maximal formula atoms : 45 ( 4 avg)
% Number of connectives : 331 ( 81 ~; 78 |; 154 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 18 con; 0-3 aty)
% Number of variables : 28 ( 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( ! [C,D] :
( ( leq(D,pred(pv5))
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(z_defuse,C,D) = use )
& ! [A,B] :
( ( leq(B,pred(pv5))
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(u_defuse,A,B) = use )
& leq(pv5,n998)
& leq(pv5,n0)
& leq(n0,pv5)
& 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,F] :
( ( leq(F,pv5)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> a_select3(u_defuse,E,F) = use ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( ! [C,D] :
( ( leq(D,pred(pv5))
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(z_defuse,C,D) = use )
& ! [A,B] :
( ( leq(B,pred(pv5))
& leq(A,n2)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(u_defuse,A,B) = use )
& leq(pv5,n998)
& leq(pv5,n0)
& leq(n0,pv5)
& 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,F] :
( ( leq(F,pv5)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
=> a_select3(u_defuse,E,F) = use ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f85,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [X] :
( ( leq(X,n2)
& leq(n0,X) )
=> ( X = n2
| X = n1
| X = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f251,plain,
( ? [E,F] :
( a_select3(u_defuse,E,F) != use
& leq(F,pv5)
& leq(E,n2)
& leq(n0,F)
& leq(n0,E) )
& ! [C,D] :
( a_select3(z_defuse,C,D) = use
| ~ leq(D,pred(pv5))
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(u_defuse,A,B) = use
| ~ leq(B,pred(pv5))
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& leq(pv5,n998)
& leq(pv5,n0)
& leq(n0,pv5)
& 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_select3(u_defuse,sK23_skl,sK24_skl) != use
& leq(sK24_skl,pv5)
& leq(sK23_skl,n2)
& leq(n0,sK24_skl)
& leq(n0,sK23_skl)
& ! [C,D] :
( a_select3(z_defuse,C,D) = use
| ~ leq(D,pred(pv5))
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(u_defuse,A,B) = use
| ~ leq(B,pred(pv5))
| ~ leq(A,n2)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& leq(pv5,n998)
& leq(pv5,n0)
& leq(n0,pv5)
& 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,sK24_skl]),skolemize(E,sK23_skl),skolemize(F,sK24_skl)],[f251]) ).
fof(f262,plain,
a_select3(u_defuse,n0,n0) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f263,plain,
a_select3(u_defuse,n1,n0) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f264,plain,
a_select3(u_defuse,n2,n0) = use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f280,plain,
leq(n0,pv5),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f281,plain,
leq(pv5,n0),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f285,plain,
leq(n0,sK23_skl),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f286,plain,
leq(n0,sK24_skl),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f287,plain,
leq(sK23_skl,n2),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f288,plain,
leq(sK24_skl,pv5),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f289,plain,
a_select3(u_defuse,sK23_skl,sK24_skl) != use,
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f322,plain,
! [X] :
( X = n0
| ~ leq(X,n0)
| ~ leq(n0,X) ),
inference(pre_NNF_transformation,[status(thm)],[f85]) ).
fof(f323,plain,
! [X0] :
( X0 = n0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f326,plain,
! [X] :
( X = n2
| X = n1
| X = n0
| ~ leq(X,n2)
| ~ leq(n0,X) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f327,plain,
! [X0] :
( X0 = n2
| X0 = n1
| X0 = n0
| ~ leq(X0,n2)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f326]) ).
fof(f521,definition,
( sQ2_spl
<=> sK23_skl = n2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( ~ sQ2_spl
| sK23_skl = n2 ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f535,definition,
( sQ6_spl
<=> pv5 = n0 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( ~ sQ6_spl
| pv5 = n0 ),
inference(component_clause,[status(thm)],[f535]) ).
fof(f542,definition,
( sQ8_spl
<=> n0 = sK24_skl ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f543,plain,
( ~ sQ8_spl
| n0 = sK24_skl ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f549,definition,
( sQ10_spl
<=> n0 = sK23_skl ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f550,plain,
( ~ sQ10_spl
| n0 = sK23_skl ),
inference(component_clause,[status(thm)],[f549]) ).
fof(f580,plain,
( ~ sQ10_spl
| a_select3(u_defuse,n0,sK24_skl) != use ),
inference(backward_demodulation,[status(thm)],[f550,f289]) ).
fof(f658,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| a_select3(u_defuse,n0,n0) != use ),
inference(forward_demodulation,[status(thm)],[f543,f580]) ).
fof(f659,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| use != use ),
inference(forward_demodulation,[status(thm)],[f262,f658]) ).
fof(f660,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f659]) ).
fof(f661,plain,
( ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f660]) ).
fof(f751,plain,
( ~ sQ2_spl
| a_select3(u_defuse,n2,sK24_skl) != use ),
inference(forward_demodulation,[status(thm)],[f522,f289]) ).
fof(f752,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| a_select3(u_defuse,n2,n0) != use ),
inference(forward_demodulation,[status(thm)],[f543,f751]) ).
fof(f753,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| use != use ),
inference(forward_demodulation,[status(thm)],[f264,f752]) ).
fof(f754,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f753]) ).
fof(f755,plain,
( ~ sQ2_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f754]) ).
fof(f1179,plain,
( sK24_skl = n0
| ~ leq(sK24_skl,n0) ),
inference(resolution,[status(thm)],[f323,f286]) ).
fof(f1180,plain,
( pv5 = n0
| ~ leq(pv5,n0) ),
inference(resolution,[status(thm)],[f323,f280]) ).
fof(f1193,definition,
( sQ29_spl
<=> leq(sK24_skl,n0) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f1195,plain,
( sQ29_spl
| ~ leq(sK24_skl,n0) ),
inference(component_clause,[status(thm)],[f1193]) ).
fof(f1196,plain,
( sQ8_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f1179,f1193,f542]) ).
fof(f1197,definition,
( sQ30_spl
<=> leq(pv5,n0) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1199,plain,
( sQ30_spl
| ~ leq(pv5,n0) ),
inference(component_clause,[status(thm)],[f1197]) ).
fof(f1200,plain,
( sQ6_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1180,f1197,f535]) ).
fof(f1218,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1199,f281]) ).
fof(f1219,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f1218]) ).
fof(f1226,plain,
( ~ sQ8_spl
| a_select3(u_defuse,sK23_skl,n0) != use ),
inference(backward_demodulation,[status(thm)],[f543,f289]) ).
fof(f1266,plain,
( ~ sQ6_spl
| leq(sK24_skl,n0) ),
inference(forward_demodulation,[status(thm)],[f536,f288]) ).
fof(f1267,plain,
( ~ sQ6_spl
| sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1266,f1195]) ).
fof(f1268,plain,
( ~ sQ6_spl
| sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f1267]) ).
fof(f1608,definition,
( sQ48_spl
<=> sK23_skl = n1 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1609,plain,
( ~ sQ48_spl
| sK23_skl = n1 ),
inference(component_clause,[status(thm)],[f1608]) ).
fof(f2076,plain,
( sK23_skl = n2
| sK23_skl = n1
| sK23_skl = n0
| ~ leq(sK23_skl,n2) ),
inference(resolution,[status(thm)],[f327,f285]) ).
fof(f2097,definition,
( sQ74_spl
<=> leq(sK23_skl,n2) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f2099,plain,
( sQ74_spl
| ~ leq(sK23_skl,n2) ),
inference(component_clause,[status(thm)],[f2097]) ).
fof(f2100,plain,
( sQ2_spl
| sQ48_spl
| sQ10_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f2076,f2097,f549,f1608,f521]) ).
fof(f2116,plain,
( ~ sQ8_spl
| ~ sQ48_spl
| a_select3(u_defuse,n1,n0) != use ),
inference(backward_demodulation,[status(thm)],[f1609,f1226]) ).
fof(f2134,plain,
( ~ sQ8_spl
| ~ sQ48_spl
| use != use ),
inference(forward_demodulation,[status(thm)],[f263,f2116]) ).
fof(f2135,plain,
( ~ sQ8_spl
| ~ sQ48_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2134]) ).
fof(f2136,plain,
( ~ sQ8_spl
| ~ sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f2135]) ).
fof(f2137,plain,
( sQ74_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f2099]) ).
fof(f2138,plain,
sQ74_spl,
inference(contradiction_clause,[status(thm)],[f2137]) ).
fof(f2139,plain,
$false,
inference(sat_refutation,[status(thm)],[f661,f755,f1196,f1200,f1219,f1268,f2100,f2136,f2138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV198+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n014.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 08:34:34 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 4.22/1.09 % Refutation found
% 4.22/1.09 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.22/1.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.38/1.12 % Elapsed time: 0.683635 seconds
% 0.38/1.12 % CPU time: 5.014679 seconds
% 0.38/1.12 % Total memory used: 140.238 MB
% 0.38/1.12 % Net memory used: 134.729 MB
%------------------------------------------------------------------------------