%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV231+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 : n002.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 02:46:56 PM UTC 2026
% Result : Theorem 0.15s 5.63s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 11 unt; 2 def)
% Number of atoms : 213 ( 149 equ)
% Maximal formula atoms : 45 ( 8 avg)
% Number of connectives : 293 ( 106 ~; 51 |; 124 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-3 aty)
% Number of variables : 22 ( 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( ! [C,D] :
( ( leq(D,n2)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
=> ! [E,F] :
( ( leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
=> ( ( n5 = F
& n5 = E
& n4 = F
& n3 = E
& ~ ( n5 = F
& n5 = E )
& ~ ( n5 = E
& n4 = F )
& ~ ( n5 = F
& n4 = E )
& ~ ( n4 = F
& n4 = E )
& ~ ( n5 = E
& n3 = F )
& ~ ( n4 = E
& n3 = F )
& ~ ( n5 = F
& n3 = E )
& ~ ( n5 = E
& n2 = F )
& ~ ( n4 = E
& n2 = F )
& ~ ( n5 = E
& n1 = F )
& ~ ( n4 = E
& n1 = F )
& ~ ( n5 = E
& n0 = F )
& ~ ( n4 = E
& n0 = F ) )
=> n0 = a_select2(xinit_noise,n5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( ! [C,D] :
( ( leq(D,n2)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
=> ! [E,F] :
( ( leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
=> ( ( n5 = F
& n5 = E
& n4 = F
& n3 = E
& ~ ( n5 = F
& n5 = E )
& ~ ( n5 = E
& n4 = F )
& ~ ( n5 = F
& n4 = E )
& ~ ( n4 = F
& n4 = E )
& ~ ( n5 = E
& n3 = F )
& ~ ( n4 = E
& n3 = F )
& ~ ( n5 = F
& n3 = E )
& ~ ( n5 = E
& n2 = F )
& ~ ( n4 = E
& n2 = F )
& ~ ( n5 = E
& n1 = F )
& ~ ( n4 = E
& n1 = F )
& ~ ( n5 = E
& n0 = F )
& ~ ( n4 = E
& n0 = F ) )
=> n0 = a_select2(xinit_noise,n5) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f244,plain,
( ? [E,F] :
( n0 != a_select2(xinit_noise,n5)
& n5 = F
& n5 = E
& n4 = F
& n3 = E
& ( n5 != F
| n5 != E )
& ( n5 != E
| n4 != F )
& ( n5 != F
| n4 != E )
& ( n4 != F
| n4 != E )
& ( n5 != E
| n3 != F )
& ( n4 != E
| n3 != F )
& ( n5 != F
| n3 != E )
& ( n5 != E
| n2 != F )
& ( n4 != E
| n2 != F )
& ( n5 != E
| n1 != F )
& ( n4 != E
| n1 != F )
& ( n5 != E
| n0 != F )
& ( n4 != E
| n0 != F )
& leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
& ! [C,D] :
( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C)
| ~ leq(D,n2)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A)
| ~ leq(B,n5)
| ~ leq(A,n5)
| ~ leq(n0,B)
| ~ leq(n0,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f245,plain,
( n0 != a_select2(xinit_noise,n5)
& n5 = sK24_skl
& n5 = sK23_skl
& n4 = sK24_skl
& n3 = sK23_skl
& ( n5 != sK24_skl
| n5 != sK23_skl )
& ( n5 != sK23_skl
| n4 != sK24_skl )
& ( n5 != sK24_skl
| n4 != sK23_skl )
& ( n4 != sK24_skl
| n4 != sK23_skl )
& ( n5 != sK23_skl
| n3 != sK24_skl )
& ( n4 != sK23_skl
| n3 != sK24_skl )
& ( n5 != sK24_skl
| n3 != sK23_skl )
& ( n5 != sK23_skl
| n2 != sK24_skl )
& ( n4 != sK23_skl
| n2 != sK24_skl )
& ( n5 != sK23_skl
| n1 != sK24_skl )
& ( n4 != sK23_skl
| n1 != sK24_skl )
& ( n5 != sK23_skl
| n0 != sK24_skl )
& ( n4 != sK23_skl
| n0 != sK24_skl )
& leq(sK24_skl,n5)
& leq(sK23_skl,n5)
& leq(n0,sK24_skl)
& leq(n0,sK23_skl)
& ! [C,D] :
( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C)
| ~ leq(D,n2)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A)
| ~ leq(B,n5)
| ~ leq(A,n5)
| ~ leq(n0,B)
| ~ leq(n0,A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl]),skolemize(E,sK23_skl),skolemize(F,sK24_skl)],[f244]) ).
fof(f264,plain,
( n5 != sK24_skl
| n5 != sK23_skl ),
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f265,plain,
n3 = sK23_skl,
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f266,plain,
n4 = sK24_skl,
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f267,plain,
n5 = sK23_skl,
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f268,plain,
n5 = sK24_skl,
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f351,definition,
( sQ2_spl
<=> n5 = sK23_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ2_spl
| n5 != sK23_skl ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f368,definition,
( sQ6_spl
<=> n5 = sK24_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( sQ6_spl
| n5 != sK24_skl ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f383,plain,
( ~ sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f264,f351,f368]) ).
fof(f395,plain,
n5 = n3,
inference(forward_demodulation,[status(thm)],[f265,f267]) ).
fof(f397,plain,
n3 = sK24_skl,
inference(forward_demodulation,[status(thm)],[f395,f268]) ).
fof(f398,plain,
n3 = sK24_skl,
inference(backward_demodulation,[status(thm)],[f399,f266]) ).
fof(f399,plain,
n3 = n4,
inference(forward_demodulation,[status(thm)],[f266,f397]) ).
fof(f400,plain,
( sQ2_spl
| n3 != sK23_skl ),
inference(forward_demodulation,[status(thm)],[f395,f353]) ).
fof(f401,plain,
( sQ2_spl
| n3 != n3 ),
inference(forward_demodulation,[status(thm)],[f265,f400]) ).
fof(f402,plain,
( sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f401]) ).
fof(f403,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f402]) ).
fof(f418,plain,
( sQ6_spl
| n3 != sK24_skl ),
inference(forward_demodulation,[status(thm)],[f395,f370]) ).
fof(f419,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f398,f418]) ).
fof(f420,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f419]) ).
fof(f421,plain,
$false,
inference(sat_refutation,[status(thm)],[f383,f403,f420]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV231+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.58 % Computer : n002.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Mon Sep 21 08:37:52 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.15/5.60 % Drodi V4.1.1
% 0.15/5.63 % Refutation found
% 0.15/5.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.66 % Elapsed time: 0.065038 seconds
% 0.15/5.66 % CPU time: 0.164942 seconds
% 0.15/5.66 % Total memory used: 109.237 MB
% 0.15/5.66 % Net memory used: 109.057 MB
%------------------------------------------------------------------------------