%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU388+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:20:23 PM UTC 2026
% Result : Theorem 48.63s 11.75s
% Output : CNFRefutation 49.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 52 ( 10 unt; 0 def)
% Number of atoms : 203 ( 27 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 251 ( 100 ~; 108 |; 31 &)
% ( 4 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 78 ( 68 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f146,axiom,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> neighborhood_system(A,B) = a_2_0_yellow19(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f458,axiom,
! [A,B,C] :
( ( element(C,the_carrier(B))
& top_str(B)
& topological_space(B)
& ~ empty_carrier(B) )
=> ( in(A,a_2_0_yellow19(B,C))
<=> ? [D] :
( A = D
& point_neighbourhood(D,B,C) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f791,conjecture,
! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( in(C,neighborhood_system(A,B))
<=> point_neighbourhood(C,A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f792,negated_conjecture,
~ ! [A] :
( ( top_str(A)
& topological_space(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( in(C,neighborhood_system(A,B))
<=> point_neighbourhood(C,A,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f791]) ).
fof(f1672,plain,
! [A] :
( ! [B] :
( neighborhood_system(A,B) = a_2_0_yellow19(A,B)
| ~ element(B,the_carrier(A)) )
| ~ top_str(A)
| ~ topological_space(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f146]) ).
fof(f1673,plain,
! [X0,X1] :
( neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1)
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f1672]) ).
fof(f2985,plain,
! [A,B,C] :
( ( in(A,a_2_0_yellow19(B,C))
<=> ? [D] :
( A = D
& point_neighbourhood(D,B,C) ) )
| ~ element(C,the_carrier(B))
| ~ top_str(B)
| ~ topological_space(B)
| empty_carrier(B) ),
inference(pre_NNF_transformation,[status(thm)],[f458]) ).
fof(f2986,plain,
! [A,B,C] :
( ( ( ! [D] :
( A != D
| ~ point_neighbourhood(D,B,C) )
| in(A,a_2_0_yellow19(B,C)) )
& ( ? [D] :
( A = D
& point_neighbourhood(D,B,C) )
| ~ in(A,a_2_0_yellow19(B,C)) ) )
| ~ element(C,the_carrier(B))
| ~ top_str(B)
| ~ topological_space(B)
| empty_carrier(B) ),
inference(NNF_transformation,[status(thm)],[f2985]) ).
fof(f2987,plain,
! [B,C] :
( ( ! [A] :
( ! [D] :
( A != D
| ~ point_neighbourhood(D,B,C) )
| in(A,a_2_0_yellow19(B,C)) )
& ! [A] :
( ? [D] :
( A = D
& point_neighbourhood(D,B,C) )
| ~ in(A,a_2_0_yellow19(B,C)) ) )
| ~ element(C,the_carrier(B))
| ~ top_str(B)
| ~ topological_space(B)
| empty_carrier(B) ),
inference(miniscoping,[status(thm)],[f2986]) ).
fof(f2988,plain,
! [B,C] :
( ( ! [A] :
( ! [D] :
( A != D
| ~ point_neighbourhood(D,B,C) )
| in(A,a_2_0_yellow19(B,C)) )
& ! [A] :
( ( A = sK167_skl(A,C,B)
& point_neighbourhood(sK167_skl(A,C,B),B,C) )
| ~ in(A,a_2_0_yellow19(B,C)) ) )
| ~ element(C,the_carrier(B))
| ~ top_str(B)
| ~ topological_space(B)
| empty_carrier(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK167_skl]),skolemize(D,sK167_skl(A,C,B))],[f2987]) ).
fof(f2989,plain,
! [X0,X1,X2] :
( point_neighbourhood(sK167_skl(X2,X1,X0),X0,X1)
| ~ in(X2,a_2_0_yellow19(X0,X1))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f2988]) ).
fof(f2990,plain,
! [X0,X1,X2] :
( X2 = sK167_skl(X2,X1,X0)
| ~ in(X2,a_2_0_yellow19(X0,X1))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f2988]) ).
fof(f2991,plain,
! [X0,X1,X2,X3] :
( X2 != X3
| ~ point_neighbourhood(X3,X0,X1)
| in(X2,a_2_0_yellow19(X0,X1))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f2988]) ).
fof(f4737,plain,
? [A] :
( ? [B] :
( ? [C] :
( in(C,neighborhood_system(A,B))
<~> point_neighbourhood(C,A,B) )
& element(B,the_carrier(A)) )
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f792]) ).
fof(f4738,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( ~ point_neighbourhood(C,A,B)
| ~ in(C,neighborhood_system(A,B)) )
& ( point_neighbourhood(C,A,B)
| in(C,neighborhood_system(A,B)) ) )
& element(B,the_carrier(A)) )
& top_str(A)
& topological_space(A)
& ~ empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f4737]) ).
fof(f4739,plain,
( ( ~ point_neighbourhood(sK475_skl,sK473_skl,sK474_skl)
| ~ in(sK475_skl,neighborhood_system(sK473_skl,sK474_skl)) )
& ( point_neighbourhood(sK475_skl,sK473_skl,sK474_skl)
| in(sK475_skl,neighborhood_system(sK473_skl,sK474_skl)) )
& element(sK474_skl,the_carrier(sK473_skl))
& top_str(sK473_skl)
& topological_space(sK473_skl)
& ~ empty_carrier(sK473_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK473_skl,sK474_skl,sK475_skl]),skolemize(A,sK473_skl),skolemize(B,sK474_skl),skolemize(C,sK475_skl)],[f4738]) ).
fof(f4740,plain,
~ empty_carrier(sK473_skl),
inference(cnf_transformation,[status(thm)],[f4739]) ).
fof(f4741,plain,
topological_space(sK473_skl),
inference(cnf_transformation,[status(thm)],[f4739]) ).
fof(f4742,plain,
top_str(sK473_skl),
inference(cnf_transformation,[status(thm)],[f4739]) ).
fof(f4743,plain,
element(sK474_skl,the_carrier(sK473_skl)),
inference(cnf_transformation,[status(thm)],[f4739]) ).
fof(f4744,plain,
( point_neighbourhood(sK475_skl,sK473_skl,sK474_skl)
| in(sK475_skl,neighborhood_system(sK473_skl,sK474_skl)) ),
inference(cnf_transformation,[status(thm)],[f4739]) ).
fof(f4745,plain,
( ~ point_neighbourhood(sK475_skl,sK473_skl,sK474_skl)
| ~ in(sK475_skl,neighborhood_system(sK473_skl,sK474_skl)) ),
inference(cnf_transformation,[status(thm)],[f4739]) ).
fof(f5643,plain,
! [X0,X1,X2] :
( ~ point_neighbourhood(X2,X0,X1)
| in(X2,a_2_0_yellow19(X0,X1))
| ~ element(X1,the_carrier(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f2991]) ).
fof(f5826,plain,
! [X0] :
( neighborhood_system(sK473_skl,X0) = a_2_0_yellow19(sK473_skl,X0)
| ~ element(X0,the_carrier(sK473_skl))
| ~ top_str(sK473_skl)
| empty_carrier(sK473_skl) ),
inference(resolution,[status(thm)],[f1673,f4741]) ).
fof(f5827,plain,
! [X0] :
( neighborhood_system(sK473_skl,X0) = a_2_0_yellow19(sK473_skl,X0)
| ~ element(X0,the_carrier(sK473_skl))
| ~ top_str(sK473_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f5826,f4740]) ).
fof(f5919,plain,
! [X0] :
( neighborhood_system(sK473_skl,X0) = a_2_0_yellow19(sK473_skl,X0)
| ~ element(X0,the_carrier(sK473_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f5827,f4742]) ).
fof(f5938,plain,
neighborhood_system(sK473_skl,sK474_skl) = a_2_0_yellow19(sK473_skl,sK474_skl),
inference(resolution,[status(thm)],[f5919,f4743]) ).
fof(f7756,plain,
! [X0,X1] :
( ~ point_neighbourhood(X1,sK473_skl,X0)
| in(X1,a_2_0_yellow19(sK473_skl,X0))
| ~ element(X0,the_carrier(sK473_skl))
| ~ top_str(sK473_skl)
| empty_carrier(sK473_skl) ),
inference(resolution,[status(thm)],[f5643,f4741]) ).
fof(f7757,plain,
! [X0,X1] :
( ~ point_neighbourhood(X1,sK473_skl,X0)
| in(X1,a_2_0_yellow19(sK473_skl,X0))
| ~ element(X0,the_carrier(sK473_skl))
| ~ top_str(sK473_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f7756,f4740]) ).
fof(f7861,plain,
! [X0,X1] :
( ~ point_neighbourhood(X1,sK473_skl,X0)
| in(X1,a_2_0_yellow19(sK473_skl,X0))
| ~ element(X0,the_carrier(sK473_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f7757,f4742]) ).
fof(f8487,plain,
! [X0,X1] :
( X1 = sK167_skl(X1,X0,sK473_skl)
| ~ in(X1,a_2_0_yellow19(sK473_skl,X0))
| ~ element(X0,the_carrier(sK473_skl))
| ~ top_str(sK473_skl)
| empty_carrier(sK473_skl) ),
inference(resolution,[status(thm)],[f2990,f4741]) ).
fof(f8488,plain,
! [X0,X1] :
( X1 = sK167_skl(X1,X0,sK473_skl)
| ~ in(X1,a_2_0_yellow19(sK473_skl,X0))
| ~ element(X0,the_carrier(sK473_skl))
| ~ top_str(sK473_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f8487,f4740]) ).
fof(f8566,plain,
! [X0,X1] :
( X1 = sK167_skl(X1,X0,sK473_skl)
| ~ in(X1,a_2_0_yellow19(sK473_skl,X0))
| ~ element(X0,the_carrier(sK473_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f8488,f4742]) ).
fof(f8630,plain,
! [X0] :
( X0 = sK167_skl(X0,sK474_skl,sK473_skl)
| ~ in(X0,a_2_0_yellow19(sK473_skl,sK474_skl)) ),
inference(resolution,[status(thm)],[f8566,f4743]) ).
fof(f8637,plain,
! [X0] :
( X0 = sK167_skl(X0,sK474_skl,sK473_skl)
| ~ in(X0,neighborhood_system(sK473_skl,sK474_skl)) ),
inference(forward_demodulation,[status(thm)],[f5938,f8630]) ).
fof(f9145,plain,
( point_neighbourhood(sK475_skl,sK473_skl,sK474_skl)
| sK475_skl = sK167_skl(sK475_skl,sK474_skl,sK473_skl) ),
inference(resolution,[status(thm)],[f8637,f4744]) ).
fof(f9284,plain,
( in(sK475_skl,a_2_0_yellow19(sK473_skl,sK474_skl))
| ~ element(sK474_skl,the_carrier(sK473_skl))
| sK475_skl = sK167_skl(sK475_skl,sK474_skl,sK473_skl) ),
inference(resolution,[status(thm)],[f9145,f7861]) ).
fof(f9286,plain,
( in(sK475_skl,neighborhood_system(sK473_skl,sK474_skl))
| ~ element(sK474_skl,the_carrier(sK473_skl))
| sK475_skl = sK167_skl(sK475_skl,sK474_skl,sK473_skl) ),
inference(forward_demodulation,[status(thm)],[f5938,f9284]) ).
fof(f9287,plain,
( in(sK475_skl,neighborhood_system(sK473_skl,sK474_skl))
| sK475_skl = sK167_skl(sK475_skl,sK474_skl,sK473_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f9286,f4743]) ).
fof(f9314,plain,
sK475_skl = sK167_skl(sK475_skl,sK474_skl,sK473_skl),
inference(forward_subsumption_resolution,[status(thm)],[f9287,f8637]) ).
fof(f10468,plain,
! [X0,X1] :
( point_neighbourhood(sK167_skl(X1,X0,sK473_skl),sK473_skl,X0)
| ~ in(X1,a_2_0_yellow19(sK473_skl,X0))
| ~ element(X0,the_carrier(sK473_skl))
| ~ top_str(sK473_skl)
| empty_carrier(sK473_skl) ),
inference(resolution,[status(thm)],[f2989,f4741]) ).
fof(f10469,plain,
! [X0,X1] :
( point_neighbourhood(sK167_skl(X1,X0,sK473_skl),sK473_skl,X0)
| ~ in(X1,a_2_0_yellow19(sK473_skl,X0))
| ~ element(X0,the_carrier(sK473_skl))
| ~ top_str(sK473_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f10468,f4740]) ).
fof(f10486,plain,
! [X0,X1] :
( point_neighbourhood(sK167_skl(X1,X0,sK473_skl),sK473_skl,X0)
| ~ in(X1,a_2_0_yellow19(sK473_skl,X0))
| ~ element(X0,the_carrier(sK473_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f10469,f4742]) ).
fof(f10490,plain,
( point_neighbourhood(sK475_skl,sK473_skl,sK474_skl)
| ~ in(sK475_skl,a_2_0_yellow19(sK473_skl,sK474_skl))
| ~ element(sK474_skl,the_carrier(sK473_skl)) ),
inference(paramodulation,[status(thm)],[f9314,f10486]) ).
fof(f10494,plain,
( point_neighbourhood(sK475_skl,sK473_skl,sK474_skl)
| ~ in(sK475_skl,neighborhood_system(sK473_skl,sK474_skl))
| ~ element(sK474_skl,the_carrier(sK473_skl)) ),
inference(forward_demodulation,[status(thm)],[f5938,f10490]) ).
fof(f10495,plain,
( point_neighbourhood(sK475_skl,sK473_skl,sK474_skl)
| ~ in(sK475_skl,neighborhood_system(sK473_skl,sK474_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f10494,f4743]) ).
fof(f11364,plain,
~ in(sK475_skl,neighborhood_system(sK473_skl,sK474_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f4745,f11366]) ).
fof(f11366,plain,
point_neighbourhood(sK475_skl,sK473_skl,sK474_skl),
inference(forward_subsumption_resolution,[status(thm)],[f10495,f4744]) ).
fof(f11368,plain,
( in(sK475_skl,a_2_0_yellow19(sK473_skl,sK474_skl))
| ~ element(sK474_skl,the_carrier(sK473_skl)) ),
inference(resolution,[status(thm)],[f11366,f7861]) ).
fof(f11371,plain,
( in(sK475_skl,neighborhood_system(sK473_skl,sK474_skl))
| ~ element(sK474_skl,the_carrier(sK473_skl)) ),
inference(forward_demodulation,[status(thm)],[f5938,f11368]) ).
fof(f11372,plain,
in(sK475_skl,neighborhood_system(sK473_skl,sK474_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f11371,f4743]) ).
fof(f17787,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f11372,f11364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU388+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n009.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 06:18:33 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.15/5.51 % Drodi V4.1.1
% 48.63/11.75 % Refutation found
% 48.63/11.75 % SZS status Theorem for theBenchmark: Theorem is valid
% 48.63/11.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 25.18/11.84 % Elapsed time: 6.433870 seconds
% 25.18/11.84 % CPU time: 49.993534 seconds
% 25.18/11.84 % Total memory used: 521.109 MB
% 25.18/11.84 % Net memory used: 494.912 MB
%------------------------------------------------------------------------------