%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU388+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:12:09 PM UTC 2026
% Result : Theorem 18.20s 12.60s
% Output : CNFRefutation 18.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 118 ( 13 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 142 ( 52 ~; 53 |; 23 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 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 : 41 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_yellow19,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_yellow19) ).
fof(t3_yellow19,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( in(X3,neighborhood_system(X1,X2))
<=> point_neighbourhood(X3,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_yellow19) ).
fof(fraenkel_a_2_0_yellow19,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& topological_space(X2)
& top_str(X2)
& element(X3,the_carrier(X2)) )
=> ( in(X1,a_2_0_yellow19(X2,X3))
<=> ? [X4] :
( point_neighbourhood(X4,X2,X3)
& X1 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_2_0_yellow19) ).
fof(c_0_3,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[d1_yellow19]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( in(X3,neighborhood_system(X1,X2))
<=> point_neighbourhood(X3,X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t3_yellow19])]) ).
fof(c_0_5,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X2)
& topological_space(X2)
& top_str(X2)
& element(X3,the_carrier(X2)) )
=> ( in(X1,a_2_0_yellow19(X2,X3))
<=> ? [X4] :
( point_neighbourhood(X4,X2,X3)
& X1 = X4 ) ) ),
inference(fof_simplification,[status(thm)],[fraenkel_a_2_0_yellow19]) ).
fof(c_0_6,plain,
! [X2751,X2752] :
( empty_carrier(X2751)
| ~ topological_space(X2751)
| ~ top_str(X2751)
| ~ element(X2752,the_carrier(X2751))
| neighborhood_system(X2751,X2752) = a_2_0_yellow19(X2751,X2752) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_7,negated_conjecture,
( ~ empty_carrier(esk532_0)
& topological_space(esk532_0)
& top_str(esk532_0)
& element(esk533_0,the_carrier(esk532_0))
& ( ~ in(esk534_0,neighborhood_system(esk532_0,esk533_0))
| ~ point_neighbourhood(esk534_0,esk532_0,esk533_0) )
& ( in(esk534_0,neighborhood_system(esk532_0,esk533_0))
| point_neighbourhood(esk534_0,esk532_0,esk533_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,plain,
! [X3508,X3509,X3510,X3512] :
( ( point_neighbourhood(esk168_3(X3508,X3509,X3510),X3509,X3510)
| ~ in(X3508,a_2_0_yellow19(X3509,X3510))
| empty_carrier(X3509)
| ~ topological_space(X3509)
| ~ top_str(X3509)
| ~ element(X3510,the_carrier(X3509)) )
& ( X3508 = esk168_3(X3508,X3509,X3510)
| ~ in(X3508,a_2_0_yellow19(X3509,X3510))
| empty_carrier(X3509)
| ~ topological_space(X3509)
| ~ top_str(X3509)
| ~ element(X3510,the_carrier(X3509)) )
& ( ~ point_neighbourhood(X3512,X3509,X3510)
| X3508 != X3512
| in(X3508,a_2_0_yellow19(X3509,X3510))
| empty_carrier(X3509)
| ~ topological_space(X3509)
| ~ top_str(X3509)
| ~ element(X3510,the_carrier(X3509)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
cnf(c_0_9,plain,
( empty_carrier(X1)
| neighborhood_system(X1,X2) = a_2_0_yellow19(X1,X2)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
element(esk533_0,the_carrier(esk532_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
top_str(esk532_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
topological_space(esk532_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
~ empty_carrier(esk532_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( point_neighbourhood(esk168_3(X1,X2,X3),X2,X3)
| empty_carrier(X2)
| ~ in(X1,a_2_0_yellow19(X2,X3))
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
a_2_0_yellow19(esk532_0,esk533_0) = neighborhood_system(esk532_0,esk533_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12])]),c_0_13]) ).
cnf(c_0_16,plain,
( X1 = esk168_3(X1,X2,X3)
| empty_carrier(X2)
| ~ in(X1,a_2_0_yellow19(X2,X3))
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( point_neighbourhood(esk168_3(X1,esk532_0,esk533_0),esk532_0,esk533_0)
| ~ in(X1,neighborhood_system(esk532_0,esk533_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_11]),c_0_12]),c_0_15])]),c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( in(esk534_0,neighborhood_system(esk532_0,esk533_0))
| point_neighbourhood(esk534_0,esk532_0,esk533_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( esk168_3(X1,esk532_0,esk533_0) = X1
| ~ in(X1,neighborhood_system(esk532_0,esk533_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_10]),c_0_11]),c_0_12]),c_0_15])]),c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( point_neighbourhood(esk168_3(esk534_0,esk532_0,esk533_0),esk532_0,esk533_0)
| point_neighbourhood(esk534_0,esk532_0,esk533_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( esk168_3(esk534_0,esk532_0,esk533_0) = esk534_0
| point_neighbourhood(esk534_0,esk532_0,esk533_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_22,plain,
( in(X4,a_2_0_yellow19(X2,X3))
| empty_carrier(X2)
| ~ point_neighbourhood(X1,X2,X3)
| X4 != X1
| ~ topological_space(X2)
| ~ top_str(X2)
| ~ element(X3,the_carrier(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(esk534_0,neighborhood_system(esk532_0,esk533_0))
| ~ point_neighbourhood(esk534_0,esk532_0,esk533_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_24,negated_conjecture,
point_neighbourhood(esk534_0,esk532_0,esk533_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( empty_carrier(X1)
| in(X2,a_2_0_yellow19(X1,X3))
| ~ point_neighbourhood(X2,X1,X3)
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X3,the_carrier(X1)) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ in(esk534_0,neighborhood_system(esk532_0,esk533_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_15]),c_0_11]),c_0_12]),c_0_10])]),c_0_13]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU388+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n028.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 03:01:30 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 18.20/12.60 % Version : CSE_E---1.7
% 18.20/12.60 % Problem : theBenchmark.p
% 18.20/12.60 % SZS status Theorem for theBenchmark.p
% 18.20/12.60 % SZS output start CNFRefutation
% See solution above
% 18.20/12.64 % Total time : 10.711s
%------------------------------------------------------------------------------