%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU372+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.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 05:12:05 PM UTC 2026
% Result : Theorem 7.14s 4.80s
% Output : CNFRefutation 7.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 89 ( 12 unt; 0 def)
% Number of atoms : 450 ( 17 equ)
% Maximal formula atoms : 76 ( 5 avg)
% Number of connectives : 616 ( 255 ~; 264 |; 47 &)
% ( 6 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 183 ( 0 sgn 88 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_connsp_2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(d13_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( X3 = topstr_closure(X1,X2)
<=> ! [X4] :
( in(X4,the_carrier(X1))
=> ( in(X4,X3)
<=> ! [X5] :
( element(X5,powerset(the_carrier(X1)))
=> ~ ( open_subset(X5,X1)
& in(X4,X5)
& disjoint(X2,X5) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_pre_topc) ).
fof(dt_k6_pre_topc,axiom,
! [X1,X2] :
( ( top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> element(topstr_closure(X1,X2),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(fc1_struct_0,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(t6_yellow_6,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,topstr_closure(X1,X2))
<=> ! [X4] :
( point_neighbourhood(X4,X1,X3)
=> ~ disjoint(X4,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_6) ).
fof(dt_l1_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> one_sorted_str(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t63_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& disjoint(X2,X3) )
=> disjoint(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(t44_tops_1,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset(interior(X1,X2),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_tops_1) ).
fof(t51_tops_1,axiom,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> open_subset(interior(X1,X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
fof(d1_connsp_2,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(dt_m1_connsp_2,axiom,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& element(X2,the_carrier(X1)) )
=> ! [X3] :
( point_neighbourhood(X3,X1,X2)
=> element(X3,powerset(the_carrier(X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_connsp_2) ).
fof(dt_k1_tops_1,axiom,
! [X1,X2] :
( ( top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> element(interior(X1,X2),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(c_0_15,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( open_subset(X2,X1)
& in(X3,X2) )
=> point_neighbourhood(X2,X1,X3) ) ) ) ),
inference(fof_simplification,[status(thm)],[t5_connsp_2]) ).
fof(c_0_16,plain,
! [X151,X152,X153] :
( empty_carrier(X151)
| ~ topological_space(X151)
| ~ top_str(X151)
| ~ element(X152,powerset(the_carrier(X151)))
| ~ element(X153,the_carrier(X151))
| ~ open_subset(X152,X151)
| ~ in(X153,X152)
| point_neighbourhood(X152,X151,X153) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_17,plain,
! [X146,X147,X148] :
( ~ in(X146,X147)
| ~ element(X147,powerset(X148))
| element(X146,X148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_18,plain,
! [X91,X92,X93,X94,X95,X99] :
( ( ~ in(X94,X93)
| ~ element(X95,powerset(the_carrier(X91)))
| ~ open_subset(X95,X91)
| ~ in(X94,X95)
| ~ disjoint(X92,X95)
| ~ in(X94,the_carrier(X91))
| X93 != topstr_closure(X91,X92)
| ~ element(X93,powerset(the_carrier(X91)))
| ~ element(X92,powerset(the_carrier(X91)))
| ~ top_str(X91) )
& ( element(esk1_4(X91,X92,X93,X94),powerset(the_carrier(X91)))
| in(X94,X93)
| ~ in(X94,the_carrier(X91))
| X93 != topstr_closure(X91,X92)
| ~ element(X93,powerset(the_carrier(X91)))
| ~ element(X92,powerset(the_carrier(X91)))
| ~ top_str(X91) )
& ( open_subset(esk1_4(X91,X92,X93,X94),X91)
| in(X94,X93)
| ~ in(X94,the_carrier(X91))
| X93 != topstr_closure(X91,X92)
| ~ element(X93,powerset(the_carrier(X91)))
| ~ element(X92,powerset(the_carrier(X91)))
| ~ top_str(X91) )
& ( in(X94,esk1_4(X91,X92,X93,X94))
| in(X94,X93)
| ~ in(X94,the_carrier(X91))
| X93 != topstr_closure(X91,X92)
| ~ element(X93,powerset(the_carrier(X91)))
| ~ element(X92,powerset(the_carrier(X91)))
| ~ top_str(X91) )
& ( disjoint(X92,esk1_4(X91,X92,X93,X94))
| in(X94,X93)
| ~ in(X94,the_carrier(X91))
| X93 != topstr_closure(X91,X92)
| ~ element(X93,powerset(the_carrier(X91)))
| ~ element(X92,powerset(the_carrier(X91)))
| ~ top_str(X91) )
& ( in(esk2_3(X91,X92,X93),the_carrier(X91))
| X93 = topstr_closure(X91,X92)
| ~ element(X93,powerset(the_carrier(X91)))
| ~ element(X92,powerset(the_carrier(X91)))
| ~ top_str(X91) )
& ( element(esk3_3(X91,X92,X93),powerset(the_carrier(X91)))
| ~ in(esk2_3(X91,X92,X93),X93)
| X93 = topstr_closure(X91,X92)
| ~ element(X93,powerset(the_carrier(X91)))
| ~ element(X92,powerset(the_carrier(X91)))
| ~ top_str(X91) )
& ( open_subset(esk3_3(X91,X92,X93),X91)
| ~ in(esk2_3(X91,X92,X93),X93)
| X93 = topstr_closure(X91,X92)
| ~ element(X93,powerset(the_carrier(X91)))
| ~ element(X92,powerset(the_carrier(X91)))
| ~ top_str(X91) )
& ( in(esk2_3(X91,X92,X93),esk3_3(X91,X92,X93))
| ~ in(esk2_3(X91,X92,X93),X93)
| X93 = topstr_closure(X91,X92)
| ~ element(X93,powerset(the_carrier(X91)))
| ~ element(X92,powerset(the_carrier(X91)))
| ~ top_str(X91) )
& ( disjoint(X92,esk3_3(X91,X92,X93))
| ~ in(esk2_3(X91,X92,X93),X93)
| X93 = topstr_closure(X91,X92)
| ~ element(X93,powerset(the_carrier(X91)))
| ~ element(X92,powerset(the_carrier(X91)))
| ~ top_str(X91) )
& ( in(esk2_3(X91,X92,X93),X93)
| ~ element(X99,powerset(the_carrier(X91)))
| ~ open_subset(X99,X91)
| ~ in(esk2_3(X91,X92,X93),X99)
| ~ disjoint(X92,X99)
| X93 = topstr_closure(X91,X92)
| ~ element(X93,powerset(the_carrier(X91)))
| ~ element(X92,powerset(the_carrier(X91)))
| ~ top_str(X91) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d13_pre_topc])])])])]) ).
fof(c_0_19,plain,
! [X105,X106] :
( ~ top_str(X105)
| ~ element(X106,powerset(the_carrier(X105)))
| element(topstr_closure(X105,X106),powerset(the_carrier(X105))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_pre_topc])]) ).
fof(c_0_20,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& one_sorted_str(X1) )
=> ~ empty(the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[fc1_struct_0]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( in(X3,topstr_closure(X1,X2))
<=> ! [X4] :
( point_neighbourhood(X4,X1,X3)
=> ~ disjoint(X4,X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t6_yellow_6])]) ).
cnf(c_0_22,plain,
( empty_carrier(X1)
| point_neighbourhood(X2,X1,X3)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ element(X3,the_carrier(X1))
| ~ open_subset(X2,X1)
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( open_subset(esk1_4(X1,X2,X3,X4),X1)
| in(X4,X3)
| ~ in(X4,the_carrier(X1))
| X3 != topstr_closure(X1,X2)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( element(topstr_closure(X1,X2),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( element(esk1_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| in(X4,X3)
| ~ in(X4,the_carrier(X1))
| X3 != topstr_closure(X1,X2)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,plain,
! [X118] :
( empty_carrier(X118)
| ~ one_sorted_str(X118)
| ~ empty(the_carrier(X118)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).
fof(c_0_28,plain,
! [X107] :
( ~ top_str(X107)
| one_sorted_str(X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l1_pre_topc])]) ).
fof(c_0_29,negated_conjecture,
! [X165] :
( ~ empty_carrier(esk20_0)
& topological_space(esk20_0)
& top_str(esk20_0)
& element(esk21_0,powerset(the_carrier(esk20_0)))
& element(esk22_0,the_carrier(esk20_0))
& ( point_neighbourhood(esk23_0,esk20_0,esk22_0)
| ~ in(esk22_0,topstr_closure(esk20_0,esk21_0)) )
& ( disjoint(esk23_0,esk21_0)
| ~ in(esk22_0,topstr_closure(esk20_0,esk21_0)) )
& ( in(esk22_0,topstr_closure(esk20_0,esk21_0))
| ~ point_neighbourhood(X165,esk20_0,esk22_0)
| ~ disjoint(X165,esk21_0) ) ),
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_21])])])])]) ).
cnf(c_0_30,plain,
( point_neighbourhood(X1,X2,X3)
| empty_carrier(X2)
| ~ topological_space(X2)
| ~ open_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ in(X3,X1) ),
inference(csr,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,plain,
( open_subset(esk1_4(X1,X2,topstr_closure(X1,X2),X3),X1)
| in(X3,topstr_closure(X1,X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ in(X3,the_carrier(X1)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_25]) ).
cnf(c_0_32,plain,
( element(esk1_4(X1,X2,topstr_closure(X1,X2),X3),powerset(the_carrier(X1)))
| in(X3,topstr_closure(X1,X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ in(X3,the_carrier(X1)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_25]) ).
fof(c_0_33,plain,
! [X136,X137] :
( ~ disjoint(X136,X137)
| disjoint(X137,X136) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
cnf(c_0_34,plain,
( disjoint(X1,esk1_4(X2,X1,X3,X4))
| in(X4,X3)
| ~ in(X4,the_carrier(X2))
| X3 != topstr_closure(X2,X1)
| ~ element(X3,powerset(the_carrier(X2)))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_35,plain,
! [X140,X141] :
( ~ element(X140,X141)
| empty(X141)
| in(X140,X141) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_36,plain,
( empty_carrier(X1)
| ~ one_sorted_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
( one_sorted_str(X1)
| ~ top_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,negated_conjecture,
( in(esk22_0,topstr_closure(esk20_0,esk21_0))
| ~ point_neighbourhood(X1,esk20_0,esk22_0)
| ~ disjoint(X1,esk21_0) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
( point_neighbourhood(esk1_4(X1,X2,topstr_closure(X1,X2),X3),X1,X4)
| empty_carrier(X1)
| in(X3,topstr_closure(X1,X2))
| ~ topological_space(X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ in(X4,esk1_4(X1,X2,topstr_closure(X1,X2),X3))
| ~ in(X3,the_carrier(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_40,negated_conjecture,
topological_space(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,negated_conjecture,
top_str(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_42,negated_conjecture,
~ empty_carrier(esk20_0),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_43,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,plain,
( disjoint(X1,esk1_4(X2,X1,topstr_closure(X2,X1),X3))
| in(X3,topstr_closure(X2,X1))
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ in(X3,the_carrier(X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_25]) ).
cnf(c_0_45,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_46,negated_conjecture,
element(esk22_0,the_carrier(esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_47,plain,
( empty_carrier(X1)
| ~ top_str(X1)
| ~ empty(the_carrier(X1)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_48,negated_conjecture,
( in(esk22_0,topstr_closure(esk20_0,esk21_0))
| in(X1,topstr_closure(esk20_0,X2))
| ~ disjoint(esk1_4(esk20_0,X2,topstr_closure(esk20_0,X2),X1),esk21_0)
| ~ element(X2,powerset(the_carrier(esk20_0)))
| ~ in(esk22_0,esk1_4(esk20_0,X2,topstr_closure(esk20_0,X2),X1))
| ~ in(X1,the_carrier(esk20_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_49,plain,
( disjoint(esk1_4(X1,X2,topstr_closure(X1,X2),X3),X2)
| in(X3,topstr_closure(X1,X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ in(X3,the_carrier(X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
element(esk21_0,powerset(the_carrier(esk20_0))),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_51,plain,
( in(X1,esk1_4(X2,X3,X4,X1))
| in(X1,X4)
| ~ in(X1,the_carrier(X2))
| X4 != topstr_closure(X2,X3)
| ~ element(X4,powerset(the_carrier(X2)))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_52,negated_conjecture,
( empty(the_carrier(esk20_0))
| in(esk22_0,the_carrier(esk20_0)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,negated_conjecture,
~ empty(the_carrier(esk20_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_47]),c_0_41])]) ).
cnf(c_0_54,plain,
( ~ in(X1,X2)
| ~ element(X3,powerset(the_carrier(X4)))
| ~ open_subset(X3,X4)
| ~ in(X1,X3)
| ~ disjoint(X5,X3)
| ~ in(X1,the_carrier(X4))
| X2 != topstr_closure(X4,X5)
| ~ element(X2,powerset(the_carrier(X4)))
| ~ element(X5,powerset(the_carrier(X4)))
| ~ top_str(X4) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_55,negated_conjecture,
( in(esk22_0,topstr_closure(esk20_0,esk21_0))
| in(X1,topstr_closure(esk20_0,esk21_0))
| ~ in(esk22_0,esk1_4(esk20_0,esk21_0,topstr_closure(esk20_0,esk21_0),X1))
| ~ in(X1,the_carrier(esk20_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_41])]) ).
cnf(c_0_56,plain,
( in(X1,esk1_4(X2,X3,topstr_closure(X2,X3),X1))
| in(X1,topstr_closure(X2,X3))
| ~ element(X3,powerset(the_carrier(X2)))
| ~ top_str(X2)
| ~ in(X1,the_carrier(X2)) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_51]),c_0_25]) ).
cnf(c_0_57,negated_conjecture,
in(esk22_0,the_carrier(esk20_0)),
inference(sr,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_58,plain,
! [X157,X158,X159] :
( ~ subset(X157,X158)
| ~ disjoint(X158,X159)
| disjoint(X157,X159) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t63_xboole_1])]) ).
fof(c_0_59,plain,
! [X144,X145] :
( ~ top_str(X144)
| ~ element(X145,powerset(the_carrier(X144)))
| subset(interior(X144,X145),X145) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t44_tops_1])])]) ).
cnf(c_0_60,plain,
( ~ disjoint(X1,X2)
| ~ open_subset(X2,X3)
| ~ element(X1,powerset(the_carrier(X3)))
| ~ element(X2,powerset(the_carrier(X3)))
| ~ top_str(X3)
| ~ in(X4,topstr_closure(X3,X1))
| ~ in(X4,the_carrier(X3))
| ~ in(X4,X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_54]),c_0_25]) ).
cnf(c_0_61,negated_conjecture,
in(esk22_0,topstr_closure(esk20_0,esk21_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_50]),c_0_41])]) ).
fof(c_0_62,plain,
! [X149,X150] :
( ~ topological_space(X149)
| ~ top_str(X149)
| ~ element(X150,powerset(the_carrier(X149)))
| open_subset(interior(X149,X150),X149) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t51_tops_1])])]) ).
cnf(c_0_63,plain,
( disjoint(X1,X3)
| ~ subset(X1,X2)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_64,plain,
( subset(interior(X1,X2),X2)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_65,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( point_neighbourhood(X3,X1,X2)
<=> in(X2,interior(X1,X3)) ) ) ) ),
inference(fof_simplification,[status(thm)],[d1_connsp_2]) ).
fof(c_0_66,plain,
! [X1,X2] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& element(X2,the_carrier(X1)) )
=> ! [X3] :
( point_neighbourhood(X3,X1,X2)
=> element(X3,powerset(the_carrier(X1))) ) ),
inference(fof_simplification,[status(thm)],[dt_m1_connsp_2]) ).
cnf(c_0_67,negated_conjecture,
( ~ disjoint(esk21_0,X1)
| ~ open_subset(X1,esk20_0)
| ~ element(X1,powerset(the_carrier(esk20_0)))
| ~ in(esk22_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_50]),c_0_41]),c_0_57])]) ).
cnf(c_0_68,plain,
( open_subset(interior(X1,X2),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_69,plain,
( disjoint(interior(X1,X2),X3)
| ~ disjoint(X2,X3)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
fof(c_0_70,plain,
! [X100,X101,X102] :
( ( ~ point_neighbourhood(X102,X100,X101)
| in(X101,interior(X100,X102))
| ~ element(X102,powerset(the_carrier(X100)))
| ~ element(X101,the_carrier(X100))
| empty_carrier(X100)
| ~ topological_space(X100)
| ~ top_str(X100) )
& ( ~ in(X101,interior(X100,X102))
| point_neighbourhood(X102,X100,X101)
| ~ element(X102,powerset(the_carrier(X100)))
| ~ element(X101,the_carrier(X100))
| empty_carrier(X100)
| ~ topological_space(X100)
| ~ top_str(X100) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])]) ).
fof(c_0_71,plain,
! [X108,X109,X110] :
( empty_carrier(X108)
| ~ topological_space(X108)
| ~ top_str(X108)
| ~ element(X109,the_carrier(X108))
| ~ point_neighbourhood(X110,X108,X109)
| element(X110,powerset(the_carrier(X108))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])])]) ).
cnf(c_0_72,negated_conjecture,
( ~ disjoint(esk21_0,interior(esk20_0,X1))
| ~ element(interior(esk20_0,X1),powerset(the_carrier(esk20_0)))
| ~ element(X1,powerset(the_carrier(esk20_0)))
| ~ in(esk22_0,interior(esk20_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_40]),c_0_41])]) ).
cnf(c_0_73,plain,
( disjoint(X1,interior(X2,X3))
| ~ disjoint(X3,X1)
| ~ element(X3,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_69]) ).
cnf(c_0_74,plain,
( in(X3,interior(X2,X1))
| empty_carrier(X2)
| ~ point_neighbourhood(X1,X2,X3)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ element(X3,the_carrier(X2))
| ~ topological_space(X2)
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_75,plain,
( empty_carrier(X1)
| element(X3,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ point_neighbourhood(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( ~ disjoint(X1,esk21_0)
| ~ element(interior(esk20_0,X1),powerset(the_carrier(esk20_0)))
| ~ element(X1,powerset(the_carrier(esk20_0)))
| ~ in(esk22_0,interior(esk20_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_41])]) ).
cnf(c_0_77,plain,
( empty_carrier(X1)
| in(X2,interior(X1,X3))
| ~ point_neighbourhood(X3,X1,X2)
| ~ topological_space(X1)
| ~ element(X2,the_carrier(X1))
| ~ top_str(X1) ),
inference(csr,[status(thm)],[c_0_74,c_0_75]) ).
fof(c_0_78,plain,
! [X103,X104] :
( ~ top_str(X103)
| ~ element(X104,powerset(the_carrier(X103)))
| element(interior(X103,X104),powerset(the_carrier(X103))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_tops_1])]) ).
cnf(c_0_79,negated_conjecture,
( point_neighbourhood(esk23_0,esk20_0,esk22_0)
| ~ in(esk22_0,topstr_closure(esk20_0,esk21_0)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_80,negated_conjecture,
( ~ point_neighbourhood(X1,esk20_0,esk22_0)
| ~ disjoint(X1,esk21_0)
| ~ element(interior(esk20_0,X1),powerset(the_carrier(esk20_0)))
| ~ element(X1,powerset(the_carrier(esk20_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_76,c_0_77]),c_0_40]),c_0_46]),c_0_41])]),c_0_42]) ).
cnf(c_0_81,plain,
( element(interior(X1,X2),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_82,negated_conjecture,
( disjoint(esk23_0,esk21_0)
| ~ in(esk22_0,topstr_closure(esk20_0,esk21_0)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_83,negated_conjecture,
( element(esk23_0,powerset(the_carrier(esk20_0)))
| ~ in(esk22_0,topstr_closure(esk20_0,esk21_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_75,c_0_79]),c_0_40]),c_0_46]),c_0_41])]),c_0_42]) ).
cnf(c_0_84,negated_conjecture,
( ~ point_neighbourhood(X1,esk20_0,esk22_0)
| ~ disjoint(X1,esk21_0)
| ~ element(X1,powerset(the_carrier(esk20_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_41])]) ).
cnf(c_0_85,negated_conjecture,
point_neighbourhood(esk23_0,esk20_0,esk22_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_61])]) ).
cnf(c_0_86,negated_conjecture,
disjoint(esk23_0,esk21_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_61])]) ).
cnf(c_0_87,negated_conjecture,
element(esk23_0,powerset(the_carrier(esk20_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_61])]) ).
cnf(c_0_88,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86]),c_0_87])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU372+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n025.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 03:00:43 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 7.14/4.80 % Version : CSE_E---1.7
% 7.14/4.80 % Problem : theBenchmark.p
% 7.14/4.80 % SZS status Theorem for theBenchmark.p
% 7.14/4.80 % SZS output start CNFRefutation
% See solution above
% 7.14/4.82 % Total time : 3.372s
%------------------------------------------------------------------------------