TSTP Solution File: SEU372+1 by Z3---4.8.9.0

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SEU372+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n029.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 Sep 20 07:29:11 EDT 2022

% Result   : Theorem 5.53s 3.80s
% Output   : Proof 5.67s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU372+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Sep  3 12:57:15 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34  Usage: tptp [options] [-file:]file
% 0.13/0.34    -h, -?       prints this message.
% 0.13/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.34    -m, -model   generate model.
% 0.13/0.34    -p, -proof   generate proof.
% 0.13/0.34    -c, -core    generate unsat core of named formulas.
% 0.13/0.34    -st, -statistics display statistics.
% 0.13/0.34    -t:timeout   set timeout (in second).
% 0.13/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34    -<param>:<value> configuration parameter and value.
% 0.13/0.34    -o:<output-file> file to place output in.
% 5.53/3.80  % SZS status Theorem
% 5.53/3.80  % SZS output start Proof
% 5.53/3.80  tff(disjoint_type, type, (
% 5.53/3.80     disjoint: ( $i * $i ) > $o)).
% 5.53/3.80  tff(tptp_fun_B_19_type, type, (
% 5.53/3.80     tptp_fun_B_19: $i)).
% 5.53/3.80  tff(tptp_fun_E_0_type, type, (
% 5.53/3.80     tptp_fun_E_0: ( $i * $i * $i ) > $i)).
% 5.53/3.80  tff(tptp_fun_A_18_type, type, (
% 5.53/3.80     tptp_fun_A_18: $i)).
% 5.53/3.80  tff(tptp_fun_C_20_type, type, (
% 5.53/3.80     tptp_fun_C_20: $i)).
% 5.53/3.80  tff(in_type, type, (
% 5.53/3.80     in: ( $i * $i ) > $o)).
% 5.53/3.80  tff(open_subset_type, type, (
% 5.53/3.80     open_subset: ( $i * $i ) > $o)).
% 5.53/3.80  tff(element_type, type, (
% 5.53/3.80     element: ( $i * $i ) > $o)).
% 5.53/3.80  tff(powerset_type, type, (
% 5.53/3.80     powerset: $i > $i)).
% 5.53/3.80  tff(the_carrier_type, type, (
% 5.53/3.80     the_carrier: $i > $i)).
% 5.53/3.80  tff(topstr_closure_type, type, (
% 5.53/3.80     topstr_closure: ( $i * $i ) > $i)).
% 5.53/3.80  tff(point_neighbourhood_type, type, (
% 5.53/3.80     point_neighbourhood: ( $i * $i * $i ) > $o)).
% 5.53/3.80  tff(tptp_fun_D_21_type, type, (
% 5.53/3.80     tptp_fun_D_21: $i)).
% 5.53/3.80  tff(top_str_type, type, (
% 5.53/3.80     top_str: $i > $o)).
% 5.53/3.80  tff(topological_space_type, type, (
% 5.53/3.80     topological_space: $i > $o)).
% 5.53/3.80  tff(empty_carrier_type, type, (
% 5.53/3.80     empty_carrier: $i > $o)).
% 5.53/3.80  tff(tptp_fun_D_1_type, type, (
% 5.53/3.80     tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 5.53/3.80  tff(tptp_fun_E_2_type, type, (
% 5.53/3.80     tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 5.53/3.80  tff(empty_type, type, (
% 5.53/3.80     empty: $i > $o)).
% 5.53/3.80  tff(one_sorted_str_type, type, (
% 5.53/3.80     one_sorted_str: $i > $o)).
% 5.53/3.80  tff(interior_type, type, (
% 5.53/3.80     interior: ( $i * $i ) > $i)).
% 5.53/3.80  tff(subset_type, type, (
% 5.53/3.80     subset: ( $i * $i ) > $o)).
% 5.53/3.80  tff(1,plain,
% 5.53/3.80      ((((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18)) & (element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))) <=> ((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18) & element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 5.53/3.80      inference(rewrite,[status(thm)],[])).
% 5.53/3.80  tff(2,plain,
% 5.53/3.80      ((element(B!19, powerset(the_carrier(A!18))) & (element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))) <=> (element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 5.53/3.80      inference(rewrite,[status(thm)],[])).
% 5.53/3.80  tff(3,plain,
% 5.53/3.80      ((element(C!20, the_carrier(A!18)) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))) <=> (element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 5.53/3.80      inference(rewrite,[status(thm)],[])).
% 5.53/3.80  tff(4,plain,
% 5.53/3.80      ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) <=> (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20))))),
% 5.53/3.80      inference(rewrite,[status(thm)],[])).
% 5.53/3.80  tff(5,plain,
% 5.53/3.80      (((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))) <=> ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 5.53/3.81      inference(monotonicity,[status(thm)],[4])).
% 5.53/3.81  tff(6,plain,
% 5.53/3.81      ((~(~element(C!20, the_carrier(A!18)))) <=> element(C!20, the_carrier(A!18))),
% 5.53/3.81      inference(rewrite,[status(thm)],[])).
% 5.53/3.81  tff(7,plain,
% 5.53/3.81      (((~(~element(C!20, the_carrier(A!18)))) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))) <=> (element(C!20, the_carrier(A!18)) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))))),
% 5.53/3.81      inference(monotonicity,[status(thm)],[6, 5])).
% 5.53/3.81  tff(8,plain,
% 5.53/3.81      (((~(~element(C!20, the_carrier(A!18)))) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))) <=> (element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 5.53/3.81      inference(transitivity,[status(thm)],[7, 3])).
% 5.53/3.81  tff(9,plain,
% 5.53/3.81      ((~(~element(B!19, powerset(the_carrier(A!18))))) <=> element(B!19, powerset(the_carrier(A!18)))),
% 5.53/3.81      inference(rewrite,[status(thm)],[])).
% 5.53/3.81  tff(10,plain,
% 5.53/3.81      (((~(~element(B!19, powerset(the_carrier(A!18))))) & ((~(~element(C!20, the_carrier(A!18)))) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))))) <=> (element(B!19, powerset(the_carrier(A!18))) & (element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))))),
% 5.53/3.81      inference(monotonicity,[status(thm)],[9, 8])).
% 5.53/3.81  tff(11,plain,
% 5.53/3.81      (((~(~element(B!19, powerset(the_carrier(A!18))))) & ((~(~element(C!20, the_carrier(A!18)))) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))))) <=> (element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 5.53/3.81      inference(transitivity,[status(thm)],[10, 2])).
% 5.53/3.81  tff(12,plain,
% 5.53/3.81      ((~(~((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18)))) <=> ((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18))),
% 5.53/3.81      inference(rewrite,[status(thm)],[])).
% 5.53/3.81  tff(13,plain,
% 5.53/3.81      (((~(~((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18)))) & ((~(~element(B!19, powerset(the_carrier(A!18))))) & ((~(~element(C!20, the_carrier(A!18)))) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))))) <=> (((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18)) & (element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))))),
% 5.67/3.81      inference(monotonicity,[status(thm)],[12, 11])).
% 5.67/3.81  tff(14,plain,
% 5.67/3.81      (((~(~((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18)))) & ((~(~element(B!19, powerset(the_carrier(A!18))))) & ((~(~element(C!20, the_carrier(A!18)))) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))))) <=> ((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18) & element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 5.67/3.81      inference(transitivity,[status(thm)],[13, 1])).
% 5.67/3.81  tff(15,plain,
% 5.67/3.81      ((~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C))))))))),
% 5.67/3.81      inference(rewrite,[status(thm)],[])).
% 5.67/3.81  tff(16,plain,
% 5.67/3.81      ((~![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (point_neighbourhood(D, A, C) => (~disjoint(D, B)))))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C))))))))),
% 5.67/3.81      inference(rewrite,[status(thm)],[])).
% 5.67/3.81  tff(17,axiom,(~![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (point_neighbourhood(D, A, C) => (~disjoint(D, B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t6_yellow_6')).
% 5.67/3.81  tff(18,plain,
% 5.67/3.81      (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[17, 16])).
% 5.67/3.81  tff(19,plain,
% 5.67/3.81      (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[18, 15])).
% 5.67/3.81  tff(20,plain,
% 5.67/3.81      (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[19, 15])).
% 5.67/3.81  tff(21,plain,
% 5.67/3.81      (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[20, 15])).
% 5.67/3.81  tff(22,plain,
% 5.67/3.81      (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[21, 15])).
% 5.67/3.81  tff(23,plain,
% 5.67/3.81      (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[22, 15])).
% 5.67/3.81  tff(24,plain,
% 5.67/3.81      (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[23, 15])).
% 5.67/3.81  tff(25,plain,
% 5.67/3.81      ((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18) & element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[24, 14])).
% 5.67/3.81  tff(26,plain,
% 5.67/3.81      (element(B!19, powerset(the_carrier(A!18)))),
% 5.67/3.81      inference(and_elim,[status(thm)],[25])).
% 5.67/3.81  tff(27,plain,
% 5.67/3.81      (top_str(A!18)),
% 5.67/3.81      inference(and_elim,[status(thm)],[25])).
% 5.67/3.81  tff(28,plain,
% 5.67/3.81      (^[A: $i, B: $i] : refl((element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))))),
% 5.67/3.81      inference(bind,[status(th)],[])).
% 5.67/3.81  tff(29,plain,
% 5.67/3.81      (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> ![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 5.67/3.81      inference(quant_intro,[status(thm)],[28])).
% 5.67/3.81  tff(30,plain,
% 5.67/3.81      (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((top_str(A) & element(B, powerset(the_carrier(A)))) <=> (~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))), ((~(top_str(A) & element(B, powerset(the_carrier(A))))) <=> (~(~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))))), rewrite((~(~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))) <=> ((~top_str(A)) | (~element(B, powerset(the_carrier(A)))))), ((~(top_str(A) & element(B, powerset(the_carrier(A))))) <=> ((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))), (((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> (((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))))), rewrite((((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))), (((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))))),
% 5.67/3.81      inference(bind,[status(th)],[])).
% 5.67/3.81  tff(31,plain,
% 5.67/3.81      (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 5.67/3.81      inference(quant_intro,[status(thm)],[30])).
% 5.67/3.81  tff(32,plain,
% 5.67/3.81      (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 5.67/3.81      inference(rewrite,[status(thm)],[])).
% 5.67/3.81  tff(33,plain,
% 5.67/3.81      (^[A: $i, B: $i] : rewrite(((top_str(A) & element(B, powerset(the_carrier(A)))) => element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))))),
% 5.67/3.81      inference(bind,[status(th)],[])).
% 5.67/3.81  tff(34,plain,
% 5.67/3.81      (![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 5.67/3.81      inference(quant_intro,[status(thm)],[33])).
% 5.67/3.81  tff(35,axiom,(![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(topstr_closure(A, B), powerset(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_pre_topc')).
% 5.67/3.81  tff(36,plain,
% 5.67/3.81      (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[35, 34])).
% 5.67/3.81  tff(37,plain,
% 5.67/3.81      (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[36, 32])).
% 5.67/3.81  tff(38,plain,(
% 5.67/3.81      ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 5.67/3.81      inference(skolemize,[status(sab)],[37])).
% 5.67/3.81  tff(39,plain,
% 5.67/3.81      (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[38, 31])).
% 5.67/3.81  tff(40,plain,
% 5.67/3.81      (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[39, 29])).
% 5.67/3.81  tff(41,plain,
% 5.67/3.81      (((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)) | element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)) | element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))))),
% 5.67/3.81      inference(rewrite,[status(thm)],[])).
% 5.67/3.81  tff(42,plain,
% 5.67/3.81      ((element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18))) <=> ((~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)) | element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))))),
% 5.67/3.81      inference(rewrite,[status(thm)],[])).
% 5.67/3.81  tff(43,plain,
% 5.67/3.81      (((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)) | element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))))),
% 5.67/3.81      inference(monotonicity,[status(thm)],[42])).
% 5.67/3.81  tff(44,plain,
% 5.67/3.81      (((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)) | element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))))),
% 5.67/3.81      inference(transitivity,[status(thm)],[43, 41])).
% 5.67/3.81  tff(45,plain,
% 5.67/3.81      ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)))),
% 5.67/3.81      inference(quant_inst,[status(thm)],[])).
% 5.67/3.81  tff(46,plain,
% 5.67/3.81      ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)) | element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))),
% 5.67/3.81      inference(modus_ponens,[status(thm)],[45, 44])).
% 5.67/3.81  tff(47,plain,
% 5.67/3.81      (element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))),
% 5.67/3.81      inference(unit_resolution,[status(thm)],[46, 40, 27, 26])).
% 5.67/3.81  tff(48,plain,
% 5.67/3.81      (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)))))))))))))))),
% 5.67/3.81      inference(bind,[status(th)],[])).
% 5.67/3.81  tff(49,plain,
% 5.67/3.81      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))))))))))))),
% 5.67/3.81      inference(quant_intro,[status(thm)],[48])).
% 5.67/3.81  tff(50,plain,
% 5.67/3.81      (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))))),
% 5.67/3.81      inference(bind,[status(th)],[])).
% 5.67/3.81  tff(51,plain,
% 5.67/3.81      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 5.67/3.81      inference(quant_intro,[status(thm)],[50])).
% 5.67/3.81  tff(52,plain,
% 5.67/3.81      (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))))),
% 5.67/3.81      inference(bind,[status(th)],[])).
% 5.67/3.81  tff(53,plain,
% 5.67/3.81      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 5.67/3.81      inference(quant_intro,[status(thm)],[52])).
% 5.67/3.81  tff(54,plain,
% 5.67/3.81      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 5.67/3.81      inference(transitivity,[status(thm)],[53, 51])).
% 5.67/3.81  tff(55,plain,
% 5.67/3.81      (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))))),
% 5.67/3.81      inference(bind,[status(th)],[])).
% 5.67/3.81  tff(56,plain,
% 5.67/3.81      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 5.67/3.81      inference(quant_intro,[status(thm)],[55])).
% 5.67/3.81  tff(57,plain,
% 5.67/3.81      (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | ((~(~in(tptp_fun_D_1(C, B, A), the_carrier(A)))) & ((in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A))))))))))))))),
% 5.67/3.81      inference(bind,[status(th)],[])).
% 5.67/3.81  tff(58,plain,
% 5.67/3.81      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | ((~(~in(tptp_fun_D_1(C, B, A), the_carrier(A)))) & ((in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))))))))))))),
% 5.67/3.82      inference(quant_intro,[status(thm)],[57])).
% 5.67/3.82  tff(59,plain,
% 5.67/3.82      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))),
% 5.67/3.82      inference(rewrite,[status(thm)],[])).
% 5.67/3.82  tff(60,plain,
% 5.67/3.82      (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))) <=> ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))), ((element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))) <=> (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))), rewrite((element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))) <=> ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))), ((element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))) <=> ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))), (![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))) <=> ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))))) <=> (element(B, powerset(the_carrier(A))) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))), rewrite((element(B, powerset(the_carrier(A))) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))))),
% 5.67/3.82      inference(bind,[status(th)],[])).
% 5.67/3.82  tff(61,plain,
% 5.67/3.82      (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))),
% 5.67/3.82      inference(quant_intro,[status(thm)],[60])).
% 5.67/3.82  tff(62,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d13_pre_topc')).
% 5.67/3.82  tff(63,plain,
% 5.67/3.82      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))),
% 5.67/3.82      inference(modus_ponens,[status(thm)],[62, 61])).
% 5.67/3.82  tff(64,plain,
% 5.67/3.82      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))),
% 5.67/3.82      inference(modus_ponens,[status(thm)],[63, 59])).
% 5.67/3.82  tff(65,plain,(
% 5.67/3.82      ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | ((~(~in(tptp_fun_D_1(C, B, A), the_carrier(A)))) & ((in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A))))))))))))))),
% 5.67/3.82      inference(skolemize,[status(sab)],[64])).
% 5.67/3.82  tff(66,plain,
% 5.67/3.82      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))))))))))))),
% 5.67/3.82      inference(modus_ponens,[status(thm)],[65, 58])).
% 5.67/3.82  tff(67,plain,
% 5.67/3.82      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 5.67/3.82      inference(modus_ponens,[status(thm)],[66, 56])).
% 5.67/3.82  tff(68,plain,
% 5.67/3.82      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 5.67/3.82      inference(modus_ponens,[status(thm)],[67, 54])).
% 5.67/3.82  tff(69,plain,
% 5.67/3.82      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))))))))))))),
% 5.67/3.82      inference(modus_ponens,[status(thm)],[68, 49])).
% 5.67/3.82  tff(70,plain,
% 5.67/3.82      (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))))))))))))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18)))))))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))))))))))))) | (~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18)))))))))))))))))),
% 5.67/3.82      inference(rewrite,[status(thm)],[])).
% 5.67/3.82  tff(71,plain,
% 5.67/3.82      (((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18)))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)))))))))))))) <=> ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18)))))))))))))))))),
% 5.67/3.82      inference(rewrite,[status(thm)],[])).
% 5.67/3.82  tff(72,plain,
% 5.67/3.82      (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))))))))))))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18)))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))))))))))))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18))))))))))))))))))),
% 5.67/3.82      inference(monotonicity,[status(thm)],[71])).
% 5.67/3.82  tff(73,plain,
% 5.67/3.82      (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))))))))))))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18)))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))))))))))))) | (~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18)))))))))))))))))),
% 5.67/3.82      inference(transitivity,[status(thm)],[72, 70])).
% 5.67/3.82  tff(74,plain,
% 5.67/3.82      ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))))))))))))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18)))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))))))))),
% 5.67/3.82      inference(quant_inst,[status(thm)],[])).
% 5.67/3.82  tff(75,plain,
% 5.67/3.82      ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~disjoint(B, E)) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E))))))))))))))) | (~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18))))))))))))))))),
% 5.67/3.82      inference(modus_ponens,[status(thm)],[74, 73])).
% 5.67/3.82  tff(76,plain,
% 5.67/3.82      (![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18))))))))))))))))),
% 5.67/3.82      inference(unit_resolution,[status(thm)],[75, 69, 27])).
% 5.67/3.82  tff(77,plain,
% 5.67/3.82      (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18))))))))))))))))) | ((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18))))))))))))))))) | (~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))))))))),
% 5.67/3.83      inference(rewrite,[status(thm)],[])).
% 5.67/3.83  tff(78,plain,
% 5.67/3.83      (((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))) <=> ((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))))))))),
% 5.67/3.83      inference(rewrite,[status(thm)],[])).
% 5.67/3.83  tff(79,plain,
% 5.67/3.83      (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18))))))))))))))))) | ((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18))))))))))))))))) | ((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))))),
% 5.67/3.83      inference(monotonicity,[status(thm)],[78])).
% 5.67/3.83  tff(80,plain,
% 5.67/3.83      (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18))))))))))))))))) | ((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18))))))))))))))))) | (~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))))))))),
% 5.67/3.83      inference(transitivity,[status(thm)],[79, 77])).
% 5.67/3.83  tff(81,plain,
% 5.67/3.83      ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18))))))))))))))))) | ((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))))))))),
% 5.67/3.83      inference(quant_inst,[status(thm)],[])).
% 5.67/3.83  tff(82,plain,
% 5.67/3.83      ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18))))))))))))))))) | (~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))),
% 5.67/3.83      inference(modus_ponens,[status(thm)],[81, 80])).
% 5.67/3.83  tff(83,plain,
% 5.67/3.83      (![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))),
% 5.67/3.83      inference(unit_resolution,[status(thm)],[82, 26, 76])).
% 5.67/3.83  tff(84,plain,
% 5.67/3.83      (((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))) | ((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))) | (~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))),
% 5.67/3.84      inference(rewrite,[status(thm)],[])).
% 5.67/3.84  tff(85,plain,
% 5.67/3.84      (((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | (~((~((topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19))) | (~((~element(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), A!18)) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))))))) | (~(in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19)) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), E))))))))) | (~((~(topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))))))) <=> ((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))),
% 5.67/3.84      inference(rewrite,[status(thm)],[])).
% 5.67/3.84  tff(86,plain,
% 5.67/3.84      (((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))) | ((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | (~((~((topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19))) | (~((~element(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), A!18)) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))))))) | (~(in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19)) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), E))))))))) | (~((~(topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))) | ((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))))),
% 5.67/3.84      inference(monotonicity,[status(thm)],[85])).
% 5.67/3.84  tff(87,plain,
% 5.67/3.84      (((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))) | ((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | (~((~((topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19))) | (~((~element(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), A!18)) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))))))) | (~(in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19)) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), E))))))))) | (~((~(topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))) | (~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))),
% 5.67/3.84      inference(transitivity,[status(thm)],[86, 84])).
% 5.67/3.84  tff(88,plain,
% 5.67/3.84      ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))) | ((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | (~((~((topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19))) | (~((~element(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), A!18)) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))))))) | (~(in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19)) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), E))))))))) | (~((~(topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))),
% 5.67/3.84      inference(quant_inst,[status(thm)],[])).
% 5.67/3.84  tff(89,plain,
% 5.67/3.84      ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))) | (~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18)))))))))))))))) | (~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[88, 87])).
% 5.67/3.84  tff(90,plain,
% 5.67/3.84      (![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))),
% 5.67/3.84      inference(unit_resolution,[status(thm)],[89, 83, 47])).
% 5.67/3.84  tff(91,plain,
% 5.67/3.84      (^[A: $i] : refl((one_sorted_str(A) | (~top_str(A))) <=> (one_sorted_str(A) | (~top_str(A))))),
% 5.67/3.84      inference(bind,[status(th)],[])).
% 5.67/3.84  tff(92,plain,
% 5.67/3.84      (![A: $i] : (one_sorted_str(A) | (~top_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 5.67/3.84      inference(quant_intro,[status(thm)],[91])).
% 5.67/3.84  tff(93,plain,
% 5.67/3.84      (![A: $i] : (one_sorted_str(A) | (~top_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 5.67/3.84      inference(rewrite,[status(thm)],[])).
% 5.67/3.84  tff(94,plain,
% 5.67/3.84      (^[A: $i] : rewrite((top_str(A) => one_sorted_str(A)) <=> (one_sorted_str(A) | (~top_str(A))))),
% 5.67/3.84      inference(bind,[status(th)],[])).
% 5.67/3.84  tff(95,plain,
% 5.67/3.84      (![A: $i] : (top_str(A) => one_sorted_str(A)) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 5.67/3.84      inference(quant_intro,[status(thm)],[94])).
% 5.67/3.84  tff(96,axiom,(![A: $i] : (top_str(A) => one_sorted_str(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 5.67/3.84  tff(97,plain,
% 5.67/3.84      (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[96, 95])).
% 5.67/3.84  tff(98,plain,
% 5.67/3.84      (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[97, 93])).
% 5.67/3.84  tff(99,plain,(
% 5.67/3.84      ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 5.67/3.84      inference(skolemize,[status(sab)],[98])).
% 5.67/3.84  tff(100,plain,
% 5.67/3.84      (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[99, 92])).
% 5.67/3.84  tff(101,plain,
% 5.67/3.84      (((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | (one_sorted_str(A!18) | (~top_str(A!18)))) <=> ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | one_sorted_str(A!18) | (~top_str(A!18)))),
% 5.67/3.84      inference(rewrite,[status(thm)],[])).
% 5.67/3.84  tff(102,plain,
% 5.67/3.84      ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | (one_sorted_str(A!18) | (~top_str(A!18)))),
% 5.67/3.84      inference(quant_inst,[status(thm)],[])).
% 5.67/3.84  tff(103,plain,
% 5.67/3.84      ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | one_sorted_str(A!18) | (~top_str(A!18))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[102, 101])).
% 5.67/3.84  tff(104,plain,
% 5.67/3.84      (one_sorted_str(A!18)),
% 5.67/3.84      inference(unit_resolution,[status(thm)],[103, 100, 27])).
% 5.67/3.84  tff(105,plain,
% 5.67/3.84      (~empty_carrier(A!18)),
% 5.67/3.84      inference(and_elim,[status(thm)],[25])).
% 5.67/3.84  tff(106,plain,
% 5.67/3.84      (^[A: $i] : refl((empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))))),
% 5.67/3.84      inference(bind,[status(th)],[])).
% 5.67/3.84  tff(107,plain,
% 5.67/3.84      (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 5.67/3.84      inference(quant_intro,[status(thm)],[106])).
% 5.67/3.84  tff(108,plain,
% 5.67/3.84      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & one_sorted_str(A)) <=> (~(empty_carrier(A) | (~one_sorted_str(A))))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (~(~(empty_carrier(A) | (~one_sorted_str(A))))))), rewrite((~(~(empty_carrier(A) | (~one_sorted_str(A))))) <=> (empty_carrier(A) | (~one_sorted_str(A)))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (empty_carrier(A) | (~one_sorted_str(A))))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))))), rewrite(((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))))),
% 5.67/3.84      inference(bind,[status(th)],[])).
% 5.67/3.84  tff(109,plain,
% 5.67/3.84      (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 5.67/3.84      inference(quant_intro,[status(thm)],[108])).
% 5.67/3.84  tff(110,plain,
% 5.67/3.84      (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 5.67/3.84      inference(rewrite,[status(thm)],[])).
% 5.67/3.84  tff(111,plain,
% 5.67/3.84      (^[A: $i] : rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))))),
% 5.67/3.84      inference(bind,[status(th)],[])).
% 5.67/3.84  tff(112,plain,
% 5.67/3.84      (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 5.67/3.84      inference(quant_intro,[status(thm)],[111])).
% 5.67/3.84  tff(113,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 5.67/3.84  tff(114,plain,
% 5.67/3.84      (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[113, 112])).
% 5.67/3.84  tff(115,plain,
% 5.67/3.84      (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[114, 110])).
% 5.67/3.84  tff(116,plain,(
% 5.67/3.84      ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 5.67/3.84      inference(skolemize,[status(sab)],[115])).
% 5.67/3.84  tff(117,plain,
% 5.67/3.84      (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[116, 109])).
% 5.67/3.84  tff(118,plain,
% 5.67/3.84      (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[117, 107])).
% 5.67/3.84  tff(119,plain,
% 5.67/3.84      (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!18) | (~one_sorted_str(A!18)) | (~empty(the_carrier(A!18))))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!18) | (~one_sorted_str(A!18)) | (~empty(the_carrier(A!18))))),
% 5.67/3.84      inference(rewrite,[status(thm)],[])).
% 5.67/3.84  tff(120,plain,
% 5.67/3.84      ((empty_carrier(A!18) | (~empty(the_carrier(A!18))) | (~one_sorted_str(A!18))) <=> (empty_carrier(A!18) | (~one_sorted_str(A!18)) | (~empty(the_carrier(A!18))))),
% 5.67/3.84      inference(rewrite,[status(thm)],[])).
% 5.67/3.84  tff(121,plain,
% 5.67/3.84      (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!18) | (~empty(the_carrier(A!18))) | (~one_sorted_str(A!18)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!18) | (~one_sorted_str(A!18)) | (~empty(the_carrier(A!18)))))),
% 5.67/3.84      inference(monotonicity,[status(thm)],[120])).
% 5.67/3.84  tff(122,plain,
% 5.67/3.84      (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!18) | (~empty(the_carrier(A!18))) | (~one_sorted_str(A!18)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!18) | (~one_sorted_str(A!18)) | (~empty(the_carrier(A!18))))),
% 5.67/3.84      inference(transitivity,[status(thm)],[121, 119])).
% 5.67/3.84  tff(123,plain,
% 5.67/3.84      ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!18) | (~empty(the_carrier(A!18))) | (~one_sorted_str(A!18)))),
% 5.67/3.84      inference(quant_inst,[status(thm)],[])).
% 5.67/3.84  tff(124,plain,
% 5.67/3.84      ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!18) | (~one_sorted_str(A!18)) | (~empty(the_carrier(A!18)))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[123, 122])).
% 5.67/3.84  tff(125,plain,
% 5.67/3.84      (~empty(the_carrier(A!18))),
% 5.67/3.84      inference(unit_resolution,[status(thm)],[124, 118, 105, 104])).
% 5.67/3.84  tff(126,plain,
% 5.67/3.84      (element(C!20, the_carrier(A!18))),
% 5.67/3.84      inference(and_elim,[status(thm)],[25])).
% 5.67/3.84  tff(127,plain,
% 5.67/3.84      (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 5.67/3.84      inference(bind,[status(th)],[])).
% 5.67/3.84  tff(128,plain,
% 5.67/3.84      (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 5.67/3.84      inference(quant_intro,[status(thm)],[127])).
% 5.67/3.84  tff(129,plain,
% 5.67/3.84      (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 5.67/3.84      inference(rewrite,[status(thm)],[])).
% 5.67/3.84  tff(130,plain,
% 5.67/3.84      (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 5.67/3.84      inference(bind,[status(th)],[])).
% 5.67/3.84  tff(131,plain,
% 5.67/3.84      (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 5.67/3.84      inference(quant_intro,[status(thm)],[130])).
% 5.67/3.84  tff(132,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 5.67/3.84  tff(133,plain,
% 5.67/3.84      (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[132, 131])).
% 5.67/3.84  tff(134,plain,
% 5.67/3.84      (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[133, 129])).
% 5.67/3.84  tff(135,plain,(
% 5.67/3.84      ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 5.67/3.84      inference(skolemize,[status(sab)],[134])).
% 5.67/3.84  tff(136,plain,
% 5.67/3.84      (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 5.67/3.84      inference(modus_ponens,[status(thm)],[135, 128])).
% 5.67/3.84  tff(137,plain,
% 5.67/3.84      (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(C!20, the_carrier(A!18))) | empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(C!20, the_carrier(A!18))) | empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)))),
% 5.67/3.85      inference(rewrite,[status(thm)],[])).
% 5.67/3.85  tff(138,plain,
% 5.67/3.85      ((empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)) | (~element(C!20, the_carrier(A!18)))) <=> ((~element(C!20, the_carrier(A!18))) | empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)))),
% 5.67/3.85      inference(rewrite,[status(thm)],[])).
% 5.67/3.85  tff(139,plain,
% 5.67/3.85      (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)) | (~element(C!20, the_carrier(A!18))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(C!20, the_carrier(A!18))) | empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18))))),
% 5.67/3.85      inference(monotonicity,[status(thm)],[138])).
% 5.67/3.85  tff(140,plain,
% 5.67/3.85      (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)) | (~element(C!20, the_carrier(A!18))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(C!20, the_carrier(A!18))) | empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)))),
% 5.67/3.85      inference(transitivity,[status(thm)],[139, 137])).
% 5.67/3.85  tff(141,plain,
% 5.67/3.85      ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)) | (~element(C!20, the_carrier(A!18))))),
% 5.67/3.85      inference(quant_inst,[status(thm)],[])).
% 5.67/3.85  tff(142,plain,
% 5.67/3.85      ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(C!20, the_carrier(A!18))) | empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18))),
% 5.67/3.85      inference(modus_ponens,[status(thm)],[141, 140])).
% 5.67/3.85  tff(143,plain,
% 5.67/3.85      (in(C!20, the_carrier(A!18))),
% 5.67/3.85      inference(unit_resolution,[status(thm)],[142, 136, 126, 125])).
% 5.67/3.85  tff(144,plain,
% 5.67/3.85      (((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))) | ((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))))))))))) <=> ((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))) | (~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))))))))))),
% 5.67/3.85      inference(rewrite,[status(thm)],[])).
% 5.67/3.85  tff(145,plain,
% 5.67/3.85      (((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(C!20, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))))))))) <=> ((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))))))))))),
% 5.67/3.85      inference(rewrite,[status(thm)],[])).
% 5.67/3.85  tff(146,plain,
% 5.67/3.85      (((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))) | ((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(C!20, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))))))))))) <=> ((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))) | ((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))))))))))),
% 5.67/3.85      inference(monotonicity,[status(thm)],[145])).
% 5.67/3.85  tff(147,plain,
% 5.67/3.85      (((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))) | ((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(C!20, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))))))))))) <=> ((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))) | (~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))))))))))),
% 5.67/3.85      inference(transitivity,[status(thm)],[146, 144])).
% 5.67/3.85  tff(148,plain,
% 5.67/3.85      ((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))) | ((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(C!20, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))))))))))),
% 5.67/3.85      inference(quant_inst,[status(thm)],[])).
% 5.67/3.85  tff(149,plain,
% 5.67/3.85      ((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))))))))))) | (~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))))))))),
% 5.67/3.85      inference(modus_ponens,[status(thm)],[148, 147])).
% 5.67/3.85  tff(150,plain,
% 5.67/3.85      (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))))))))),
% 5.67/3.85      inference(unit_resolution,[status(thm)],[149, 143, 90])).
% 5.67/3.85  tff(151,plain,
% 5.67/3.85      (((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))))))) | (in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))))))),
% 5.67/3.85      inference(tautology,[status(thm)],[])).
% 5.67/3.85  tff(152,plain,
% 5.67/3.85      (in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))))),
% 5.67/3.85      inference(unit_resolution,[status(thm)],[151, 150])).
% 5.67/3.85  tff(153,assumption,(~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))), introduced(assumption)).
% 5.67/3.85  tff(154,plain,
% 5.67/3.85      (((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))) | point_neighbourhood(D!21, A!18, C!20)),
% 5.67/3.85      inference(tautology,[status(thm)],[])).
% 5.67/3.85  tff(155,plain,
% 5.67/3.85      (point_neighbourhood(D!21, A!18, C!20)),
% 5.67/3.85      inference(unit_resolution,[status(thm)],[154, 153])).
% 5.67/3.85  tff(156,plain,
% 5.67/3.85      (((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))) | disjoint(D!21, B!19)),
% 5.67/3.85      inference(tautology,[status(thm)],[])).
% 5.67/3.85  tff(157,plain,
% 5.67/3.85      (disjoint(D!21, B!19)),
% 5.67/3.85      inference(unit_resolution,[status(thm)],[156, 153])).
% 5.67/3.85  tff(158,plain,
% 5.67/3.85      (topological_space(A!18)),
% 5.67/3.85      inference(and_elim,[status(thm)],[25])).
% 5.67/3.85  tff(159,plain,
% 5.67/3.85      (^[A: $i, B: $i] : rewrite((empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))))),
% 5.67/3.85      inference(bind,[status(th)],[])).
% 5.67/3.85  tff(160,plain,
% 5.67/3.85      (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 5.67/3.85      inference(quant_intro,[status(thm)],[159])).
% 5.67/3.85  tff(161,plain,
% 5.67/3.85      (^[A: $i, B: $i] : refl((empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))))),
% 5.67/3.85      inference(bind,[status(th)],[])).
% 5.67/3.85  tff(162,plain,
% 5.67/3.85      (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 5.67/3.85      inference(quant_intro,[status(thm)],[161])).
% 5.67/3.85  tff(163,plain,
% 5.67/3.85      (^[A: $i, B: $i] : rewrite((empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))))),
% 5.67/3.85      inference(bind,[status(th)],[])).
% 5.67/3.85  tff(164,plain,
% 5.67/3.85      (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 5.67/3.85      inference(quant_intro,[status(thm)],[163])).
% 5.67/3.85  tff(165,plain,
% 5.67/3.85      (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 5.67/3.85      inference(transitivity,[status(thm)],[164, 162])).
% 5.67/3.85  tff(166,plain,
% 5.67/3.85      (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A))) <=> (~(empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A))))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) <=> (~(~(empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A))))))), rewrite((~(~(empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A))))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))) <=> ((empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))))), rewrite(((empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))))),
% 5.67/3.85      inference(bind,[status(th)],[])).
% 5.67/3.85  tff(167,plain,
% 5.67/3.85      (![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))) <=> ![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 5.67/3.85      inference(quant_intro,[status(thm)],[166])).
% 5.67/3.85  tff(168,plain,
% 5.67/3.85      (![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 5.67/3.85      inference(rewrite,[status(thm)],[])).
% 5.67/3.85  tff(169,plain,
% 5.67/3.85      (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & element(B, the_carrier(A))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A)) & element(B, the_carrier(A))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A))))), quant_intro(proof_bind(^[C: $i] : rewrite((point_neighbourhood(C, A, B) => element(C, powerset(the_carrier(A)))) <=> ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))), (![C: $i] : (point_neighbourhood(C, A, B) => element(C, powerset(the_carrier(A)))) <=> ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))), ((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & element(B, the_carrier(A))) => ![C: $i] : (point_neighbourhood(C, A, B) => element(C, powerset(the_carrier(A))))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A))) => ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A))) => ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))), ((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & element(B, the_carrier(A))) => ![C: $i] : (point_neighbourhood(C, A, B) => element(C, powerset(the_carrier(A))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))))),
% 5.67/3.85      inference(bind,[status(th)],[])).
% 5.67/3.85  tff(170,plain,
% 5.67/3.85      (![A: $i, B: $i] : (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & element(B, the_carrier(A))) => ![C: $i] : (point_neighbourhood(C, A, B) => element(C, powerset(the_carrier(A))))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 5.67/3.85      inference(quant_intro,[status(thm)],[169])).
% 5.67/3.85  tff(171,axiom,(![A: $i, B: $i] : (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & element(B, the_carrier(A))) => ![C: $i] : (point_neighbourhood(C, A, B) => element(C, powerset(the_carrier(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_connsp_2')).
% 5.67/3.85  tff(172,plain,
% 5.67/3.85      (![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 5.67/3.85      inference(modus_ponens,[status(thm)],[171, 170])).
% 5.67/3.85  tff(173,plain,
% 5.67/3.85      (![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 5.67/3.85      inference(modus_ponens,[status(thm)],[172, 168])).
% 5.67/3.85  tff(174,plain,(
% 5.67/3.85      ![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 5.67/3.85      inference(skolemize,[status(sab)],[173])).
% 5.67/3.85  tff(175,plain,
% 5.67/3.85      (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 5.67/3.85      inference(modus_ponens,[status(thm)],[174, 167])).
% 5.67/3.85  tff(176,plain,
% 5.67/3.85      (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 5.67/3.85      inference(modus_ponens,[status(thm)],[175, 165])).
% 5.67/3.85  tff(177,plain,
% 5.67/3.85      (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 5.67/3.85      inference(modus_ponens,[status(thm)],[176, 160])).
% 5.67/3.85  tff(178,plain,
% 5.67/3.85      (((~![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))) | (empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~top_str(A!18)) | (~topological_space(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18)))))) <=> ((~![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))) | empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~top_str(A!18)) | (~topological_space(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18)))))),
% 5.67/3.85      inference(rewrite,[status(thm)],[])).
% 5.67/3.85  tff(179,plain,
% 5.67/3.85      ((~![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))) | (empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~top_str(A!18)) | (~topological_space(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18)))))),
% 5.67/3.85      inference(quant_inst,[status(thm)],[])).
% 5.67/3.85  tff(180,plain,
% 5.67/3.85      ((~![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))) | empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~top_str(A!18)) | (~topological_space(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))),
% 5.67/3.85      inference(modus_ponens,[status(thm)],[179, 178])).
% 5.67/3.85  tff(181,plain,
% 5.67/3.85      (![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))),
% 5.67/3.85      inference(unit_resolution,[status(thm)],[180, 177, 105, 158, 27, 126])).
% 5.67/3.85  tff(182,plain,
% 5.67/3.85      (((~![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))) | ((~point_neighbourhood(D!21, A!18, C!20)) | element(D!21, powerset(the_carrier(A!18))))) <=> ((~![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))) | (~point_neighbourhood(D!21, A!18, C!20)) | element(D!21, powerset(the_carrier(A!18))))),
% 5.67/3.85      inference(rewrite,[status(thm)],[])).
% 5.67/3.85  tff(183,plain,
% 5.67/3.85      ((~![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))) | ((~point_neighbourhood(D!21, A!18, C!20)) | element(D!21, powerset(the_carrier(A!18))))),
% 5.67/3.85      inference(quant_inst,[status(thm)],[])).
% 5.67/3.85  tff(184,plain,
% 5.67/3.85      ((~![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))) | (~point_neighbourhood(D!21, A!18, C!20)) | element(D!21, powerset(the_carrier(A!18)))),
% 5.67/3.85      inference(modus_ponens,[status(thm)],[183, 182])).
% 5.67/3.85  tff(185,plain,
% 5.67/3.85      (element(D!21, powerset(the_carrier(A!18)))),
% 5.67/3.85      inference(unit_resolution,[status(thm)],[184, 155, 181])).
% 5.67/3.85  tff(186,plain,
% 5.67/3.85      (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))))),
% 5.67/3.85      inference(bind,[status(th)],[])).
% 5.67/3.85  tff(187,plain,
% 5.67/3.85      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 5.67/3.85      inference(quant_intro,[status(thm)],[186])).
% 5.67/3.85  tff(188,plain,
% 5.67/3.85      (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))))),
% 5.67/3.85      inference(bind,[status(th)],[])).
% 5.67/3.85  tff(189,plain,
% 5.67/3.85      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 5.67/3.85      inference(quant_intro,[status(thm)],[188])).
% 5.67/3.85  tff(190,plain,
% 5.67/3.85      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 5.67/3.85      inference(transitivity,[status(thm)],[189, 187])).
% 5.67/3.85  tff(191,plain,
% 5.67/3.85      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 5.67/3.85      inference(rewrite,[status(thm)],[])).
% 5.67/3.85  tff(192,plain,
% 5.67/3.85      (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => subset(interior(A, B), B)) <=> ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))), (![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B)) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))))),
% 5.67/3.85      inference(bind,[status(th)],[])).
% 5.67/3.85  tff(193,plain,
% 5.67/3.85      (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 5.67/3.85      inference(quant_intro,[status(thm)],[192])).
% 5.67/3.85  tff(194,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t44_tops_1')).
% 5.67/3.85  tff(195,plain,
% 5.67/3.85      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 5.67/3.85      inference(modus_ponens,[status(thm)],[194, 193])).
% 5.67/3.85  tff(196,plain,
% 5.67/3.85      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 5.67/3.85      inference(modus_ponens,[status(thm)],[195, 191])).
% 5.67/3.85  tff(197,plain,(
% 5.67/3.85      ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 5.67/3.85      inference(skolemize,[status(sab)],[196])).
% 5.67/3.85  tff(198,plain,
% 5.67/3.85      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 5.67/3.85      inference(modus_ponens,[status(thm)],[197, 190])).
% 5.67/3.85  tff(199,plain,
% 5.67/3.85      (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B)))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))) | (~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B)))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(200,plain,
% 5.67/3.86      ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B)))),
% 5.67/3.86      inference(quant_inst,[status(thm)],[])).
% 5.67/3.86  tff(201,plain,
% 5.67/3.86      ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))) | (~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[200, 199])).
% 5.67/3.86  tff(202,plain,
% 5.67/3.86      (![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B))),
% 5.67/3.86      inference(unit_resolution,[status(thm)],[201, 198, 27])).
% 5.67/3.86  tff(203,plain,
% 5.67/3.86      (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B))) | ((~element(D!21, powerset(the_carrier(A!18)))) | subset(interior(A!18, D!21), D!21))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B))) | (~element(D!21, powerset(the_carrier(A!18)))) | subset(interior(A!18, D!21), D!21))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(204,plain,
% 5.67/3.86      ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B))) | ((~element(D!21, powerset(the_carrier(A!18)))) | subset(interior(A!18, D!21), D!21))),
% 5.67/3.86      inference(quant_inst,[status(thm)],[])).
% 5.67/3.86  tff(205,plain,
% 5.67/3.86      ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B))) | (~element(D!21, powerset(the_carrier(A!18)))) | subset(interior(A!18, D!21), D!21)),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[204, 203])).
% 5.67/3.86  tff(206,plain,
% 5.67/3.86      (subset(interior(A!18, D!21), D!21)),
% 5.67/3.86      inference(unit_resolution,[status(thm)],[205, 202, 185])).
% 5.67/3.86  tff(207,assumption,(~disjoint(interior(A!18, D!21), B!19)), introduced(assumption)).
% 5.67/3.86  tff(208,assumption,(subset(interior(A!18, D!21), D!21)), introduced(assumption)).
% 5.67/3.86  tff(209,assumption,(disjoint(D!21, B!19)), introduced(assumption)).
% 5.67/3.86  tff(210,plain,
% 5.67/3.86      (^[A: $i, B: $i, C: $i] : refl((disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B))) <=> (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(211,plain,
% 5.67/3.86      (![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[210])).
% 5.67/3.86  tff(212,plain,
% 5.67/3.86      (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & disjoint(B, C)) <=> (~((~disjoint(B, C)) | (~subset(A, B))))), ((~(subset(A, B) & disjoint(B, C))) <=> (~(~((~disjoint(B, C)) | (~subset(A, B))))))), rewrite((~(~((~disjoint(B, C)) | (~subset(A, B))))) <=> ((~disjoint(B, C)) | (~subset(A, B)))), ((~(subset(A, B) & disjoint(B, C))) <=> ((~disjoint(B, C)) | (~subset(A, B))))), (((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)) <=> (((~disjoint(B, C)) | (~subset(A, B))) | disjoint(A, C)))), rewrite((((~disjoint(B, C)) | (~subset(A, B))) | disjoint(A, C)) <=> (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))), (((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)) <=> (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(213,plain,
% 5.67/3.86      (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)) <=> ![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[212])).
% 5.67/3.86  tff(214,plain,
% 5.67/3.86      (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(215,plain,
% 5.67/3.86      (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & disjoint(B, C)) => disjoint(A, C)) <=> ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(216,plain,
% 5.67/3.86      (![A: $i, B: $i, C: $i] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[215])).
% 5.67/3.86  tff(217,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t63_xboole_1')).
% 5.67/3.86  tff(218,plain,
% 5.67/3.86      (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[217, 216])).
% 5.67/3.86  tff(219,plain,
% 5.67/3.86      (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[218, 214])).
% 5.67/3.86  tff(220,plain,(
% 5.67/3.86      ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 5.67/3.86      inference(skolemize,[status(sab)],[219])).
% 5.67/3.86  tff(221,plain,
% 5.67/3.86      (![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[220, 213])).
% 5.67/3.86  tff(222,plain,
% 5.67/3.86      (![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[221, 211])).
% 5.67/3.86  tff(223,plain,
% 5.67/3.86      (((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | ((~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)) | disjoint(interior(A!18, D!21), B!19))) <=> ((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)) | disjoint(interior(A!18, D!21), B!19))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(224,plain,
% 5.67/3.86      ((disjoint(interior(A!18, D!21), B!19) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21))) <=> ((~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)) | disjoint(interior(A!18, D!21), B!19))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(225,plain,
% 5.67/3.86      (((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | (disjoint(interior(A!18, D!21), B!19) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)))) <=> ((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | ((~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)) | disjoint(interior(A!18, D!21), B!19)))),
% 5.67/3.86      inference(monotonicity,[status(thm)],[224])).
% 5.67/3.86  tff(226,plain,
% 5.67/3.86      (((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | (disjoint(interior(A!18, D!21), B!19) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)))) <=> ((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)) | disjoint(interior(A!18, D!21), B!19))),
% 5.67/3.86      inference(transitivity,[status(thm)],[225, 223])).
% 5.67/3.86  tff(227,plain,
% 5.67/3.86      ((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | (disjoint(interior(A!18, D!21), B!19) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)))),
% 5.67/3.86      inference(quant_inst,[status(thm)],[])).
% 5.67/3.86  tff(228,plain,
% 5.67/3.86      ((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)) | disjoint(interior(A!18, D!21), B!19)),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[227, 226])).
% 5.67/3.86  tff(229,plain,
% 5.67/3.86      ($false),
% 5.67/3.86      inference(unit_resolution,[status(thm)],[228, 222, 209, 208, 207])).
% 5.67/3.86  tff(230,plain,(disjoint(interior(A!18, D!21), B!19) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21))), inference(lemma,lemma(discharge,[]))).
% 5.67/3.86  tff(231,plain,
% 5.67/3.86      (disjoint(interior(A!18, D!21), B!19)),
% 5.67/3.86      inference(unit_resolution,[status(thm)],[230, 157, 206])).
% 5.67/3.86  tff(232,plain,
% 5.67/3.86      (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(233,plain,
% 5.67/3.86      (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[232])).
% 5.67/3.86  tff(234,plain,
% 5.67/3.86      (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(235,plain,
% 5.67/3.86      (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(236,plain,
% 5.67/3.86      (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[235])).
% 5.67/3.86  tff(237,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 5.67/3.86  tff(238,plain,
% 5.67/3.86      (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[237, 236])).
% 5.67/3.86  tff(239,plain,
% 5.67/3.86      (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[238, 234])).
% 5.67/3.86  tff(240,plain,(
% 5.67/3.86      ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 5.67/3.86      inference(skolemize,[status(sab)],[239])).
% 5.67/3.86  tff(241,plain,
% 5.67/3.86      (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[240, 233])).
% 5.67/3.86  tff(242,plain,
% 5.67/3.86      (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(interior(A!18, D!21), B!19)) | disjoint(B!19, interior(A!18, D!21)))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(interior(A!18, D!21), B!19)) | disjoint(B!19, interior(A!18, D!21)))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(243,plain,
% 5.67/3.86      ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(interior(A!18, D!21), B!19)) | disjoint(B!19, interior(A!18, D!21)))),
% 5.67/3.86      inference(quant_inst,[status(thm)],[])).
% 5.67/3.86  tff(244,plain,
% 5.67/3.86      ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(interior(A!18, D!21), B!19)) | disjoint(B!19, interior(A!18, D!21))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[243, 242])).
% 5.67/3.86  tff(245,plain,
% 5.67/3.86      (disjoint(B!19, interior(A!18, D!21))),
% 5.67/3.86      inference(unit_resolution,[status(thm)],[244, 241, 231])).
% 5.67/3.86  tff(246,plain,
% 5.67/3.86      (^[A: $i, B: $i] : refl((element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(247,plain,
% 5.67/3.86      (![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> ![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[246])).
% 5.67/3.86  tff(248,plain,
% 5.67/3.86      (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((top_str(A) & element(B, powerset(the_carrier(A)))) <=> (~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))), ((~(top_str(A) & element(B, powerset(the_carrier(A))))) <=> (~(~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))))), rewrite((~(~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))) <=> ((~top_str(A)) | (~element(B, powerset(the_carrier(A)))))), ((~(top_str(A) & element(B, powerset(the_carrier(A))))) <=> ((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))), (((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> (((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))))), rewrite((((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))), (((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(249,plain,
% 5.67/3.86      (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[248])).
% 5.67/3.86  tff(250,plain,
% 5.67/3.86      (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(251,plain,
% 5.67/3.86      (^[A: $i, B: $i] : rewrite(((top_str(A) & element(B, powerset(the_carrier(A)))) => element(interior(A, B), powerset(the_carrier(A)))) <=> ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(252,plain,
% 5.67/3.86      (![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(interior(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[251])).
% 5.67/3.86  tff(253,axiom,(![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(interior(A, B), powerset(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_tops_1')).
% 5.67/3.86  tff(254,plain,
% 5.67/3.86      (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[253, 252])).
% 5.67/3.86  tff(255,plain,
% 5.67/3.86      (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[254, 250])).
% 5.67/3.86  tff(256,plain,(
% 5.67/3.86      ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 5.67/3.86      inference(skolemize,[status(sab)],[255])).
% 5.67/3.86  tff(257,plain,
% 5.67/3.86      (![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[256, 249])).
% 5.67/3.86  tff(258,plain,
% 5.67/3.86      (![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[257, 247])).
% 5.67/3.86  tff(259,plain,
% 5.67/3.86      (((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!18)) | (~element(D!21, powerset(the_carrier(A!18)))) | element(interior(A!18, D!21), powerset(the_carrier(A!18))))) <=> ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!18)) | (~element(D!21, powerset(the_carrier(A!18)))) | element(interior(A!18, D!21), powerset(the_carrier(A!18))))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(260,plain,
% 5.67/3.86      ((element(interior(A!18, D!21), powerset(the_carrier(A!18))) | (~element(D!21, powerset(the_carrier(A!18)))) | (~top_str(A!18))) <=> ((~top_str(A!18)) | (~element(D!21, powerset(the_carrier(A!18)))) | element(interior(A!18, D!21), powerset(the_carrier(A!18))))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(261,plain,
% 5.67/3.86      (((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(interior(A!18, D!21), powerset(the_carrier(A!18))) | (~element(D!21, powerset(the_carrier(A!18)))) | (~top_str(A!18)))) <=> ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!18)) | (~element(D!21, powerset(the_carrier(A!18)))) | element(interior(A!18, D!21), powerset(the_carrier(A!18)))))),
% 5.67/3.86      inference(monotonicity,[status(thm)],[260])).
% 5.67/3.86  tff(262,plain,
% 5.67/3.86      (((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(interior(A!18, D!21), powerset(the_carrier(A!18))) | (~element(D!21, powerset(the_carrier(A!18)))) | (~top_str(A!18)))) <=> ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!18)) | (~element(D!21, powerset(the_carrier(A!18)))) | element(interior(A!18, D!21), powerset(the_carrier(A!18))))),
% 5.67/3.86      inference(transitivity,[status(thm)],[261, 259])).
% 5.67/3.86  tff(263,plain,
% 5.67/3.86      ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(interior(A!18, D!21), powerset(the_carrier(A!18))) | (~element(D!21, powerset(the_carrier(A!18)))) | (~top_str(A!18)))),
% 5.67/3.86      inference(quant_inst,[status(thm)],[])).
% 5.67/3.86  tff(264,plain,
% 5.67/3.86      ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!18)) | (~element(D!21, powerset(the_carrier(A!18)))) | element(interior(A!18, D!21), powerset(the_carrier(A!18)))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[263, 262])).
% 5.67/3.86  tff(265,plain,
% 5.67/3.86      (element(interior(A!18, D!21), powerset(the_carrier(A!18)))),
% 5.67/3.86      inference(unit_resolution,[status(thm)],[264, 258, 27, 185])).
% 5.67/3.86  tff(266,plain,
% 5.67/3.86      (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(267,plain,
% 5.67/3.86      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[266])).
% 5.67/3.86  tff(268,plain,
% 5.67/3.86      (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(269,plain,
% 5.67/3.86      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[268])).
% 5.67/3.86  tff(270,plain,
% 5.67/3.86      (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(271,plain,
% 5.67/3.86      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[270])).
% 5.67/3.86  tff(272,plain,
% 5.67/3.86      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))),
% 5.67/3.86      inference(transitivity,[status(thm)],[271, 269])).
% 5.67/3.86  tff(273,plain,
% 5.67/3.86      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((topological_space(A) & top_str(A)) <=> (~((~top_str(A)) | (~topological_space(A))))), ((~(topological_space(A) & top_str(A))) <=> (~(~((~top_str(A)) | (~topological_space(A))))))), rewrite((~(~((~top_str(A)) | (~topological_space(A))))) <=> ((~top_str(A)) | (~topological_space(A)))), ((~(topological_space(A) & top_str(A))) <=> ((~top_str(A)) | (~topological_space(A))))), (((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))) <=> (((~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))))), rewrite((((~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))), (((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(274,plain,
% 5.67/3.86      (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[273])).
% 5.67/3.86  tff(275,plain,
% 5.67/3.86      (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))) <=> ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(276,plain,
% 5.67/3.86      (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => open_subset(interior(A, B), A)) <=> ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))), (![B: $i] : (element(B, powerset(the_carrier(A))) => open_subset(interior(A, B), A)) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))), (((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => open_subset(interior(A, B), A))) <=> ((topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))))), rewrite(((topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))) <=> ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))), (((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => open_subset(interior(A, B), A))) <=> ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(277,plain,
% 5.67/3.86      (![A: $i] : ((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => open_subset(interior(A, B), A))) <=> ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[276])).
% 5.67/3.86  tff(278,axiom,(![A: $i] : ((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => open_subset(interior(A, B), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t51_tops_1')).
% 5.67/3.86  tff(279,plain,
% 5.67/3.86      (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[278, 277])).
% 5.67/3.86  tff(280,plain,
% 5.67/3.86      (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[279, 275])).
% 5.67/3.86  tff(281,plain,(
% 5.67/3.86      ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 5.67/3.86      inference(skolemize,[status(sab)],[280])).
% 5.67/3.86  tff(282,plain,
% 5.67/3.86      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[281, 274])).
% 5.67/3.86  tff(283,plain,
% 5.67/3.86      (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[282, 272])).
% 5.67/3.86  tff(284,plain,
% 5.67/3.86      (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[283, 267])).
% 5.67/3.86  tff(285,plain,
% 5.67/3.86      (((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))) | ((~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18)))) <=> ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18)))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(286,plain,
% 5.67/3.86      ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))) | ((~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18)))),
% 5.67/3.86      inference(quant_inst,[status(thm)],[])).
% 5.67/3.86  tff(287,plain,
% 5.67/3.86      ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[286, 285])).
% 5.67/3.86  tff(288,plain,
% 5.67/3.86      (![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18))),
% 5.67/3.86      inference(unit_resolution,[status(thm)],[287, 284, 158, 27])).
% 5.67/3.86  tff(289,plain,
% 5.67/3.86      (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18))) | ((~element(D!21, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, D!21), A!18))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18))) | (~element(D!21, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, D!21), A!18))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(290,plain,
% 5.67/3.86      ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18))) | ((~element(D!21, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, D!21), A!18))),
% 5.67/3.86      inference(quant_inst,[status(thm)],[])).
% 5.67/3.86  tff(291,plain,
% 5.67/3.86      ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18))) | (~element(D!21, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, D!21), A!18)),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[290, 289])).
% 5.67/3.86  tff(292,plain,
% 5.67/3.86      (open_subset(interior(A!18, D!21), A!18)),
% 5.67/3.86      inference(unit_resolution,[status(thm)],[291, 288, 185])).
% 5.67/3.86  tff(293,plain,
% 5.67/3.86      (^[A: $i] : rewrite((empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(294,plain,
% 5.67/3.86      (![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[293])).
% 5.67/3.86  tff(295,plain,
% 5.67/3.86      (^[A: $i] : refl((empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(296,plain,
% 5.67/3.86      (![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[295])).
% 5.67/3.86  tff(297,plain,
% 5.67/3.86      (^[A: $i] : rewrite((empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(298,plain,
% 5.67/3.86      (![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[297])).
% 5.67/3.86  tff(299,plain,
% 5.67/3.86      (![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))),
% 5.67/3.86      inference(transitivity,[status(thm)],[298, 296])).
% 5.67/3.86  tff(300,plain,
% 5.67/3.86      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & topological_space(A) & top_str(A)) <=> (~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))))), rewrite((~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))))), rewrite(((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(301,plain,
% 5.67/3.86      (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[300])).
% 5.67/3.86  tff(302,plain,
% 5.67/3.86      (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 5.67/3.86      inference(rewrite,[status(thm)],[])).
% 5.67/3.86  tff(303,plain,
% 5.67/3.86      (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))) <=> ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))), (![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))) <=> ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))))),
% 5.67/3.86      inference(bind,[status(th)],[])).
% 5.67/3.86  tff(304,plain,
% 5.67/3.86      (![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 5.67/3.86      inference(quant_intro,[status(thm)],[303])).
% 5.67/3.86  tff(305,axiom,(![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_connsp_2')).
% 5.67/3.86  tff(306,plain,
% 5.67/3.86      (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[305, 304])).
% 5.67/3.86  tff(307,plain,
% 5.67/3.86      (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[306, 302])).
% 5.67/3.86  tff(308,plain,(
% 5.67/3.86      ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 5.67/3.86      inference(skolemize,[status(sab)],[307])).
% 5.67/3.86  tff(309,plain,
% 5.67/3.86      (![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[308, 301])).
% 5.67/3.86  tff(310,plain,
% 5.67/3.86      (![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[309, 299])).
% 5.67/3.86  tff(311,plain,
% 5.67/3.86      (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 5.67/3.86      inference(modus_ponens,[status(thm)],[310, 294])).
% 5.67/3.86  tff(312,plain,
% 5.67/3.86      (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))) | empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C))))))),
% 5.67/3.87      inference(rewrite,[status(thm)],[])).
% 5.67/3.87  tff(313,plain,
% 5.67/3.87      ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C))))))),
% 5.67/3.87      inference(quant_inst,[status(thm)],[])).
% 5.67/3.87  tff(314,plain,
% 5.67/3.87      ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))) | empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C)))))),
% 5.67/3.87      inference(modus_ponens,[status(thm)],[313, 312])).
% 5.67/3.87  tff(315,plain,
% 5.67/3.87      (![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C)))))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[314, 311, 105, 158, 27])).
% 5.67/3.87  tff(316,plain,
% 5.67/3.87      (((~![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C)))))) | ((~element(C!20, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C)))))) | (~element(C!20, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C)))))),
% 5.67/3.87      inference(rewrite,[status(thm)],[])).
% 5.67/3.87  tff(317,plain,
% 5.67/3.87      ((~![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C)))))) | ((~element(C!20, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C)))))),
% 5.67/3.87      inference(quant_inst,[status(thm)],[])).
% 5.67/3.87  tff(318,plain,
% 5.67/3.87      ((~![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C)))))) | (~element(C!20, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C))))),
% 5.67/3.87      inference(modus_ponens,[status(thm)],[317, 316])).
% 5.67/3.87  tff(319,plain,
% 5.67/3.87      (![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C))))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[318, 126, 315])).
% 5.67/3.87  tff(320,plain,
% 5.67/3.87      (((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C))))) | ((~element(D!21, powerset(the_carrier(A!18)))) | (point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C))))) | (~element(D!21, powerset(the_carrier(A!18)))) | (point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21))))),
% 5.67/3.87      inference(rewrite,[status(thm)],[])).
% 5.67/3.87  tff(321,plain,
% 5.67/3.87      ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C))))) | ((~element(D!21, powerset(the_carrier(A!18)))) | (point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21))))),
% 5.67/3.87      inference(quant_inst,[status(thm)],[])).
% 5.67/3.87  tff(322,plain,
% 5.67/3.87      ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C))))) | (~element(D!21, powerset(the_carrier(A!18)))) | (point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21)))),
% 5.67/3.87      inference(modus_ponens,[status(thm)],[321, 320])).
% 5.67/3.87  tff(323,plain,
% 5.67/3.87      (point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[322, 319, 185])).
% 5.67/3.87  tff(324,plain,
% 5.67/3.87      ((~(point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21)))) | (~point_neighbourhood(D!21, A!18, C!20)) | in(C!20, interior(A!18, D!21))),
% 5.67/3.87      inference(tautology,[status(thm)],[])).
% 5.67/3.87  tff(325,plain,
% 5.67/3.87      ((~(point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21)))) | in(C!20, interior(A!18, D!21))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[324, 155])).
% 5.67/3.87  tff(326,plain,
% 5.67/3.87      (in(C!20, interior(A!18, D!21))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[325, 323])).
% 5.67/3.87  tff(327,assumption,(![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))), introduced(assumption)).
% 5.67/3.87  tff(328,assumption,(disjoint(B!19, interior(A!18, D!21))), introduced(assumption)).
% 5.67/3.87  tff(329,assumption,(element(interior(A!18, D!21), powerset(the_carrier(A!18)))), introduced(assumption)).
% 5.67/3.87  tff(330,assumption,(open_subset(interior(A!18, D!21), A!18)), introduced(assumption)).
% 5.67/3.87  tff(331,assumption,(in(C!20, interior(A!18, D!21))), introduced(assumption)).
% 5.67/3.87  tff(332,plain,
% 5.67/3.87      (((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | ((~in(C!20, interior(A!18, D!21))) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21))))) <=> ((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | (~in(C!20, interior(A!18, D!21))) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21))))),
% 5.67/3.87      inference(rewrite,[status(thm)],[])).
% 5.67/3.87  tff(333,plain,
% 5.67/3.87      (((~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21))) | (~in(C!20, interior(A!18, D!21)))) <=> ((~in(C!20, interior(A!18, D!21))) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21))))),
% 5.67/3.87      inference(rewrite,[status(thm)],[])).
% 5.67/3.87  tff(334,plain,
% 5.67/3.87      (((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | ((~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21))) | (~in(C!20, interior(A!18, D!21))))) <=> ((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | ((~in(C!20, interior(A!18, D!21))) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21)))))),
% 5.67/3.87      inference(monotonicity,[status(thm)],[333])).
% 5.67/3.87  tff(335,plain,
% 5.67/3.87      (((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | ((~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21))) | (~in(C!20, interior(A!18, D!21))))) <=> ((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | (~in(C!20, interior(A!18, D!21))) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21))))),
% 5.67/3.87      inference(transitivity,[status(thm)],[334, 332])).
% 5.67/3.87  tff(336,plain,
% 5.67/3.87      ((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | ((~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21))) | (~in(C!20, interior(A!18, D!21))))),
% 5.67/3.87      inference(quant_inst,[status(thm)],[])).
% 5.67/3.87  tff(337,plain,
% 5.67/3.87      ((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | (~in(C!20, interior(A!18, D!21))) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21)))),
% 5.67/3.87      inference(modus_ponens,[status(thm)],[336, 335])).
% 5.67/3.87  tff(338,plain,
% 5.67/3.87      ($false),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[337, 331, 330, 329, 328, 327])).
% 5.67/3.87  tff(339,plain,((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | (~in(C!20, interior(A!18, D!21))) | (~open_subset(interior(A!18, D!21), A!18)) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~disjoint(B!19, interior(A!18, D!21)))), inference(lemma,lemma(discharge,[]))).
% 5.67/3.87  tff(340,plain,
% 5.67/3.87      (~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[339, 326, 292, 265, 245])).
% 5.67/3.87  tff(341,assumption,(~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))), introduced(assumption)).
% 5.67/3.87  tff(342,assumption,(in(C!20, topstr_closure(A!18, B!19))), introduced(assumption)).
% 5.67/3.87  tff(343,plain,
% 5.67/3.87      ((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))),
% 5.67/3.87      inference(tautology,[status(thm)],[])).
% 5.67/3.87  tff(344,plain,
% 5.67/3.87      (~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[343, 342, 341])).
% 5.67/3.87  tff(345,plain,
% 5.67/3.87      (((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))))))) | ((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))),
% 5.67/3.87      inference(tautology,[status(thm)],[])).
% 5.67/3.87  tff(346,plain,
% 5.67/3.87      ((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))))))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[345, 344])).
% 5.67/3.87  tff(347,plain,
% 5.67/3.87      ($false),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[149, 143, 90, 346])).
% 5.67/3.87  tff(348,plain,((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))), inference(lemma,lemma(discharge,[]))).
% 5.67/3.87  tff(349,plain,
% 5.67/3.87      (~in(C!20, topstr_closure(A!18, B!19))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[348, 340])).
% 5.67/3.87  tff(350,plain,
% 5.67/3.87      ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) <=> (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20))))),
% 5.67/3.87      inference(rewrite,[status(thm)],[])).
% 5.67/3.87  tff(351,plain,
% 5.67/3.87      (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))),
% 5.67/3.87      inference(and_elim,[status(thm)],[25])).
% 5.67/3.87  tff(352,plain,
% 5.67/3.87      (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))),
% 5.67/3.87      inference(modus_ponens,[status(thm)],[351, 350])).
% 5.67/3.87  tff(353,plain,
% 5.67/3.87      (![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[352, 349])).
% 5.67/3.87  tff(354,plain,
% 5.67/3.87      (((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | ((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))) <=> ((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | (~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))),
% 5.67/3.87      inference(rewrite,[status(thm)],[])).
% 5.67/3.87  tff(355,plain,
% 5.67/3.87      ((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | ((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))),
% 5.67/3.87      inference(quant_inst,[status(thm)],[])).
% 5.67/3.87  tff(356,plain,
% 5.67/3.87      ((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | (~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))),
% 5.67/3.87      inference(modus_ponens,[status(thm)],[355, 354])).
% 5.67/3.87  tff(357,plain,
% 5.67/3.87      ($false),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[356, 353, 157, 155])).
% 5.67/3.87  tff(358,plain,((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))), inference(lemma,lemma(discharge,[]))).
% 5.67/3.87  tff(359,plain,
% 5.67/3.87      ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))),
% 5.67/3.87      inference(and_elim,[status(thm)],[25])).
% 5.67/3.87  tff(360,plain,
% 5.67/3.87      (~in(C!20, topstr_closure(A!18, B!19))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[359, 358])).
% 5.67/3.87  tff(361,plain,
% 5.67/3.87      ((~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))))))) | in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))))),
% 5.67/3.87      inference(tautology,[status(thm)],[])).
% 5.67/3.87  tff(362,plain,
% 5.67/3.87      ((~(in(C!20, topstr_closure(A!18, B!19)) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))))))) | (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[361, 360])).
% 5.67/3.87  tff(363,plain,
% 5.67/3.87      (~((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[362, 152])).
% 5.67/3.87  tff(364,plain,
% 5.67/3.87      (((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))) | disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))),
% 5.67/3.87      inference(tautology,[status(thm)],[])).
% 5.67/3.87  tff(365,plain,
% 5.67/3.87      (disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[364, 363])).
% 5.67/3.87  tff(366,plain,
% 5.67/3.87      (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19))),
% 5.67/3.87      inference(rewrite,[status(thm)],[])).
% 5.67/3.87  tff(367,plain,
% 5.67/3.87      ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19))),
% 5.67/3.87      inference(quant_inst,[status(thm)],[])).
% 5.67/3.87  tff(368,plain,
% 5.67/3.87      ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19)),
% 5.67/3.87      inference(modus_ponens,[status(thm)],[367, 366])).
% 5.67/3.87  tff(369,plain,
% 5.67/3.87      (disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19)),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[368, 241, 365])).
% 5.67/3.87  tff(370,plain,
% 5.67/3.87      (((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))) | element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))),
% 5.67/3.87      inference(tautology,[status(thm)],[])).
% 5.67/3.87  tff(371,plain,
% 5.67/3.87      (element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))),
% 5.67/3.87      inference(unit_resolution,[status(thm)],[370, 363])).
% 5.67/3.87  tff(372,plain,
% 5.67/3.87      (^[A: $i] : refl((empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))))),
% 5.67/3.87      inference(bind,[status(th)],[])).
% 5.67/3.87  tff(373,plain,
% 5.67/3.87      (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))),
% 5.67/3.87      inference(quant_intro,[status(thm)],[372])).
% 5.67/3.87  tff(374,plain,
% 5.67/3.87      (^[A: $i] : rewrite((empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))))),
% 5.67/3.87      inference(bind,[status(th)],[])).
% 5.67/3.87  tff(375,plain,
% 5.67/3.87      (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))),
% 5.67/3.87      inference(quant_intro,[status(thm)],[374])).
% 5.67/3.87  tff(376,plain,
% 5.67/3.87      (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))),
% 5.67/3.87      inference(transitivity,[status(thm)],[375, 373])).
% 5.67/3.87  tff(377,plain,
% 5.67/3.87      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & topological_space(A) & top_str(A)) <=> (~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))))), rewrite((~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))), (![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))) <=> ((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))))), rewrite(((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))))),
% 5.67/3.87      inference(bind,[status(th)],[])).
% 5.67/3.87  tff(378,plain,
% 5.67/3.87      (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))),
% 5.67/3.87      inference(quant_intro,[status(thm)],[377])).
% 5.67/3.87  tff(379,plain,
% 5.67/3.87      (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 5.67/3.87      inference(rewrite,[status(thm)],[])).
% 5.67/3.87  tff(380,plain,
% 5.67/3.87      (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C)) <=> ((~(open_subset(B, A) & in(C, B))) | point_neighbourhood(B, A, C))), ((element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C))) <=> (element(C, the_carrier(A)) => ((~(open_subset(B, A) & in(C, B))) | point_neighbourhood(B, A, C))))), rewrite((element(C, the_carrier(A)) => ((~(open_subset(B, A) & in(C, B))) | point_neighbourhood(B, A, C))) <=> (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))), ((element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C))) <=> (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))), (![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C))) <=> ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C)))) <=> (element(B, powerset(the_carrier(A))) => ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))), rewrite((element(B, powerset(the_carrier(A))) => ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C)))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C)))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C))))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))))),
% 5.67/3.87      inference(bind,[status(th)],[])).
% 5.67/3.87  tff(381,plain,
% 5.67/3.87      (![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 5.67/3.87      inference(quant_intro,[status(thm)],[380])).
% 5.67/3.87  tff(382,axiom,(![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_connsp_2')).
% 5.67/3.87  tff(383,plain,
% 5.67/3.87      (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 5.67/3.87      inference(modus_ponens,[status(thm)],[382, 381])).
% 5.67/3.87  tff(384,plain,
% 5.67/3.87      (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 5.67/3.87      inference(modus_ponens,[status(thm)],[383, 379])).
% 5.67/3.87  tff(385,plain,(
% 5.67/3.87      ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 5.67/3.87      inference(skolemize,[status(sab)],[384])).
% 5.67/3.87  tff(386,plain,
% 5.67/3.87      (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))),
% 5.67/3.87      inference(modus_ponens,[status(thm)],[385, 378])).
% 5.67/3.87  tff(387,plain,
% 5.67/3.87      (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))),
% 5.67/3.87      inference(modus_ponens,[status(thm)],[386, 376])).
% 5.67/3.87  tff(388,plain,
% 5.67/3.87      (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18)))))),
% 5.67/3.87      inference(rewrite,[status(thm)],[])).
% 5.67/3.88  tff(389,plain,
% 5.67/3.88      ((empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A!18, C) | (~element(C, the_carrier(A!18))) | (~open_subset(B, A!18))))) <=> (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18)))))),
% 5.67/3.88      inference(rewrite,[status(thm)],[])).
% 5.67/3.88  tff(390,plain,
% 5.67/3.88      (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A!18, C) | (~element(C, the_carrier(A!18))) | (~open_subset(B, A!18)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))))),
% 5.67/3.88      inference(monotonicity,[status(thm)],[389])).
% 5.67/3.88  tff(391,plain,
% 5.67/3.88      (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A!18, C) | (~element(C, the_carrier(A!18))) | (~open_subset(B, A!18)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18)))))),
% 5.67/3.88      inference(transitivity,[status(thm)],[390, 388])).
% 5.67/3.88  tff(392,plain,
% 5.67/3.88      ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A!18, C) | (~element(C, the_carrier(A!18))) | (~open_subset(B, A!18)))))),
% 5.67/3.88      inference(quant_inst,[status(thm)],[])).
% 5.67/3.88  tff(393,plain,
% 5.67/3.88      ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))),
% 5.67/3.88      inference(modus_ponens,[status(thm)],[392, 391])).
% 5.67/3.88  tff(394,plain,
% 5.67/3.88      (![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))),
% 5.67/3.88      inference(unit_resolution,[status(thm)],[393, 387, 105, 158, 27])).
% 5.67/3.88  tff(395,plain,
% 5.67/3.88      (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | ((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))),
% 5.67/3.88      inference(rewrite,[status(thm)],[])).
% 5.67/3.88  tff(396,plain,
% 5.67/3.88      (((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | (~element(C, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) <=> ((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))),
% 5.67/3.88      inference(rewrite,[status(thm)],[])).
% 5.67/3.88  tff(397,plain,
% 5.67/3.88      (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | ((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | (~element(C, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | ((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))))),
% 5.67/3.88      inference(monotonicity,[status(thm)],[396])).
% 5.67/3.88  tff(398,plain,
% 5.67/3.88      (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | ((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | (~element(C, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))),
% 5.67/3.88      inference(transitivity,[status(thm)],[397, 395])).
% 5.67/3.88  tff(399,plain,
% 5.67/3.88      ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | ((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | (~element(C, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))),
% 5.67/3.88      inference(quant_inst,[status(thm)],[])).
% 5.67/3.88  tff(400,plain,
% 5.67/3.88      ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))),
% 5.67/3.88      inference(modus_ponens,[status(thm)],[399, 398])).
% 5.67/3.88  tff(401,plain,
% 5.67/3.88      (![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))),
% 5.67/3.88      inference(unit_resolution,[status(thm)],[400, 394, 371])).
% 5.67/3.88  tff(402,plain,
% 5.67/3.88      (((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))) | in(C!20, tptp_fun_E_0(C!20, B!19, A!18))),
% 5.67/3.88      inference(tautology,[status(thm)],[])).
% 5.67/3.88  tff(403,plain,
% 5.67/3.88      (in(C!20, tptp_fun_E_0(C!20, B!19, A!18))),
% 5.67/3.88      inference(unit_resolution,[status(thm)],[402, 363])).
% 5.67/3.88  tff(404,plain,
% 5.67/3.88      (((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18)))) | open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)),
% 5.67/3.88      inference(tautology,[status(thm)],[])).
% 5.67/3.88  tff(405,plain,
% 5.67/3.88      (open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)),
% 5.67/3.88      inference(unit_resolution,[status(thm)],[404, 363])).
% 5.67/3.88  tff(406,plain,
% 5.67/3.88      (((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | ((~element(C!20, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | (~element(C!20, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))))),
% 5.67/3.88      inference(rewrite,[status(thm)],[])).
% 5.67/3.88  tff(407,plain,
% 5.67/3.88      (((~element(C!20, the_carrier(A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))) <=> ((~element(C!20, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))))),
% 5.67/3.88      inference(rewrite,[status(thm)],[])).
% 5.67/3.88  tff(408,plain,
% 5.67/3.88      (((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | ((~element(C!20, the_carrier(A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | ((~element(C!20, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18)))))),
% 5.67/3.89      inference(monotonicity,[status(thm)],[407])).
% 5.67/3.89  tff(409,plain,
% 5.67/3.89      (((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | ((~element(C!20, the_carrier(A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | (~element(C!20, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))))),
% 5.67/3.89      inference(transitivity,[status(thm)],[408, 406])).
% 5.67/3.89  tff(410,plain,
% 5.67/3.89      ((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | ((~element(C!20, the_carrier(A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))),
% 5.67/3.89      inference(quant_inst,[status(thm)],[])).
% 5.67/3.89  tff(411,plain,
% 5.67/3.89      ((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | (~element(C!20, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18)))),
% 5.67/3.89      inference(modus_ponens,[status(thm)],[410, 409])).
% 5.67/3.89  tff(412,plain,
% 5.67/3.89      (point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20)),
% 5.67/3.89      inference(unit_resolution,[status(thm)],[411, 126, 405, 403, 401])).
% 5.67/3.89  tff(413,plain,
% 5.67/3.89      (![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))),
% 5.67/3.89      inference(unit_resolution,[status(thm)],[352, 360])).
% 5.67/3.89  tff(414,plain,
% 5.67/3.89      (((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | ((~disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19)) | (~point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20)))) <=> ((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | (~disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19)) | (~point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20)))),
% 5.67/3.89      inference(rewrite,[status(thm)],[])).
% 5.67/3.89  tff(415,plain,
% 5.67/3.89      ((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | ((~disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19)) | (~point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20)))),
% 5.67/3.89      inference(quant_inst,[status(thm)],[])).
% 5.67/3.89  tff(416,plain,
% 5.67/3.89      ((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | (~disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19)) | (~point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20))),
% 5.67/3.89      inference(modus_ponens,[status(thm)],[415, 414])).
% 5.67/3.89  tff(417,plain,
% 5.67/3.89      ($false),
% 5.67/3.89      inference(unit_resolution,[status(thm)],[416, 413, 412, 369])).
% 5.67/3.89  % SZS output end Proof
%------------------------------------------------------------------------------