TSTP Solution File: SEU323+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU323+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.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 07:28:55 EDT 2022
% Result : Theorem 0.16s 0.35s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU323+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n006.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat Sep 3 12:04:09 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.31 Usage: tptp [options] [-file:]file
% 0.16/0.31 -h, -? prints this message.
% 0.16/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.31 -m, -model generate model.
% 0.16/0.31 -p, -proof generate proof.
% 0.16/0.31 -c, -core generate unsat core of named formulas.
% 0.16/0.31 -st, -statistics display statistics.
% 0.16/0.31 -t:timeout set timeout (in second).
% 0.16/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.31 -<param>:<value> configuration parameter and value.
% 0.16/0.31 -o:<output-file> file to place output in.
% 0.16/0.35 % SZS status Theorem
% 0.16/0.35 % SZS output start Proof
% 0.16/0.35 tff(open_subset_type, type, (
% 0.16/0.35 open_subset: ( $i * $i ) > $o)).
% 0.16/0.35 tff(tptp_fun_A_5_type, type, (
% 0.16/0.35 tptp_fun_A_5: $i)).
% 0.16/0.35 tff(subset_complement_type, type, (
% 0.16/0.35 subset_complement: ( $i * $i ) > $i)).
% 0.16/0.35 tff(topstr_closure_type, type, (
% 0.16/0.35 topstr_closure: ( $i * $i ) > $i)).
% 0.16/0.35 tff(tptp_fun_B_6_type, type, (
% 0.16/0.35 tptp_fun_B_6: $i)).
% 0.16/0.35 tff(the_carrier_type, type, (
% 0.16/0.35 the_carrier: $i > $i)).
% 0.16/0.35 tff(interior_type, type, (
% 0.16/0.35 interior: ( $i * $i ) > $i)).
% 0.16/0.35 tff(element_type, type, (
% 0.16/0.35 element: ( $i * $i ) > $o)).
% 0.16/0.35 tff(powerset_type, type, (
% 0.16/0.35 powerset: $i > $i)).
% 0.16/0.35 tff(top_str_type, type, (
% 0.16/0.35 top_str: $i > $o)).
% 0.16/0.35 tff(topological_space_type, type, (
% 0.16/0.35 topological_space: $i > $o)).
% 0.16/0.35 tff(closed_subset_type, type, (
% 0.16/0.35 closed_subset: ( $i * $i ) > $o)).
% 0.16/0.35 tff(1,plain,
% 0.16/0.35 (((topological_space(A!5) & top_str(A!5)) & (~((~element(B!6, powerset(the_carrier(A!5)))) | open_subset(interior(A!5, B!6), A!5)))) <=> (topological_space(A!5) & top_str(A!5) & (~((~element(B!6, powerset(the_carrier(A!5)))) | open_subset(interior(A!5, B!6), A!5))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(2,plain,
% 0.16/0.35 ((~(~(topological_space(A!5) & top_str(A!5)))) <=> (topological_space(A!5) & top_str(A!5))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(3,plain,
% 0.16/0.35 (((~(~(topological_space(A!5) & top_str(A!5)))) & (~((~element(B!6, powerset(the_carrier(A!5)))) | open_subset(interior(A!5, B!6), A!5)))) <=> ((topological_space(A!5) & top_str(A!5)) & (~((~element(B!6, powerset(the_carrier(A!5)))) | open_subset(interior(A!5, B!6), A!5))))),
% 0.16/0.35 inference(monotonicity,[status(thm)],[2])).
% 0.16/0.35 tff(4,plain,
% 0.16/0.35 (((~(~(topological_space(A!5) & top_str(A!5)))) & (~((~element(B!6, powerset(the_carrier(A!5)))) | open_subset(interior(A!5, B!6), A!5)))) <=> (topological_space(A!5) & top_str(A!5) & (~((~element(B!6, powerset(the_carrier(A!5)))) | open_subset(interior(A!5, B!6), A!5))))),
% 0.16/0.35 inference(transitivity,[status(thm)],[3, 1])).
% 0.16/0.35 tff(5,plain,
% 0.16/0.35 ((~![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))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(6,plain,
% 0.16/0.35 ((~![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))))),
% 0.16/0.35 inference(rewrite,[status(thm)],[])).
% 0.16/0.35 tff(7,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')).
% 0.16/0.35 tff(8,plain,
% 0.16/0.35 (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.16/0.35 tff(9,plain,
% 0.16/0.35 (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.16/0.35 tff(10,plain,
% 0.16/0.35 (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.16/0.35 tff(11,plain,
% 0.16/0.35 (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.16/0.35 tff(12,plain,
% 0.16/0.35 (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 0.16/0.35 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.16/0.35 tff(13,plain,
% 0.16/0.35 (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.16/0.36 tff(14,plain,
% 0.16/0.36 (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[13, 5])).
% 0.16/0.36 tff(15,plain,
% 0.16/0.36 (topological_space(A!5) & top_str(A!5) & (~((~element(B!6, powerset(the_carrier(A!5)))) | open_subset(interior(A!5, B!6), A!5)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[14, 4])).
% 0.16/0.36 tff(16,plain,
% 0.16/0.36 (top_str(A!5)),
% 0.16/0.36 inference(and_elim,[status(thm)],[15])).
% 0.16/0.36 tff(17,plain,
% 0.16/0.36 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(18,plain,
% 0.16/0.36 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[17])).
% 0.16/0.36 tff(19,plain,
% 0.16/0.36 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(20,plain,
% 0.16/0.36 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[19])).
% 0.16/0.36 tff(21,plain,
% 0.16/0.36 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.16/0.36 inference(transitivity,[status(thm)],[20, 18])).
% 0.16/0.36 tff(22,plain,
% 0.16/0.36 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(23,plain,
% 0.16/0.36 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))) <=> ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(24,plain,
% 0.16/0.36 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B)))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[23])).
% 0.16/0.36 tff(25,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tops_1')).
% 0.16/0.36 tff(26,plain,
% 0.16/0.36 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.16/0.36 tff(27,plain,
% 0.16/0.36 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.16/0.36 tff(28,plain,(
% 0.16/0.36 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.16/0.36 inference(skolemize,[status(sab)],[27])).
% 0.16/0.36 tff(29,plain,
% 0.16/0.36 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.16/0.36 tff(30,plain,
% 0.16/0.36 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))) | ((~top_str(A!5)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (interior(A!5, B) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))) | (~top_str(A!5)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (interior(A!5, B) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B))))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(31,plain,
% 0.16/0.36 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))) | ((~top_str(A!5)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (interior(A!5, B) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B))))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(32,plain,
% 0.16/0.36 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (interior(A, B) = subset_complement(the_carrier(A), topstr_closure(A, subset_complement(the_carrier(A), B))))))) | (~top_str(A!5)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (interior(A!5, B) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B)))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.16/0.36 tff(33,plain,
% 0.16/0.36 (![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (interior(A!5, B) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B)))))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[32, 29, 16])).
% 0.16/0.36 tff(34,plain,
% 0.16/0.36 (~((~element(B!6, powerset(the_carrier(A!5)))) | open_subset(interior(A!5, B!6), A!5))),
% 0.16/0.36 inference(and_elim,[status(thm)],[15])).
% 0.16/0.36 tff(35,plain,
% 0.16/0.36 (element(B!6, powerset(the_carrier(A!5)))),
% 0.16/0.36 inference(or_elim,[status(thm)],[34])).
% 0.16/0.36 tff(36,plain,
% 0.16/0.36 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (interior(A!5, B) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B)))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | (interior(A!5, B!6) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (interior(A!5, B) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B)))))) | (~element(B!6, powerset(the_carrier(A!5)))) | (interior(A!5, B!6) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(37,plain,
% 0.16/0.36 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (interior(A!5, B) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B)))))) | ((~element(B!6, powerset(the_carrier(A!5)))) | (interior(A!5, B!6) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(38,plain,
% 0.16/0.36 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!5)))) | (interior(A!5, B) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B)))))) | (~element(B!6, powerset(the_carrier(A!5)))) | (interior(A!5, B!6) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.16/0.36 tff(39,plain,
% 0.16/0.36 (interior(A!5, B!6) = subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[38, 35, 33])).
% 0.16/0.36 tff(40,plain,
% 0.16/0.36 (subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))) = interior(A!5, B!6)),
% 0.16/0.36 inference(symmetry,[status(thm)],[39])).
% 0.16/0.36 tff(41,plain,
% 0.16/0.36 (open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5) <=> open_subset(interior(A!5, B!6), A!5)),
% 0.16/0.36 inference(monotonicity,[status(thm)],[40])).
% 0.16/0.36 tff(42,plain,
% 0.16/0.36 (open_subset(interior(A!5, B!6), A!5) <=> open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5)),
% 0.16/0.36 inference(symmetry,[status(thm)],[41])).
% 0.16/0.36 tff(43,plain,
% 0.16/0.36 ((~open_subset(interior(A!5, B!6), A!5)) <=> (~open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5))),
% 0.16/0.36 inference(monotonicity,[status(thm)],[42])).
% 0.16/0.36 tff(44,plain,
% 0.16/0.36 (~open_subset(interior(A!5, B!6), A!5)),
% 0.16/0.36 inference(or_elim,[status(thm)],[34])).
% 0.16/0.36 tff(45,plain,
% 0.16/0.36 (~open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5)),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.16/0.36 tff(46,plain,
% 0.16/0.36 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(47,plain,
% 0.16/0.36 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[46])).
% 0.16/0.36 tff(48,plain,
% 0.16/0.36 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(49,plain,
% 0.16/0.36 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => element(subset_complement(A, B), powerset(A))) <=> ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(50,plain,
% 0.16/0.36 (![A: $i, B: $i] : (element(B, powerset(A)) => element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[49])).
% 0.16/0.36 tff(51,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => element(subset_complement(A, B), powerset(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_subset_1')).
% 0.16/0.36 tff(52,plain,
% 0.16/0.36 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.16/0.36 tff(53,plain,
% 0.16/0.36 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.16/0.36 tff(54,plain,(
% 0.16/0.36 ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.16/0.36 inference(skolemize,[status(sab)],[53])).
% 0.16/0.36 tff(55,plain,
% 0.16/0.36 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.16/0.36 tff(56,plain,
% 0.16/0.36 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(B!6, powerset(the_carrier(A!5)))) | element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(B!6, powerset(the_carrier(A!5)))) | element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5))))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(57,plain,
% 0.16/0.36 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(B!6, powerset(the_carrier(A!5)))) | element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(58,plain,
% 0.16/0.36 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(B!6, powerset(the_carrier(A!5)))) | element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.16/0.36 tff(59,plain,
% 0.16/0.36 (element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[58, 55, 35])).
% 0.16/0.36 tff(60,plain,
% 0.16/0.36 (topological_space(A!5)),
% 0.16/0.36 inference(and_elim,[status(thm)],[15])).
% 0.16/0.36 tff(61,plain,
% 0.16/0.36 (^[A: $i, B: $i] : refl((closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A))) <=> (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(62,plain,
% 0.16/0.36 (![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A))) <=> ![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[61])).
% 0.16/0.36 tff(63,plain,
% 0.16/0.36 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A)))) <=> (~((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A))))), ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) <=> (~(~((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A))))))), rewrite((~(~((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A))))) <=> ((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))), ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) <=> ((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A))))), (((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | closed_subset(topstr_closure(A, B), A)) <=> (((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A))) | closed_subset(topstr_closure(A, B), A)))), rewrite((((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A))) | closed_subset(topstr_closure(A, B), A)) <=> (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))), (((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | closed_subset(topstr_closure(A, B), A)) <=> (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(64,plain,
% 0.16/0.36 (![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | closed_subset(topstr_closure(A, B), A)) <=> ![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[63])).
% 0.16/0.36 tff(65,plain,
% 0.16/0.36 (![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | closed_subset(topstr_closure(A, B), A)) <=> ![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | closed_subset(topstr_closure(A, B), A))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(66,plain,
% 0.16/0.36 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((topological_space(A) & top_str(A)) & element(B, powerset(the_carrier(A)))) <=> (topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))), ((((topological_space(A) & top_str(A)) & element(B, powerset(the_carrier(A)))) => closed_subset(topstr_closure(A, B), A)) <=> ((topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A)))) => closed_subset(topstr_closure(A, B), A)))), rewrite(((topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A)))) => closed_subset(topstr_closure(A, B), A)) <=> ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | closed_subset(topstr_closure(A, B), A))), ((((topological_space(A) & top_str(A)) & element(B, powerset(the_carrier(A)))) => closed_subset(topstr_closure(A, B), A)) <=> ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | closed_subset(topstr_closure(A, B), A))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(67,plain,
% 0.16/0.36 (![A: $i, B: $i] : (((topological_space(A) & top_str(A)) & element(B, powerset(the_carrier(A)))) => closed_subset(topstr_closure(A, B), A)) <=> ![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | closed_subset(topstr_closure(A, B), A))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[66])).
% 0.16/0.36 tff(68,axiom,(![A: $i, B: $i] : (((topological_space(A) & top_str(A)) & element(B, powerset(the_carrier(A)))) => closed_subset(topstr_closure(A, B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_tops_1')).
% 0.16/0.36 tff(69,plain,
% 0.16/0.36 (![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | closed_subset(topstr_closure(A, B), A))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.16/0.36 tff(70,plain,
% 0.16/0.36 (![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | closed_subset(topstr_closure(A, B), A))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.16/0.36 tff(71,plain,(
% 0.16/0.36 ![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | closed_subset(topstr_closure(A, B), A))),
% 0.16/0.36 inference(skolemize,[status(sab)],[70])).
% 0.16/0.36 tff(72,plain,
% 0.16/0.36 (![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.16/0.36 tff(73,plain,
% 0.16/0.36 (![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[72, 62])).
% 0.16/0.36 tff(74,plain,
% 0.16/0.36 (((~![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))) | ((~topological_space(A!5)) | (~top_str(A!5)) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5))) <=> ((~![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))) | (~topological_space(A!5)) | (~top_str(A!5)) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(75,plain,
% 0.16/0.36 ((closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | (~topological_space(A!5)) | (~top_str(A!5))) <=> ((~topological_space(A!5)) | (~top_str(A!5)) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(76,plain,
% 0.16/0.36 (((~![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))) | (closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | (~topological_space(A!5)) | (~top_str(A!5)))) <=> ((~![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))) | ((~topological_space(A!5)) | (~top_str(A!5)) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5)))),
% 0.16/0.36 inference(monotonicity,[status(thm)],[75])).
% 0.16/0.36 tff(77,plain,
% 0.16/0.36 (((~![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))) | (closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | (~topological_space(A!5)) | (~top_str(A!5)))) <=> ((~![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))) | (~topological_space(A!5)) | (~top_str(A!5)) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5))),
% 0.16/0.36 inference(transitivity,[status(thm)],[76, 74])).
% 0.16/0.36 tff(78,plain,
% 0.16/0.36 ((~![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))) | (closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | (~topological_space(A!5)) | (~top_str(A!5)))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(79,plain,
% 0.16/0.37 ((~![A: $i, B: $i] : (closed_subset(topstr_closure(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)))) | (~topological_space(A!5)) | (~top_str(A!5)) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5)),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.16/0.37 tff(80,plain,
% 0.16/0.37 (closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5)),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[79, 73, 60, 16, 59])).
% 0.16/0.37 tff(81,plain,
% 0.16/0.37 (^[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))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(82,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[81])).
% 0.16/0.37 tff(83,plain,
% 0.16/0.37 (^[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)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(84,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[83])).
% 0.16/0.37 tff(85,plain,
% 0.16/0.37 (![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))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(86,plain,
% 0.16/0.37 (^[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)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(87,plain,
% 0.16/0.37 (![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))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[86])).
% 0.16/0.37 tff(88,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')).
% 0.16/0.37 tff(89,plain,
% 0.16/0.37 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.16/0.37 tff(90,plain,
% 0.16/0.37 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.16/0.37 tff(91,plain,(
% 0.16/0.37 ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 0.16/0.37 inference(skolemize,[status(sab)],[90])).
% 0.16/0.37 tff(92,plain,
% 0.16/0.37 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.16/0.37 tff(93,plain,
% 0.16/0.37 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.16/0.37 tff(94,plain,
% 0.16/0.37 (((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!5)) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5))))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!5)) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(95,plain,
% 0.16/0.37 ((element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5))) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | (~top_str(A!5))) <=> ((~top_str(A!5)) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(96,plain,
% 0.16/0.37 (((~![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!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5))) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | (~top_str(A!5)))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!5)) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))))),
% 0.16/0.37 inference(monotonicity,[status(thm)],[95])).
% 0.16/0.37 tff(97,plain,
% 0.16/0.37 (((~![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!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5))) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | (~top_str(A!5)))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!5)) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5))))),
% 0.16/0.37 inference(transitivity,[status(thm)],[96, 94])).
% 0.16/0.37 tff(98,plain,
% 0.16/0.37 ((~![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!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5))) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | (~top_str(A!5)))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(99,plain,
% 0.16/0.37 ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!5)) | (~element(subset_complement(the_carrier(A!5), B!6), powerset(the_carrier(A!5)))) | element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.16/0.37 tff(100,plain,
% 0.16/0.37 (element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[99, 93, 16, 59])).
% 0.16/0.37 tff(101,plain,
% 0.16/0.37 (^[A: $i, B: $i] : refl((open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A))) <=> (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(102,plain,
% 0.16/0.37 (![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A))) <=> ![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[101])).
% 0.16/0.37 tff(103,plain,
% 0.16/0.37 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A)))) <=> (~((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A))))), ((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) <=> (~(~((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A))))))), rewrite((~(~((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A))))) <=> ((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))), ((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) <=> ((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A))))), (((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) | open_subset(subset_complement(the_carrier(A), B), A)) <=> (((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A))) | open_subset(subset_complement(the_carrier(A), B), A)))), rewrite((((~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A))) | open_subset(subset_complement(the_carrier(A), B), A)) <=> (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))), (((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) | open_subset(subset_complement(the_carrier(A), B), A)) <=> (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(104,plain,
% 0.16/0.37 (![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) | open_subset(subset_complement(the_carrier(A), B), A)) <=> ![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[103])).
% 0.16/0.37 tff(105,plain,
% 0.16/0.37 (![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) | open_subset(subset_complement(the_carrier(A), B), A)) <=> ![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) | open_subset(subset_complement(the_carrier(A), B), A))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(106,plain,
% 0.16/0.37 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((topological_space(A) & top_str(A)) & closed_subset(B, A)) <=> (topological_space(A) & top_str(A) & closed_subset(B, A))), ((((topological_space(A) & top_str(A)) & closed_subset(B, A)) & element(B, powerset(the_carrier(A)))) <=> ((topological_space(A) & top_str(A) & closed_subset(B, A)) & element(B, powerset(the_carrier(A)))))), rewrite(((topological_space(A) & top_str(A) & closed_subset(B, A)) & element(B, powerset(the_carrier(A)))) <=> (topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))), ((((topological_space(A) & top_str(A)) & closed_subset(B, A)) & element(B, powerset(the_carrier(A)))) <=> (topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A)))))), (((((topological_space(A) & top_str(A)) & closed_subset(B, A)) & element(B, powerset(the_carrier(A)))) => open_subset(subset_complement(the_carrier(A), B), A)) <=> ((topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A)))) => open_subset(subset_complement(the_carrier(A), B), A)))), rewrite(((topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A)))) => open_subset(subset_complement(the_carrier(A), B), A)) <=> ((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) | open_subset(subset_complement(the_carrier(A), B), A))), (((((topological_space(A) & top_str(A)) & closed_subset(B, A)) & element(B, powerset(the_carrier(A)))) => open_subset(subset_complement(the_carrier(A), B), A)) <=> ((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) | open_subset(subset_complement(the_carrier(A), B), A))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(107,plain,
% 0.16/0.37 (![A: $i, B: $i] : ((((topological_space(A) & top_str(A)) & closed_subset(B, A)) & element(B, powerset(the_carrier(A)))) => open_subset(subset_complement(the_carrier(A), B), A)) <=> ![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) | open_subset(subset_complement(the_carrier(A), B), A))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[106])).
% 0.16/0.37 tff(108,axiom,(![A: $i, B: $i] : ((((topological_space(A) & top_str(A)) & closed_subset(B, A)) & element(B, powerset(the_carrier(A)))) => open_subset(subset_complement(the_carrier(A), B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc3_tops_1')).
% 0.16/0.37 tff(109,plain,
% 0.16/0.37 (![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) | open_subset(subset_complement(the_carrier(A), B), A))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.16/0.37 tff(110,plain,
% 0.16/0.37 (![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) | open_subset(subset_complement(the_carrier(A), B), A))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.16/0.37 tff(111,plain,(
% 0.16/0.37 ![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & closed_subset(B, A) & element(B, powerset(the_carrier(A))))) | open_subset(subset_complement(the_carrier(A), B), A))),
% 0.16/0.37 inference(skolemize,[status(sab)],[110])).
% 0.16/0.37 tff(112,plain,
% 0.16/0.37 (![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.16/0.37 tff(113,plain,
% 0.16/0.37 (![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[112, 102])).
% 0.16/0.37 tff(114,plain,
% 0.16/0.37 (((~![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))) | ((~topological_space(A!5)) | (~top_str(A!5)) | (~element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))) | open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5) | (~closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5)))) <=> ((~![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))) | (~topological_space(A!5)) | (~top_str(A!5)) | (~element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))) | open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5) | (~closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(115,plain,
% 0.16/0.37 ((open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5) | (~element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))) | (~topological_space(A!5)) | (~top_str(A!5)) | (~closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5))) <=> ((~topological_space(A!5)) | (~top_str(A!5)) | (~element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))) | open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5) | (~closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(116,plain,
% 0.16/0.37 (((~![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))) | (open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5) | (~element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))) | (~topological_space(A!5)) | (~top_str(A!5)) | (~closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5)))) <=> ((~![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))) | ((~topological_space(A!5)) | (~top_str(A!5)) | (~element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))) | open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5) | (~closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5))))),
% 0.16/0.37 inference(monotonicity,[status(thm)],[115])).
% 0.16/0.37 tff(117,plain,
% 0.16/0.37 (((~![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))) | (open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5) | (~element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))) | (~topological_space(A!5)) | (~top_str(A!5)) | (~closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5)))) <=> ((~![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))) | (~topological_space(A!5)) | (~top_str(A!5)) | (~element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))) | open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5) | (~closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5)))),
% 0.16/0.38 inference(transitivity,[status(thm)],[116, 114])).
% 0.16/0.38 tff(118,plain,
% 0.16/0.38 ((~![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))) | (open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5) | (~element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))) | (~topological_space(A!5)) | (~top_str(A!5)) | (~closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5)))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(119,plain,
% 0.16/0.38 ((~![A: $i, B: $i] : (open_subset(subset_complement(the_carrier(A), B), A) | (~element(B, powerset(the_carrier(A)))) | (~topological_space(A)) | (~top_str(A)) | (~closed_subset(B, A)))) | (~topological_space(A!5)) | (~top_str(A!5)) | (~element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))) | open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5) | (~closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.16/0.38 tff(120,plain,
% 0.16/0.38 ((~element(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), powerset(the_carrier(A!5)))) | open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5) | (~closed_subset(topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6)), A!5))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[119, 113, 60, 16])).
% 0.16/0.38 tff(121,plain,
% 0.16/0.38 (open_subset(subset_complement(the_carrier(A!5), topstr_closure(A!5, subset_complement(the_carrier(A!5), B!6))), A!5)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[120, 100, 80])).
% 0.16/0.38 tff(122,plain,
% 0.16/0.38 ($false),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[121, 45])).
% 0.16/0.38 % SZS output end Proof
%------------------------------------------------------------------------------