%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU324+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 : Sat Jun 21 05:27:36 AM UTC 2025
% Result : Theorem 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU324+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n001.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:49:05 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.43 % SZS status Theorem
% 0.22/0.43 % SZS output start Proof
% 0.22/0.43 tff(tptp_fun_D_9_type, type, (
% 0.22/0.43 tptp_fun_D_9: $i)).
% 0.22/0.43 tff(interior_type, type, (
% 0.22/0.43 interior: ( $i * $i ) > $i)).
% 0.22/0.43 tff(tptp_fun_B_7_type, type, (
% 0.22/0.43 tptp_fun_B_7: $i)).
% 0.22/0.43 tff(subset_complement_type, type, (
% 0.22/0.43 subset_complement: ( $i * $i ) > $i)).
% 0.22/0.43 tff(the_carrier_type, type, (
% 0.22/0.43 the_carrier: $i > $i)).
% 0.22/0.43 tff(element_type, type, (
% 0.22/0.43 element: ( $i * $i ) > $o)).
% 0.22/0.43 tff(powerset_type, type, (
% 0.22/0.43 powerset: $i > $i)).
% 0.22/0.43 tff(open_subset_type, type, (
% 0.22/0.43 open_subset: ( $i * $i ) > $o)).
% 0.22/0.43 tff(tptp_fun_A_6_type, type, (
% 0.22/0.43 tptp_fun_A_6: $i)).
% 0.22/0.43 tff(tptp_fun_C_8_type, type, (
% 0.22/0.43 tptp_fun_C_8: $i)).
% 0.22/0.43 tff(top_str_type, type, (
% 0.22/0.43 top_str: $i > $o)).
% 0.22/0.43 tff(topological_space_type, type, (
% 0.22/0.43 topological_space: $i > $o)).
% 0.22/0.43 tff(topstr_closure_type, type, (
% 0.22/0.43 topstr_closure: ( $i * $i ) > $i)).
% 0.22/0.43 tff(closed_subset_type, type, (
% 0.22/0.43 closed_subset: ( $i * $i ) > $o)).
% 0.22/0.43 tff(1,plain,
% 0.22/0.43 (((topological_space(A!6) & top_str(A!6)) & (top_str(B!7) & element(C!8, powerset(the_carrier(A!6))) & (~((~element(D!9, powerset(the_carrier(B!7)))) | (((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6))))))) <=> (topological_space(A!6) & top_str(A!6) & top_str(B!7) & element(C!8, powerset(the_carrier(A!6))) & (~((~element(D!9, powerset(the_carrier(B!7)))) | (((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(2,plain,
% 0.22/0.43 ((top_str(B!7) & (element(C!8, powerset(the_carrier(A!6))) & (~((~element(D!9, powerset(the_carrier(B!7)))) | (((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6))))))) <=> (top_str(B!7) & element(C!8, powerset(the_carrier(A!6))) & (~((~element(D!9, powerset(the_carrier(B!7)))) | (((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(3,plain,
% 0.22/0.43 (((topological_space(A!6) & top_str(A!6)) & (top_str(B!7) & (element(C!8, powerset(the_carrier(A!6))) & (~((~element(D!9, powerset(the_carrier(B!7)))) | (((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)))))))) <=> ((topological_space(A!6) & top_str(A!6)) & (top_str(B!7) & element(C!8, powerset(the_carrier(A!6))) & (~((~element(D!9, powerset(the_carrier(B!7)))) | (((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)))))))),
% 0.22/0.43 inference(monotonicity,[status(thm)],[2])).
% 0.22/0.43 tff(4,plain,
% 0.22/0.43 (((topological_space(A!6) & top_str(A!6)) & (top_str(B!7) & (element(C!8, powerset(the_carrier(A!6))) & (~((~element(D!9, powerset(the_carrier(B!7)))) | (((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)))))))) <=> (topological_space(A!6) & top_str(A!6) & top_str(B!7) & element(C!8, powerset(the_carrier(A!6))) & (~((~element(D!9, powerset(the_carrier(B!7)))) | (((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6))))))),
% 0.22/0.43 inference(transitivity,[status(thm)],[3, 1])).
% 0.22/0.43 tff(5,plain,
% 0.22/0.43 ((~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))) <=> (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(6,plain,
% 0.22/0.43 ((~![A: $i] : ((topological_space(A) & top_str(A)) => ![B: $i] : (top_str(B) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A)))))))) <=> (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A))))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(7,axiom,(~![A: $i] : ((topological_space(A) & top_str(A)) => ![B: $i] : (top_str(B) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ![D: $i] : (element(D, powerset(the_carrier(B))) => ((open_subset(D, B) => (interior(B, D) = D)) & ((interior(A, C) = C) => open_subset(C, A)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t55_tops_1')).
% 0.22/0.43 tff(8,plain,
% 0.22/0.43 (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.22/0.43 tff(9,plain,
% 0.22/0.43 (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.22/0.43 tff(10,plain,
% 0.22/0.43 (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.22/0.43 tff(11,plain,
% 0.22/0.43 (~![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~top_str(B)) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ![D: $i] : ((~element(D, powerset(the_carrier(B)))) | (((~open_subset(D, B)) | (interior(B, D) = D)) & ((~(interior(A, C) = C)) | open_subset(C, A)))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.22/0.43 tff(12,plain,
% 0.22/0.43 (topological_space(A!6) & top_str(A!6) & top_str(B!7) & element(C!8, powerset(the_carrier(A!6))) & (~((~element(D!9, powerset(the_carrier(B!7)))) | (((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.22/0.43 tff(13,plain,
% 0.22/0.43 (~((~element(D!9, powerset(the_carrier(B!7)))) | (((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6))))),
% 0.22/0.43 inference(and_elim,[status(thm)],[12])).
% 0.22/0.43 tff(14,plain,
% 0.22/0.43 (element(D!9, powerset(the_carrier(B!7)))),
% 0.22/0.43 inference(or_elim,[status(thm)],[13])).
% 0.22/0.43 tff(15,plain,
% 0.22/0.43 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(16,plain,
% 0.22/0.43 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[15])).
% 0.22/0.43 tff(17,plain,
% 0.22/0.43 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(18,plain,
% 0.22/0.43 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B)) <=> ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(19,plain,
% 0.22/0.43 (![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.22/0.43 tff(20,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','involutiveness_k3_subset_1')).
% 0.22/0.43 tff(21,plain,
% 0.22/0.43 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.22/0.43 tff(22,plain,
% 0.22/0.43 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.22/0.43 tff(23,plain,(
% 0.22/0.43 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.22/0.43 inference(skolemize,[status(sab)],[22])).
% 0.22/0.43 tff(24,plain,
% 0.22/0.43 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.22/0.44 tff(25,plain,
% 0.22/0.44 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(D!9, powerset(the_carrier(B!7)))) | (subset_complement(the_carrier(B!7), subset_complement(the_carrier(B!7), D!9)) = D!9))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(D!9, powerset(the_carrier(B!7)))) | (subset_complement(the_carrier(B!7), subset_complement(the_carrier(B!7), D!9)) = D!9))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(26,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(D!9, powerset(the_carrier(B!7)))) | (subset_complement(the_carrier(B!7), subset_complement(the_carrier(B!7), D!9)) = D!9))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(27,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(D!9, powerset(the_carrier(B!7)))) | (subset_complement(the_carrier(B!7), subset_complement(the_carrier(B!7), D!9)) = D!9)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.22/0.44 tff(28,plain,
% 0.22/0.44 (subset_complement(the_carrier(B!7), subset_complement(the_carrier(B!7), D!9)) = D!9),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.22/0.44 tff(29,assumption,(~((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6))), introduced(assumption)).
% 0.22/0.44 tff(30,plain,
% 0.22/0.44 (((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)) | (interior(A!6, C!8) = C!8)),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(31,plain,
% 0.22/0.44 (interior(A!6, C!8) = C!8),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.22/0.44 tff(32,plain,
% 0.22/0.44 (C!8 = interior(A!6, C!8)),
% 0.22/0.44 inference(symmetry,[status(thm)],[31])).
% 0.22/0.44 tff(33,plain,
% 0.22/0.44 (open_subset(C!8, A!6) <=> open_subset(interior(A!6, C!8), A!6)),
% 0.22/0.44 inference(monotonicity,[status(thm)],[32])).
% 0.22/0.44 tff(34,plain,
% 0.22/0.44 (open_subset(interior(A!6, C!8), A!6) <=> open_subset(C!8, A!6)),
% 0.22/0.44 inference(symmetry,[status(thm)],[33])).
% 0.22/0.44 tff(35,plain,
% 0.22/0.44 (element(C!8, powerset(the_carrier(A!6)))),
% 0.22/0.44 inference(and_elim,[status(thm)],[12])).
% 0.22/0.44 tff(36,plain,
% 0.22/0.44 (top_str(A!6)),
% 0.22/0.44 inference(and_elim,[status(thm)],[12])).
% 0.22/0.44 tff(37,plain,
% 0.22/0.44 (topological_space(A!6)),
% 0.22/0.44 inference(and_elim,[status(thm)],[12])).
% 0.22/0.44 tff(38,plain,
% 0.22/0.44 (^[A: $i, B: $i] : refl((open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(39,plain,
% 0.22/0.44 (![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[38])).
% 0.22/0.44 tff(40,plain,
% 0.22/0.44 (^[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)))) | (~top_str(A)) | (~topological_space(A))))), ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) <=> (~(~((~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))))))), rewrite((~(~((~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))))) <=> ((~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))), ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) <=> ((~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))))), (((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | open_subset(interior(A, B), A)) <=> (((~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) | open_subset(interior(A, B), A)))), rewrite((((~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) | open_subset(interior(A, B), A)) <=> (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))), (((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | open_subset(interior(A, B), A)) <=> (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(41,plain,
% 0.22/0.44 (![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | open_subset(interior(A, B), A)) <=> ![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.44 tff(42,plain,
% 0.22/0.44 (![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | open_subset(interior(A, B), A)) <=> ![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | open_subset(interior(A, B), A))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(43,plain,
% 0.22/0.44 (^[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)))) => open_subset(interior(A, B), A)) <=> ((topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A)))) => open_subset(interior(A, B), A)))), rewrite(((topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A)))) => open_subset(interior(A, B), A)) <=> ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | open_subset(interior(A, B), A))), ((((topological_space(A) & top_str(A)) & element(B, powerset(the_carrier(A)))) => open_subset(interior(A, B), A)) <=> ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | open_subset(interior(A, B), A))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(44,plain,
% 0.22/0.44 (![A: $i, B: $i] : (((topological_space(A) & top_str(A)) & element(B, powerset(the_carrier(A)))) => open_subset(interior(A, B), A)) <=> ![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | open_subset(interior(A, B), A))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[43])).
% 0.22/0.44 tff(45,axiom,(![A: $i, B: $i] : (((topological_space(A) & top_str(A)) & element(B, powerset(the_carrier(A)))) => open_subset(interior(A, B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_tops_1')).
% 0.22/0.44 tff(46,plain,
% 0.22/0.44 (![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | open_subset(interior(A, B), A))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.22/0.44 tff(47,plain,
% 0.22/0.44 (![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | open_subset(interior(A, B), A))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.22/0.44 tff(48,plain,(
% 0.22/0.44 ![A: $i, B: $i] : ((~(topological_space(A) & top_str(A) & element(B, powerset(the_carrier(A))))) | open_subset(interior(A, B), A))),
% 0.22/0.44 inference(skolemize,[status(sab)],[47])).
% 0.22/0.44 tff(49,plain,
% 0.22/0.44 (![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.22/0.44 tff(50,plain,
% 0.22/0.44 (![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.22/0.44 tff(51,plain,
% 0.22/0.44 (((~![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))) | ((~element(C!8, powerset(the_carrier(A!6)))) | (~topological_space(A!6)) | (~top_str(A!6)) | open_subset(interior(A!6, C!8), A!6))) <=> ((~![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))) | (~element(C!8, powerset(the_carrier(A!6)))) | (~topological_space(A!6)) | (~top_str(A!6)) | open_subset(interior(A!6, C!8), A!6))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(52,plain,
% 0.22/0.44 ((open_subset(interior(A!6, C!8), A!6) | (~element(C!8, powerset(the_carrier(A!6)))) | (~top_str(A!6)) | (~topological_space(A!6))) <=> ((~element(C!8, powerset(the_carrier(A!6)))) | (~topological_space(A!6)) | (~top_str(A!6)) | open_subset(interior(A!6, C!8), A!6))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(53,plain,
% 0.22/0.44 (((~![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))) | (open_subset(interior(A!6, C!8), A!6) | (~element(C!8, powerset(the_carrier(A!6)))) | (~top_str(A!6)) | (~topological_space(A!6)))) <=> ((~![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))) | ((~element(C!8, powerset(the_carrier(A!6)))) | (~topological_space(A!6)) | (~top_str(A!6)) | open_subset(interior(A!6, C!8), A!6)))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[52])).
% 0.22/0.44 tff(54,plain,
% 0.22/0.44 (((~![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))) | (open_subset(interior(A!6, C!8), A!6) | (~element(C!8, powerset(the_carrier(A!6)))) | (~top_str(A!6)) | (~topological_space(A!6)))) <=> ((~![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))) | (~element(C!8, powerset(the_carrier(A!6)))) | (~topological_space(A!6)) | (~top_str(A!6)) | open_subset(interior(A!6, C!8), A!6))),
% 0.22/0.44 inference(transitivity,[status(thm)],[53, 51])).
% 0.22/0.44 tff(55,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))) | (open_subset(interior(A!6, C!8), A!6) | (~element(C!8, powerset(the_carrier(A!6)))) | (~top_str(A!6)) | (~topological_space(A!6)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(56,plain,
% 0.22/0.44 ((~![A: $i, B: $i] : (open_subset(interior(A, B), A) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))) | (~element(C!8, powerset(the_carrier(A!6)))) | (~topological_space(A!6)) | (~top_str(A!6)) | open_subset(interior(A!6, C!8), A!6)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.22/0.44 tff(57,plain,
% 0.22/0.44 (open_subset(interior(A!6, C!8), A!6)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[56, 50, 37, 36, 35])).
% 0.22/0.44 tff(58,plain,
% 0.22/0.44 (open_subset(C!8, A!6)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[57, 34])).
% 0.22/0.44 tff(59,plain,
% 0.22/0.44 (((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)) | (~open_subset(C!8, A!6))),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(60,plain,
% 0.22/0.44 (~open_subset(C!8, A!6)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[59, 29])).
% 0.22/0.44 tff(61,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[60, 58])).
% 0.22/0.44 tff(62,plain,((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(63,plain,
% 0.22/0.44 ((~(~((~((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9))) | (~((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)))))) <=> ((~((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9))) | (~((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(64,plain,
% 0.22/0.44 ((((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6))) <=> (~((~((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9))) | (~((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(65,plain,
% 0.22/0.44 ((~(((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)))) <=> (~(~((~((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9))) | (~((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6))))))),
% 0.22/0.44 inference(monotonicity,[status(thm)],[64])).
% 0.22/0.44 tff(66,plain,
% 0.22/0.44 ((~(((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)))) <=> ((~((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9))) | (~((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[65, 63])).
% 0.22/0.44 tff(67,plain,
% 0.22/0.44 (~(((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) & ((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)))),
% 0.22/0.44 inference(or_elim,[status(thm)],[13])).
% 0.22/0.44 tff(68,plain,
% 0.22/0.44 ((~((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9))) | (~((~(interior(A!6, C!8) = C!8)) | open_subset(C!8, A!6)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.22/0.44 tff(69,plain,
% 0.22/0.44 (~((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[68, 62])).
% 0.22/0.44 tff(70,plain,
% 0.22/0.44 (((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) | open_subset(D!9, B!7)),
% 0.22/0.44 inference(tautology,[status(thm)],[])).
% 0.22/0.44 tff(71,plain,
% 0.22/0.44 (open_subset(D!9, B!7)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.22/0.44 tff(72,plain,
% 0.22/0.44 (top_str(B!7)),
% 0.22/0.44 inference(and_elim,[status(thm)],[12])).
% 0.22/0.44 tff(73,plain,
% 0.22/0.44 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(74,plain,
% 0.22/0.44 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[73])).
% 0.22/0.44 tff(75,plain,
% 0.22/0.44 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(76,plain,
% 0.22/0.44 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[75])).
% 0.22/0.44 tff(77,plain,
% 0.22/0.44 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))),
% 0.22/0.44 inference(transitivity,[status(thm)],[76, 74])).
% 0.22/0.44 tff(78,plain,
% 0.22/0.44 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(79,plain,
% 0.22/0.44 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))) <=> ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(80,plain,
% 0.22/0.44 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[79])).
% 0.22/0.44 tff(81,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t30_tops_1')).
% 0.22/0.44 tff(82,plain,
% 0.22/0.44 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.22/0.44 tff(83,plain,
% 0.22/0.44 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.22/0.44 tff(84,plain,(
% 0.22/0.44 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[83])).
% 0.22/0.44 tff(85,plain,
% 0.22/0.44 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.22/0.44 tff(86,plain,
% 0.22/0.44 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))) | ((~top_str(B!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (open_subset(B, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), B), B!7))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))) | (~top_str(B!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (open_subset(B, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), B), B!7))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(87,plain,
% 0.22/0.45 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))) | ((~top_str(B!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (open_subset(B, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), B), B!7))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(88,plain,
% 0.22/0.45 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (open_subset(B, A) <=> closed_subset(subset_complement(the_carrier(A), B), A))))) | (~top_str(B!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (open_subset(B, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), B), B!7)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.22/0.45 tff(89,plain,
% 0.22/0.45 (![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (open_subset(B, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), B), B!7)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[88, 85, 72])).
% 0.22/0.45 tff(90,plain,
% 0.22/0.45 (((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (open_subset(B, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), B), B!7)))) | ((~element(D!9, powerset(the_carrier(B!7)))) | (open_subset(D!9, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (open_subset(B, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), B), B!7)))) | (~element(D!9, powerset(the_carrier(B!7)))) | (open_subset(D!9, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(91,plain,
% 0.22/0.45 ((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (open_subset(B, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), B), B!7)))) | ((~element(D!9, powerset(the_carrier(B!7)))) | (open_subset(D!9, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(92,plain,
% 0.22/0.45 ((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (open_subset(B, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), B), B!7)))) | (~element(D!9, powerset(the_carrier(B!7)))) | (open_subset(D!9, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), D!9), B!7))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.22/0.45 tff(93,plain,
% 0.22/0.45 (open_subset(D!9, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[92, 14, 89])).
% 0.22/0.45 tff(94,plain,
% 0.22/0.45 ((~(open_subset(D!9, B!7) <=> closed_subset(subset_complement(the_carrier(B!7), D!9), B!7))) | (~open_subset(D!9, B!7)) | closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(95,plain,
% 0.22/0.45 ((~open_subset(D!9, B!7)) | closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.22/0.45 tff(96,plain,
% 0.22/0.45 (closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[95, 71])).
% 0.22/0.45 tff(97,plain,
% 0.22/0.45 (^[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))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(98,plain,
% 0.22/0.45 (![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)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[97])).
% 0.22/0.45 tff(99,plain,
% 0.22/0.45 (![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)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(100,plain,
% 0.22/0.45 (^[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))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(101,plain,
% 0.22/0.45 (![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)))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[100])).
% 0.22/0.45 tff(102,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')).
% 0.22/0.45 tff(103,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.22/0.45 tff(104,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.22/0.45 tff(105,plain,(
% 0.22/0.45 ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.22/0.45 inference(skolemize,[status(sab)],[104])).
% 0.22/0.45 tff(106,plain,
% 0.22/0.45 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.22/0.45 tff(107,plain,
% 0.22/0.45 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(D!9, powerset(the_carrier(B!7)))) | element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(D!9, powerset(the_carrier(B!7)))) | element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(108,plain,
% 0.22/0.45 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(D!9, powerset(the_carrier(B!7)))) | element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(109,plain,
% 0.22/0.45 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(D!9, powerset(the_carrier(B!7)))) | element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.22/0.45 tff(110,plain,
% 0.22/0.45 (element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[109, 106, 14])).
% 0.22/0.45 tff(111,plain,
% 0.22/0.45 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B)))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B)))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(112,plain,
% 0.22/0.45 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B)))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B))))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[111])).
% 0.22/0.45 tff(113,plain,
% 0.22/0.45 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B)))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B)))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(114,plain,
% 0.22/0.45 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B)))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B))))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[113])).
% 0.22/0.45 tff(115,plain,
% 0.22/0.45 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B)))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B))))))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[114, 112])).
% 0.22/0.45 tff(116,plain,
% 0.22/0.45 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B)))))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(117,plain,
% 0.22/0.45 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B))))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[116])).
% 0.22/0.45 tff(118,plain,
% 0.22/0.45 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(119,plain,
% 0.22/0.45 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((closed_subset(B, A) => (topstr_closure(A, B) = B)) & ((topological_space(A) & (topstr_closure(A, B) = B)) => closed_subset(B, A))) <=> (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))), ((element(B, powerset(the_carrier(A))) => ((closed_subset(B, A) => (topstr_closure(A, B) = B)) & ((topological_space(A) & (topstr_closure(A, B) = B)) => closed_subset(B, A)))) <=> (element(B, powerset(the_carrier(A))) => (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))), rewrite((element(B, powerset(the_carrier(A))) => (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))) <=> ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A))))), ((element(B, powerset(the_carrier(A))) => ((closed_subset(B, A) => (topstr_closure(A, B) = B)) & ((topological_space(A) & (topstr_closure(A, B) = B)) => closed_subset(B, A)))) <=> ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => ((closed_subset(B, A) => (topstr_closure(A, B) = B)) & ((topological_space(A) & (topstr_closure(A, B) = B)) => closed_subset(B, A)))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ((closed_subset(B, A) => (topstr_closure(A, B) = B)) & ((topological_space(A) & (topstr_closure(A, B) = B)) => closed_subset(B, A))))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A))))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ((closed_subset(B, A) => (topstr_closure(A, B) = B)) & ((topological_space(A) & (topstr_closure(A, B) = B)) => closed_subset(B, A))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(120,plain,
% 0.22/0.45 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ((closed_subset(B, A) => (topstr_closure(A, B) = B)) & ((topological_space(A) & (topstr_closure(A, B) = B)) => closed_subset(B, A))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[119])).
% 0.22/0.45 tff(121,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ((closed_subset(B, A) => (topstr_closure(A, B) = B)) & ((topological_space(A) & (topstr_closure(A, B) = B)) => closed_subset(B, A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t52_pre_topc')).
% 0.22/0.45 tff(122,plain,
% 0.22/0.45 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.22/0.45 tff(123,plain,
% 0.22/0.45 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.22/0.45 tff(124,plain,(
% 0.22/0.45 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))),
% 0.22/0.45 inference(skolemize,[status(sab)],[123])).
% 0.22/0.45 tff(125,plain,
% 0.22/0.45 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B))))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.22/0.45 tff(126,plain,
% 0.22/0.45 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B))))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[125, 115])).
% 0.22/0.45 tff(127,plain,
% 0.22/0.45 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B))))))))) | ((~top_str(B!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B))))))))) | (~top_str(B!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B))))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(128,plain,
% 0.22/0.45 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B))))))))) | ((~top_str(B!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B))))))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(129,plain,
% 0.22/0.45 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~((~closed_subset(B, A)) | (topstr_closure(A, B) = B))) | (~(closed_subset(B, A) | (~topological_space(A)) | (~(topstr_closure(A, B) = B))))))))) | (~top_str(B!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B)))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.22/0.45 tff(130,plain,
% 0.22/0.45 (![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B)))))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[129, 126, 72])).
% 0.22/0.45 tff(131,plain,
% 0.22/0.45 (((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B)))))))) | ((~element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7)))) | (~((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~((~topological_space(B!7)) | closed_subset(subset_complement(the_carrier(B!7), D!9), B!7) | (~(topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B)))))))) | (~element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7)))) | (~((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~((~topological_space(B!7)) | closed_subset(subset_complement(the_carrier(B!7), D!9), B!7) | (~(topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9))))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(132,plain,
% 0.22/0.45 (((~element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7)))) | (~((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~(closed_subset(subset_complement(the_carrier(B!7), D!9), B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))))))) <=> ((~element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7)))) | (~((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~((~topological_space(B!7)) | closed_subset(subset_complement(the_carrier(B!7), D!9), B!7) | (~(topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9))))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(133,plain,
% 0.22/0.46 (((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B)))))))) | ((~element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7)))) | (~((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~(closed_subset(subset_complement(the_carrier(B!7), D!9), B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B)))))))) | ((~element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7)))) | (~((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~((~topological_space(B!7)) | closed_subset(subset_complement(the_carrier(B!7), D!9), B!7) | (~(topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))))))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[132])).
% 0.22/0.46 tff(134,plain,
% 0.22/0.46 (((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B)))))))) | ((~element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7)))) | (~((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~(closed_subset(subset_complement(the_carrier(B!7), D!9), B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B)))))))) | (~element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7)))) | (~((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~((~topological_space(B!7)) | closed_subset(subset_complement(the_carrier(B!7), D!9), B!7) | (~(topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9))))))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[133, 131])).
% 0.22/0.46 tff(135,plain,
% 0.22/0.46 ((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B)))))))) | ((~element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7)))) | (~((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~(closed_subset(subset_complement(the_carrier(B!7), D!9), B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9))))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(136,plain,
% 0.22/0.46 ((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (~((~((~closed_subset(B, B!7)) | (topstr_closure(B!7, B) = B))) | (~(closed_subset(B, B!7) | (~topological_space(B!7)) | (~(topstr_closure(B!7, B) = B)))))))) | (~element(subset_complement(the_carrier(B!7), D!9), powerset(the_carrier(B!7)))) | (~((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~((~topological_space(B!7)) | closed_subset(subset_complement(the_carrier(B!7), D!9), B!7) | (~(topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.22/0.46 tff(137,plain,
% 0.22/0.46 (~((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~((~topological_space(B!7)) | closed_subset(subset_complement(the_carrier(B!7), D!9), B!7) | (~(topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9))))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[136, 130, 110])).
% 0.22/0.46 tff(138,plain,
% 0.22/0.46 (((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~((~topological_space(B!7)) | closed_subset(subset_complement(the_carrier(B!7), D!9), B!7) | (~(topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))))) | ((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(139,plain,
% 0.22/0.46 ((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.22/0.46 tff(140,plain,
% 0.22/0.46 ((~((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)))) | (~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(141,plain,
% 0.22/0.46 ((~closed_subset(subset_complement(the_carrier(B!7), D!9), B!7)) | (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.22/0.46 tff(142,plain,
% 0.22/0.46 (topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), D!9)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[141, 96])).
% 0.22/0.46 tff(143,plain,
% 0.22/0.46 (subset_complement(the_carrier(B!7), D!9) = topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9))),
% 0.22/0.46 inference(symmetry,[status(thm)],[142])).
% 0.22/0.46 tff(144,plain,
% 0.22/0.46 (subset_complement(the_carrier(B!7), subset_complement(the_carrier(B!7), D!9)) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[143])).
% 0.22/0.46 tff(145,plain,
% 0.22/0.46 (subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9))) = subset_complement(the_carrier(B!7), subset_complement(the_carrier(B!7), D!9))),
% 0.22/0.46 inference(symmetry,[status(thm)],[144])).
% 0.22/0.46 tff(146,plain,
% 0.22/0.46 (^[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)))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(147,plain,
% 0.22/0.46 (![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))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[146])).
% 0.22/0.46 tff(148,plain,
% 0.22/0.46 (^[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)))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(149,plain,
% 0.22/0.46 (![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))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[148])).
% 0.22/0.46 tff(150,plain,
% 0.22/0.46 (![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))))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[149, 147])).
% 0.22/0.46 tff(151,plain,
% 0.22/0.46 (![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))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(152,plain,
% 0.22/0.46 (^[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))))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(153,plain,
% 0.22/0.46 (![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))))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[152])).
% 0.22/0.46 tff(154,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')).
% 0.22/0.46 tff(155,plain,
% 0.22/0.46 (![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))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.22/0.46 tff(156,plain,
% 0.22/0.46 (![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))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.22/0.46 tff(157,plain,(
% 0.22/0.46 ![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))))))),
% 0.22/0.46 inference(skolemize,[status(sab)],[156])).
% 0.22/0.46 tff(158,plain,
% 0.22/0.46 (![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))))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.22/0.46 tff(159,plain,
% 0.22/0.46 (((~![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(B!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (interior(B!7, B) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), 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(B!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (interior(B!7, B) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), B))))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(160,plain,
% 0.22/0.46 ((~![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(B!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (interior(B!7, B) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), B))))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(161,plain,
% 0.22/0.46 ((~![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(B!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (interior(B!7, B) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), B)))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.22/0.47 tff(162,plain,
% 0.22/0.47 (![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (interior(B!7, B) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), B)))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[161, 158, 72])).
% 0.22/0.47 tff(163,plain,
% 0.22/0.47 (((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (interior(B!7, B) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), B)))))) | ((~element(D!9, powerset(the_carrier(B!7)))) | (interior(B!7, D!9) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (interior(B!7, B) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), B)))))) | (~element(D!9, powerset(the_carrier(B!7)))) | (interior(B!7, D!9) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(164,plain,
% 0.22/0.47 ((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (interior(B!7, B) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), B)))))) | ((~element(D!9, powerset(the_carrier(B!7)))) | (interior(B!7, D!9) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(165,plain,
% 0.22/0.47 ((~![B: $i] : ((~element(B, powerset(the_carrier(B!7)))) | (interior(B!7, B) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), B)))))) | (~element(D!9, powerset(the_carrier(B!7)))) | (interior(B!7, D!9) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.22/0.47 tff(166,plain,
% 0.22/0.47 (interior(B!7, D!9) = subset_complement(the_carrier(B!7), topstr_closure(B!7, subset_complement(the_carrier(B!7), D!9)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[165, 14, 162])).
% 0.22/0.47 tff(167,plain,
% 0.22/0.47 (interior(B!7, D!9) = D!9),
% 0.22/0.47 inference(transitivity,[status(thm)],[166, 145, 28])).
% 0.22/0.47 tff(168,plain,
% 0.22/0.47 (((~open_subset(D!9, B!7)) | (interior(B!7, D!9) = D!9)) | (~(interior(B!7, D!9) = D!9))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(169,plain,
% 0.22/0.47 (~(interior(B!7, D!9) = D!9)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[168, 69])).
% 0.22/0.47 tff(170,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[169, 167])).
% 0.22/0.47 % SZS output end Proof
% 0.22/0.47 % E exiting
%------------------------------------------------------------------------------