%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU322+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU322+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 06:44:56 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(in_type, type, (
% 0.21/0.41 in: ( $i * $i ) > $o)).
% 0.21/0.41 tff(subset_complement_type, type, (
% 0.21/0.41 subset_complement: ( $i * $i ) > $i)).
% 0.21/0.41 tff(tptp_fun_B_8_type, type, (
% 0.21/0.41 tptp_fun_B_8: $i)).
% 0.21/0.41 tff(the_carrier_type, type, (
% 0.21/0.41 the_carrier: $i > $i)).
% 0.21/0.41 tff(tptp_fun_A_7_type, type, (
% 0.21/0.41 tptp_fun_A_7: $i)).
% 0.21/0.41 tff(tptp_fun_C_0_type, type, (
% 0.21/0.41 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.21/0.41 tff(interior_type, type, (
% 0.21/0.41 interior: ( $i * $i ) > $i)).
% 0.21/0.41 tff(element_type, type, (
% 0.21/0.41 element: ( $i * $i ) > $o)).
% 0.21/0.41 tff(powerset_type, type, (
% 0.21/0.41 powerset: $i > $i)).
% 0.21/0.41 tff(subset_type, type, (
% 0.21/0.41 subset: ( $i * $i ) > $o)).
% 0.21/0.41 tff(top_str_type, type, (
% 0.21/0.41 top_str: $i > $o)).
% 0.21/0.41 tff(topstr_closure_type, type, (
% 0.21/0.41 topstr_closure: ( $i * $i ) > $i)).
% 0.21/0.41 tff(one_sorted_str_type, type, (
% 0.21/0.41 one_sorted_str: $i > $o)).
% 0.21/0.41 tff(empty_carrier_type, type, (
% 0.21/0.41 empty_carrier: $i > $o)).
% 0.21/0.41 tff(empty_type, type, (
% 0.21/0.41 empty: $i > $o)).
% 0.21/0.41 tff(1,plain,
% 0.21/0.41 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))) <=> (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 ((~![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B)))) <=> (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(3,axiom,(~![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t44_tops_1')).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (~((~element(B!8, powerset(the_carrier(A!7)))) | subset(interior(A!7, B!8), B!8))),
% 0.21/0.41 inference(and_elim,[status(thm)],[7])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (element(B!8, powerset(the_carrier(A!7)))),
% 0.21/0.41 inference(or_elim,[status(thm)],[8])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (^[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)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (![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))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (^[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)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (![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))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.42 tff(15,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')).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.42 tff(18,plain,(
% 0.21/0.42 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.21/0.42 inference(skolemize,[status(sab)],[17])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)) = B!8))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(B!8, powerset(the_carrier(A!7)))) | (subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)) = B!8))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)) = B!8))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(B!8, powerset(the_carrier(A!7)))) | (subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)) = B!8)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)) = B!8),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)))),
% 0.21/0.42 inference(symmetry,[status(thm)],[24])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)) <=> (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[25])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[30, 28])).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.42 tff(37,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.42 tff(40,plain,(
% 0.21/0.42 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[39])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(interior(A!7, B!8), B!8)) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, B!8)))) | (~(subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (~((~((~subset(interior(A!7, B!8), B!8)) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, B!8)))) | (~(subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (((~((~subset(interior(A!7, B!8), B!8)) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, B!8)))) | (~(subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)))))) | (subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (~subset(interior(A!7, B!8), B!8)),
% 0.21/0.42 inference(or_elim,[status(thm)],[8])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 ((~(subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8))))) | subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 ((~(subset(interior(A!7, B!8), B!8) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8))))) | (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (~((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[52, 26])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) | (~(subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))) | (~((~in(tptp_fun_C_0(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (~((~((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) | (~(subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))) | (~((~in(tptp_fun_C_0(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[54, 42])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 (((~((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) | (~(subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))) | (~((~in(tptp_fun_C_0(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), subset_complement(the_carrier(A!7), B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))))) | ((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 ((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.43 tff(63,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')).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.21/0.43 tff(66,plain,(
% 0.21/0.43 ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[65])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(B!8, powerset(the_carrier(A!7)))) | element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(B!8, powerset(the_carrier(A!7)))) | element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(B!8, powerset(the_carrier(A!7)))) | element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(B!8, powerset(the_carrier(A!7)))) | element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 (element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[70, 67, 9])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[75, 73])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))) <=> ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B)))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.43 tff(80,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t48_pre_topc')).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.21/0.43 tff(83,plain,(
% 0.21/0.43 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[82])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (top_str(A!7)),
% 0.21/0.43 inference(and_elim,[status(thm)],[7])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) | ((~top_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) | (~top_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) | ((~top_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) | (~top_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[88, 85, 84])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B)))) | ((~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B)))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B)))) | ((~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | subset(B, topstr_closure(A!7, B)))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[92, 89, 71])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 ((~((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) | (~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 ((~((~subset(subset_complement(the_carrier(A!7), B!8), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) | ![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[95, 57])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (^[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)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 (^[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)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[99])).
% 0.21/0.43 tff(101,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[100, 98])).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 (^[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))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[103])).
% 0.21/0.43 tff(105,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')).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.21/0.43 tff(108,plain,(
% 0.21/0.43 ![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))))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[107])).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 (![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))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 (((~![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!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!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(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 ((~![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!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 ((~![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!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B)))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[112, 109, 85])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B)))))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (interior(A!7, B!8) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B)))))) | (~element(B!8, powerset(the_carrier(A!7)))) | (interior(A!7, B!8) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B)))))) | ((~element(B!8, powerset(the_carrier(A!7)))) | (interior(A!7, B!8) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | (interior(A!7, B) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B)))))) | (~element(B!8, powerset(the_carrier(A!7)))) | (interior(A!7, B!8) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (interior(A!7, B!8) = subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[116, 9, 113])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))) = interior(A!7, B!8)),
% 0.21/0.44 inference(symmetry,[status(thm)],[117])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[118])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8)) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.44 inference(symmetry,[status(thm)],[119])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), B!8)) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[121, 50])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[122, 120])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (^[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))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[124])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (![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)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.44 tff(131,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')).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.21/0.44 tff(134,plain,(
% 0.21/0.44 ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[133])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[135, 125])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 (((~![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!7)) | element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))))) <=> ((~![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!7)) | element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 ((element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | (~top_str(A!7))) <=> ((~top_str(A!7)) | element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (((~![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!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | (~top_str(A!7)))) <=> ((~![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!7)) | element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[138])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 (((~![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!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | (~top_str(A!7)))) <=> ((~![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!7)) | element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[139, 137])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 ((~![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!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | (~top_str(A!7)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 ((~![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!7)) | element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 (element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[142, 136, 85, 71])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 (^[A: $i, B: $i, C: $i] : refl(((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C)))) <=> ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C)))) <=> ![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[144])).
% 0.21/0.44 tff(146,plain,
% 0.21/0.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(B, subset_complement(A, C)) & in(B, C)) <=> (~((~in(B, C)) | (~in(B, subset_complement(A, C)))))), ((~(in(B, subset_complement(A, C)) & in(B, C))) <=> (~(~((~in(B, C)) | (~in(B, subset_complement(A, C)))))))), rewrite((~(~((~in(B, C)) | (~in(B, subset_complement(A, C)))))) <=> ((~in(B, C)) | (~in(B, subset_complement(A, C))))), ((~(in(B, subset_complement(A, C)) & in(B, C))) <=> ((~in(B, C)) | (~in(B, subset_complement(A, C)))))), (((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ((~element(C, powerset(A))) | ((~in(B, C)) | (~in(B, subset_complement(A, C))))))), rewrite(((~element(C, powerset(A))) | ((~in(B, C)) | (~in(B, subset_complement(A, C))))) <=> ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))), (((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[146])).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(149,plain,
% 0.21/0.44 (^[A: $i, B: $i, C: $i] : rewrite((element(C, powerset(A)) => (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(150,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : (element(C, powerset(A)) => (~(in(B, subset_complement(A, C)) & in(B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[149])).
% 0.21/0.44 tff(151,axiom,(![A: $i, B: $i, C: $i] : (element(C, powerset(A)) => (~(in(B, subset_complement(A, C)) & in(B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t54_subset_1')).
% 0.21/0.44 tff(152,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.21/0.44 tff(153,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.21/0.44 tff(154,plain,(
% 0.21/0.44 ![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[153])).
% 0.21/0.44 tff(155,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.21/0.44 tff(156,plain,
% 0.21/0.44 (![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[155, 145])).
% 0.21/0.44 tff(157,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | ((~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(158,plain,
% 0.21/0.44 (((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))) <=> ((~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(159,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | ((~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[158])).
% 0.21/0.44 tff(160,plain,
% 0.21/0.44 (((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[159, 157])).
% 0.21/0.45 tff(161,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(162,plain,
% 0.21/0.45 ((~![A: $i, B: $i, C: $i] : ((~in(B, C)) | (~element(C, powerset(A))) | (~in(B, subset_complement(A, C))))) | (~element(topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)), powerset(the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.45 tff(163,plain,
% 0.21/0.45 ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[162, 156, 143])).
% 0.21/0.45 tff(164,plain,
% 0.21/0.45 (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[163, 123])).
% 0.21/0.45 tff(165,plain,
% 0.21/0.45 (((~![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))) <=> ((~![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(166,plain,
% 0.21/0.45 ((~![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(167,plain,
% 0.21/0.45 ((~![C: $i] : ((~in(C, subset_complement(the_carrier(A!7), B!8))) | in(C, topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8))))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), topstr_closure(A!7, subset_complement(the_carrier(A!7), B!8)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.21/0.45 tff(168,plain,
% 0.21/0.45 (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[167, 164, 96])).
% 0.21/0.45 tff(169,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7))))) | (~(subset(interior(A!7, B!8), the_carrier(A!7)) | (~((~in(tptp_fun_C_0(the_carrier(A!7), interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(the_carrier(A!7), interior(A!7, B!8)), the_carrier(A!7))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(170,plain,
% 0.21/0.45 (~((~((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7))))) | (~(subset(interior(A!7, B!8), the_carrier(A!7)) | (~((~in(tptp_fun_C_0(the_carrier(A!7), interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(the_carrier(A!7), interior(A!7, B!8)), the_carrier(A!7)))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[169, 42])).
% 0.21/0.45 tff(171,plain,
% 0.21/0.45 (((~((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7))))) | (~(subset(interior(A!7, B!8), the_carrier(A!7)) | (~((~in(tptp_fun_C_0(the_carrier(A!7), interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(the_carrier(A!7), interior(A!7, B!8)), the_carrier(A!7))))))) | ((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(172,plain,
% 0.21/0.45 ((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.21/0.45 tff(173,plain,
% 0.21/0.45 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(174,plain,
% 0.21/0.45 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.45 tff(175,plain,
% 0.21/0.45 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(176,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 0.21/0.45 tff(177,plain,
% 0.21/0.45 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.21/0.45 tff(178,plain,(
% 0.21/0.45 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.21/0.45 inference(skolemize,[status(sab)],[177])).
% 0.21/0.45 tff(179,plain,
% 0.21/0.45 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.21/0.45 tff(180,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(interior(A!7, B!8), powerset(the_carrier(A!7))) <=> subset(interior(A!7, B!8), the_carrier(A!7)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(181,plain,
% 0.21/0.45 (element(interior(A!7, B!8), powerset(the_carrier(A!7))) <=> subset(interior(A!7, B!8), the_carrier(A!7))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.21/0.45 tff(182,plain,
% 0.21/0.45 (^[A: $i, B: $i] : refl((element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(183,plain,
% 0.21/0.45 (![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> ![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[182])).
% 0.21/0.45 tff(184,plain,
% 0.21/0.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((top_str(A) & element(B, powerset(the_carrier(A)))) <=> (~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))), ((~(top_str(A) & element(B, powerset(the_carrier(A))))) <=> (~(~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))))), rewrite((~(~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))) <=> ((~top_str(A)) | (~element(B, powerset(the_carrier(A)))))), ((~(top_str(A) & element(B, powerset(the_carrier(A))))) <=> ((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))), (((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> (((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))))), rewrite((((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))), (((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(185,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[184])).
% 0.21/0.45 tff(186,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(187,plain,
% 0.21/0.45 (^[A: $i, B: $i] : rewrite(((top_str(A) & element(B, powerset(the_carrier(A)))) => element(interior(A, B), powerset(the_carrier(A)))) <=> ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(188,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(interior(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[187])).
% 0.21/0.45 tff(189,axiom,(![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(interior(A, B), powerset(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_tops_1')).
% 0.21/0.45 tff(190,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.21/0.45 tff(191,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.21/0.45 tff(192,plain,(
% 0.21/0.45 ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[191])).
% 0.21/0.45 tff(193,plain,
% 0.21/0.45 (![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.21/0.45 tff(194,plain,
% 0.21/0.45 (![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[193, 183])).
% 0.21/0.45 tff(195,plain,
% 0.21/0.45 (((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!7)) | (~element(B!8, powerset(the_carrier(A!7)))) | element(interior(A!7, B!8), powerset(the_carrier(A!7))))) <=> ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!7)) | (~element(B!8, powerset(the_carrier(A!7)))) | element(interior(A!7, B!8), powerset(the_carrier(A!7))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(196,plain,
% 0.21/0.46 ((element(interior(A!7, B!8), powerset(the_carrier(A!7))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~top_str(A!7))) <=> ((~top_str(A!7)) | (~element(B!8, powerset(the_carrier(A!7)))) | element(interior(A!7, B!8), powerset(the_carrier(A!7))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(197,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(interior(A!7, B!8), powerset(the_carrier(A!7))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~top_str(A!7)))) <=> ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!7)) | (~element(B!8, powerset(the_carrier(A!7)))) | element(interior(A!7, B!8), powerset(the_carrier(A!7)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[196])).
% 0.21/0.46 tff(198,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(interior(A!7, B!8), powerset(the_carrier(A!7))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~top_str(A!7)))) <=> ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!7)) | (~element(B!8, powerset(the_carrier(A!7)))) | element(interior(A!7, B!8), powerset(the_carrier(A!7))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[197, 195])).
% 0.21/0.46 tff(199,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(interior(A!7, B!8), powerset(the_carrier(A!7))) | (~element(B!8, powerset(the_carrier(A!7)))) | (~top_str(A!7)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(200,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!7)) | (~element(B!8, powerset(the_carrier(A!7)))) | element(interior(A!7, B!8), powerset(the_carrier(A!7)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.21/0.46 tff(201,plain,
% 0.21/0.46 (element(interior(A!7, B!8), powerset(the_carrier(A!7)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[200, 194, 85, 9])).
% 0.21/0.46 tff(202,plain,
% 0.21/0.46 ((~(element(interior(A!7, B!8), powerset(the_carrier(A!7))) <=> subset(interior(A!7, B!8), the_carrier(A!7)))) | (~element(interior(A!7, B!8), powerset(the_carrier(A!7)))) | subset(interior(A!7, B!8), the_carrier(A!7))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(203,plain,
% 0.21/0.46 ((~(element(interior(A!7, B!8), powerset(the_carrier(A!7))) <=> subset(interior(A!7, B!8), the_carrier(A!7)))) | subset(interior(A!7, B!8), the_carrier(A!7))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.21/0.46 tff(204,plain,
% 0.21/0.46 (subset(interior(A!7, B!8), the_carrier(A!7))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[203, 181])).
% 0.21/0.46 tff(205,plain,
% 0.21/0.46 ((~((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7))))) | (~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(206,plain,
% 0.21/0.46 ((~((~subset(interior(A!7, B!8), the_carrier(A!7))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7))))) | ![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.21/0.46 tff(207,plain,
% 0.21/0.46 (![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[206, 172])).
% 0.21/0.46 tff(208,plain,
% 0.21/0.46 (((~![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7)))) <=> ((~![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(209,plain,
% 0.21/0.46 ((~![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(210,plain,
% 0.21/0.46 ((~![C: $i] : ((~in(C, interior(A!7, B!8))) | in(C, the_carrier(A!7)))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.21/0.46 tff(211,plain,
% 0.21/0.46 (in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[210, 122, 207])).
% 0.21/0.46 tff(212,plain,
% 0.21/0.46 (^[A: $i, B: $i] : refl(((~in(A, B)) | element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(213,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[212])).
% 0.21/0.46 tff(214,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(215,plain,
% 0.21/0.46 (^[A: $i, B: $i] : rewrite((in(A, B) => element(A, B)) <=> ((~in(A, B)) | element(A, B)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(216,plain,
% 0.21/0.46 (![A: $i, B: $i] : (in(A, B) => element(A, B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[215])).
% 0.21/0.46 tff(217,axiom,(![A: $i, B: $i] : (in(A, B) => element(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_subset')).
% 0.21/0.46 tff(218,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.21/0.46 tff(219,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.21/0.46 tff(220,plain,(
% 0.21/0.46 ![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.46 inference(skolemize,[status(sab)],[219])).
% 0.21/0.46 tff(221,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~in(A, B)) | element(A, B))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[220, 213])).
% 0.21/0.46 tff(222,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(223,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | ((~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(224,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : ((~in(A, B)) | element(A, B))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.21/0.46 tff(225,plain,
% 0.21/0.46 (element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[224, 221, 211])).
% 0.21/0.46 tff(226,plain,
% 0.21/0.46 (^[A: $i] : refl((one_sorted_str(A) | (~top_str(A))) <=> (one_sorted_str(A) | (~top_str(A))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(227,plain,
% 0.21/0.46 (![A: $i] : (one_sorted_str(A) | (~top_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[226])).
% 0.21/0.46 tff(228,plain,
% 0.21/0.46 (![A: $i] : (one_sorted_str(A) | (~top_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(229,plain,
% 0.21/0.46 (^[A: $i] : rewrite((top_str(A) => one_sorted_str(A)) <=> (one_sorted_str(A) | (~top_str(A))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(230,plain,
% 0.21/0.46 (![A: $i] : (top_str(A) => one_sorted_str(A)) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[229])).
% 0.21/0.46 tff(231,axiom,(![A: $i] : (top_str(A) => one_sorted_str(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 0.21/0.46 tff(232,plain,
% 0.21/0.46 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.21/0.46 tff(233,plain,
% 0.21/0.46 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.21/0.46 tff(234,plain,(
% 0.21/0.46 ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[233])).
% 0.21/0.46 tff(235,plain,
% 0.21/0.46 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.21/0.46 tff(236,plain,
% 0.21/0.46 (((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | (one_sorted_str(A!7) | (~top_str(A!7)))) <=> ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | one_sorted_str(A!7) | (~top_str(A!7)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(237,plain,
% 0.21/0.46 ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | (one_sorted_str(A!7) | (~top_str(A!7)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(238,plain,
% 0.21/0.46 ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | one_sorted_str(A!7) | (~top_str(A!7))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.21/0.46 tff(239,plain,
% 0.21/0.46 (one_sorted_str(A!7)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[238, 235, 85])).
% 0.21/0.46 tff(240,plain,
% 0.21/0.46 (^[A: $i] : refl(((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A)))) <=> ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(241,plain,
% 0.21/0.46 (![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[240])).
% 0.21/0.46 tff(242,plain,
% 0.21/0.46 (![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(243,plain,
% 0.21/0.46 (^[A: $i] : rewrite((one_sorted_str(A) => (empty_carrier(A) <=> empty(the_carrier(A)))) <=> ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(244,plain,
% 0.21/0.46 (![A: $i] : (one_sorted_str(A) => (empty_carrier(A) <=> empty(the_carrier(A)))) <=> ![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[243])).
% 0.21/0.46 tff(245,axiom,(![A: $i] : (one_sorted_str(A) => (empty_carrier(A) <=> empty(the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_struct_0')).
% 0.21/0.46 tff(246,plain,
% 0.21/0.46 (![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.21/0.46 tff(247,plain,
% 0.21/0.46 (![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[246, 242])).
% 0.21/0.46 tff(248,plain,(
% 0.21/0.46 ![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[247])).
% 0.21/0.46 tff(249,plain,
% 0.21/0.46 (![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[248, 241])).
% 0.21/0.46 tff(250,plain,
% 0.21/0.46 (((~![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))) | ((~one_sorted_str(A!7)) | (empty_carrier(A!7) <=> empty(the_carrier(A!7))))) <=> ((~![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))) | (~one_sorted_str(A!7)) | (empty_carrier(A!7) <=> empty(the_carrier(A!7))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(251,plain,
% 0.21/0.46 ((~![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))) | ((~one_sorted_str(A!7)) | (empty_carrier(A!7) <=> empty(the_carrier(A!7))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(252,plain,
% 0.21/0.46 ((~![A: $i] : ((~one_sorted_str(A)) | (empty_carrier(A) <=> empty(the_carrier(A))))) | (~one_sorted_str(A!7)) | (empty_carrier(A!7) <=> empty(the_carrier(A!7)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.21/0.46 tff(253,plain,
% 0.21/0.46 ((~one_sorted_str(A!7)) | (empty_carrier(A!7) <=> empty(the_carrier(A!7)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[252, 249])).
% 0.21/0.46 tff(254,plain,
% 0.21/0.46 (empty_carrier(A!7) <=> empty(the_carrier(A!7))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[253, 239])).
% 0.21/0.46 tff(255,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : refl(((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(256,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[255])).
% 0.21/0.46 tff(257,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C)) & empty(C)) <=> (~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> (~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(258,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[257])).
% 0.21/0.46 tff(259,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(260,plain,
% 0.21/0.46 (^[A: $i, B: $i, C: $i] : rewrite((~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> (~(in(A, B) & element(B, powerset(C)) & empty(C))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(261,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C))) <=> ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[260])).
% 0.21/0.46 tff(262,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_subset')).
% 0.21/0.46 tff(263,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.21/0.46 tff(264,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.21/0.46 tff(265,plain,(
% 0.21/0.46 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[264])).
% 0.21/0.46 tff(266,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.21/0.46 tff(267,plain,
% 0.21/0.46 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[266, 256])).
% 0.21/0.46 tff(268,plain,
% 0.21/0.46 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(the_carrier(A!7))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | (~element(interior(A!7, B!8), powerset(the_carrier(A!7)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(the_carrier(A!7))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | (~element(interior(A!7, B!8), powerset(the_carrier(A!7)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(269,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(the_carrier(A!7))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | (~element(interior(A!7, B!8), powerset(the_carrier(A!7)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(270,plain,
% 0.21/0.46 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(the_carrier(A!7))) | (~in(tptp_fun_C_0(B!8, interior(A!7, B!8)), interior(A!7, B!8))) | (~element(interior(A!7, B!8), powerset(the_carrier(A!7))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.21/0.46 tff(271,plain,
% 0.21/0.46 (~empty(the_carrier(A!7))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[270, 267, 122, 201])).
% 0.21/0.46 tff(272,plain,
% 0.21/0.46 ((~(empty_carrier(A!7) <=> empty(the_carrier(A!7)))) | (~empty_carrier(A!7)) | empty(the_carrier(A!7))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(273,plain,
% 0.21/0.46 (~empty_carrier(A!7)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[272, 271, 254])).
% 0.21/0.46 tff(274,plain,
% 0.21/0.46 (^[A: $i] : refl((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(275,plain,
% 0.21/0.46 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[274])).
% 0.21/0.46 tff(276,plain,
% 0.21/0.46 (^[A: $i] : rewrite((empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(277,plain,
% 0.21/0.46 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[276])).
% 0.21/0.46 tff(278,plain,
% 0.21/0.46 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[277, 275])).
% 0.21/0.46 tff(279,plain,
% 0.21/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & one_sorted_str(A)) <=> (~(empty_carrier(A) | (~one_sorted_str(A))))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (~(~(empty_carrier(A) | (~one_sorted_str(A))))))), rewrite((~(~(empty_carrier(A) | (~one_sorted_str(A))))) <=> (empty_carrier(A) | (~one_sorted_str(A)))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (empty_carrier(A) | (~one_sorted_str(A))))), (((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))) <=> ((empty_carrier(A) | (~one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))))), rewrite(((empty_carrier(A) | (~one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))), (((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))) <=> (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(280,plain,
% 0.21/0.47 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))) <=> ![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[279])).
% 0.21/0.47 tff(281,plain,
% 0.21/0.47 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(282,plain,
% 0.21/0.47 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(rewrite((in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))) <=> (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))), rewrite((~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))) <=> (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))), ((in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))) <=> (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))), ((element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))) <=> (element(C, the_carrier(A)) => (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))), rewrite((element(C, the_carrier(A)) => (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))) <=> ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))), ((element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))) <=> ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))), (![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))) <=> (element(B, powerset(the_carrier(A))) => ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))), rewrite((element(B, powerset(the_carrier(A))) => ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))), ((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))))), rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B))))))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))), ((((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(283,plain,
% 0.21/0.47 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[282])).
% 0.21/0.47 tff(284,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, subset_complement(the_carrier(A), B)) <=> (~in(C, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l40_tops_1')).
% 0.21/0.47 tff(285,plain,
% 0.21/0.47 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.21/0.47 tff(286,plain,
% 0.21/0.47 (![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[285, 281])).
% 0.21/0.47 tff(287,plain,(
% 0.21/0.47 ![A: $i] : ((~((~empty_carrier(A)) & one_sorted_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[286])).
% 0.21/0.47 tff(288,plain,
% 0.21/0.47 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[287, 280])).
% 0.21/0.47 tff(289,plain,
% 0.21/0.47 (![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[288, 278])).
% 0.21/0.47 tff(290,plain,
% 0.21/0.47 (((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))) | (empty_carrier(A!7) | (~one_sorted_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A!7), B)))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))) | empty_carrier(A!7) | (~one_sorted_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A!7), B)))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(291,plain,
% 0.21/0.47 ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))) | (empty_carrier(A!7) | (~one_sorted_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A!7), B)))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(292,plain,
% 0.21/0.47 ((~![A: $i] : (empty_carrier(A) | (~one_sorted_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A), B)))))))) | empty_carrier(A!7) | (~one_sorted_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A!7), B))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.21/0.47 tff(293,plain,
% 0.21/0.47 (empty_carrier(A!7) | (~one_sorted_str(A!7)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A!7), B))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[292, 289])).
% 0.21/0.47 tff(294,plain,
% 0.21/0.47 (![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A!7), B))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[293, 273, 239])).
% 0.21/0.47 tff(295,plain,
% 0.21/0.47 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A!7), B))))))) | ((~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, subset_complement(the_carrier(A!7), B!8)) <=> in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A!7), B))))))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, subset_complement(the_carrier(A!7), B!8)) <=> in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(296,plain,
% 0.21/0.47 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A!7), B))))))) | ((~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, subset_complement(the_carrier(A!7), B!8)) <=> in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(297,plain,
% 0.21/0.47 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, B) <=> in(C, subset_complement(the_carrier(A!7), B))))))) | (~element(subset_complement(the_carrier(A!7), B!8), powerset(the_carrier(A!7)))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, subset_complement(the_carrier(A!7), B!8)) <=> in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.21/0.47 tff(298,plain,
% 0.21/0.47 (![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, subset_complement(the_carrier(A!7), B!8)) <=> in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[297, 294, 71])).
% 0.21/0.47 tff(299,plain,
% 0.21/0.47 (((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, subset_complement(the_carrier(A!7), B!8)) <=> in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))))))) | ((~element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | (~(in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8)) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, subset_complement(the_carrier(A!7), B!8)) <=> in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))))))) | (~element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | (~(in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8)) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(300,plain,
% 0.21/0.47 ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, subset_complement(the_carrier(A!7), B!8)) <=> in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))))))) | ((~element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | (~(in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8)) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(301,plain,
% 0.21/0.47 ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~(in(C, subset_complement(the_carrier(A!7), B!8)) <=> in(C, subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))))))) | (~element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | (~(in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8)) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.21/0.47 tff(302,plain,
% 0.21/0.47 ((~element(tptp_fun_C_0(B!8, interior(A!7, B!8)), the_carrier(A!7))) | (~(in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8)) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[301, 298])).
% 0.21/0.47 tff(303,plain,
% 0.21/0.47 (~(in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8)) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[302, 225])).
% 0.21/0.47 tff(304,plain,
% 0.21/0.47 ((in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8)) <=> in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)))) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), B!8)) | in(tptp_fun_C_0(B!8, interior(A!7, B!8)), subset_complement(the_carrier(A!7), subset_complement(the_carrier(A!7), B!8)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(305,plain,
% 0.21/0.47 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[304, 303, 168, 53])).
% 0.21/0.48 % SZS output end Proof
% 0.21/0.48 % E exiting
%------------------------------------------------------------------------------