%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU117+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:55 AM UTC 2025
% Result : Theorem 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU117+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:05:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(in_type, type, (
% 0.20/0.39 in: ( $i * $i ) > $o)).
% 0.20/0.39 tff(finite_subsets_type, type, (
% 0.20/0.39 finite_subsets: $i > $i)).
% 0.20/0.39 tff(tptp_fun_A_10_type, type, (
% 0.20/0.39 tptp_fun_A_10: $i)).
% 0.20/0.39 tff(tptp_fun_B_9_type, type, (
% 0.20/0.39 tptp_fun_B_9: $i)).
% 0.20/0.39 tff(subset_type, type, (
% 0.20/0.39 subset: ( $i * $i ) > $o)).
% 0.20/0.39 tff(finite_type, type, (
% 0.20/0.39 finite: $i > $o)).
% 0.20/0.39 tff(element_type, type, (
% 0.20/0.39 element: ( $i * $i ) > $o)).
% 0.20/0.39 tff(powerset_type, type, (
% 0.20/0.39 powerset: $i > $i)).
% 0.20/0.39 tff(empty_type, type, (
% 0.20/0.39 empty: $i > $o)).
% 0.20/0.39 tff(preboolean_type, type, (
% 0.20/0.39 preboolean: $i > $o)).
% 0.20/0.39 tff(diff_closed_type, type, (
% 0.20/0.39 diff_closed: $i > $o)).
% 0.20/0.39 tff(cup_closed_type, type, (
% 0.20/0.39 cup_closed: $i > $o)).
% 0.20/0.39 tff(tptp_fun_C_11_type, type, (
% 0.20/0.39 tptp_fun_C_11: ( $i * $i ) > $i)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(4,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.39 tff(6,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.20/0.39 inference(skolemize,[status(sab)],[5])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(B!9, powerset(A!10)) <=> subset(B!9, A!10))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (element(B!9, powerset(A!10)) <=> subset(B!9, A!10)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))) <=> (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (element(B, finite_subsets(A)) => element(B, powerset(A)))) <=> (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(12,axiom,(~![A: $i, B: $i] : (element(B, finite_subsets(A)) => element(B, powerset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t32_finsub_1')).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (~![A: $i, B: $i] : ((~element(B, finite_subsets(A))) | element(B, powerset(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.20/0.39 tff(17,plain,(
% 0.20/0.39 ~((~element(B!9, finite_subsets(A!10))) | element(B!9, powerset(A!10)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[16])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (~element(B!9, powerset(A!10))),
% 0.20/0.39 inference(or_elim,[status(thm)],[17])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 ((~(element(B!9, powerset(A!10)) <=> subset(B!9, A!10))) | element(B!9, powerset(A!10)) | (~subset(B!9, A!10))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 ((~(element(B!9, powerset(A!10)) <=> subset(B!9, A!10))) | (~subset(B!9, A!10))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (~subset(B!9, A!10)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[20, 9])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (((~finite(B!9)) | (~subset(B!9, A!10))) | subset(B!9, A!10)),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 ((~finite(B!9)) | (~subset(B!9, A!10))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (^[A: $i] : refl((~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A))))) <=> (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (![A: $i] : (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A))))) <=> ![A: $i] : (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (^[A: $i] : rewrite(((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A))) <=> (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A))) <=> ![A: $i] : (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A)))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A))) <=> ![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (^[A: $i] : trans(monotonicity(rewrite((((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A))) & diff_closed(finite_subsets(A))) <=> ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)))), (((((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A))) & diff_closed(finite_subsets(A))) & preboolean(finite_subsets(A))) <=> (((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A))) & preboolean(finite_subsets(A))))), rewrite((((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A))) & preboolean(finite_subsets(A))) <=> ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))), (((((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A))) & diff_closed(finite_subsets(A))) & preboolean(finite_subsets(A))) <=> ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (![A: $i] : ((((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A))) & diff_closed(finite_subsets(A))) & preboolean(finite_subsets(A))) <=> ![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.39 tff(31,axiom,(![A: $i] : ((((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A))) & diff_closed(finite_subsets(A))) & preboolean(finite_subsets(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc2_finsub_1')).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.39 tff(34,plain,(
% 0.20/0.39 ![A: $i] : ((~empty(finite_subsets(A))) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[33])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (![A: $i] : (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (![A: $i] : (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 ((~![A: $i] : (~(empty(finite_subsets(A)) | (~cup_closed(finite_subsets(A))) | (~diff_closed(finite_subsets(A))) | (~preboolean(finite_subsets(A)))))) | (~(empty(finite_subsets(A!10)) | (~cup_closed(finite_subsets(A!10))) | (~diff_closed(finite_subsets(A!10))) | (~preboolean(finite_subsets(A!10)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (~(empty(finite_subsets(A!10)) | (~cup_closed(finite_subsets(A!10))) | (~diff_closed(finite_subsets(A!10))) | (~preboolean(finite_subsets(A!10))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 ((empty(finite_subsets(A!10)) | (~cup_closed(finite_subsets(A!10))) | (~diff_closed(finite_subsets(A!10))) | (~preboolean(finite_subsets(A!10)))) | (~empty(finite_subsets(A!10)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (~empty(finite_subsets(A!10))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (element(B!9, finite_subsets(A!10))),
% 0.20/0.39 inference(or_elim,[status(thm)],[17])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.39 tff(47,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.39 tff(50,plain,(
% 0.20/0.39 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[49])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(B!9, finite_subsets(A!10))) | empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(B!9, finite_subsets(A!10))) | empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)) | (~element(B!9, finite_subsets(A!10)))) <=> ((~element(B!9, finite_subsets(A!10))) | empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)) | (~element(B!9, finite_subsets(A!10))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(B!9, finite_subsets(A!10))) | empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)) | (~element(B!9, finite_subsets(A!10))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(B!9, finite_subsets(A!10))) | empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10)) | (~element(B!9, finite_subsets(A!10))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(B!9, finite_subsets(A!10))) | empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (empty(finite_subsets(A!10)) | in(B!9, finite_subsets(A!10))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[57, 51, 41])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (in(B!9, finite_subsets(A!10))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[58, 40])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 ((((~finite(B!9)) | (~subset(B!9, A!10))) <=> in(B!9, finite_subsets(A!10))) | (~((~finite(B!9)) | (~subset(B!9, A!10)))) | (~in(B!9, finite_subsets(A!10)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (((~finite(B!9)) | (~subset(B!9, A!10))) <=> in(B!9, finite_subsets(A!10))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[60, 59, 23])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (^[A: $i] : refl(preboolean(finite_subsets(A)) <=> preboolean(finite_subsets(A)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (![A: $i] : preboolean(finite_subsets(A)) <=> ![A: $i] : preboolean(finite_subsets(A))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(65,axiom,(![A: $i] : preboolean(finite_subsets(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_finsub_1')).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (![A: $i] : preboolean(finite_subsets(A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.39 tff(67,plain,(
% 0.20/0.39 ![A: $i] : preboolean(finite_subsets(A))),
% 0.20/0.39 inference(skolemize,[status(sab)],[66])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 (![A: $i] : preboolean(finite_subsets(A))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.20/0.39 tff(69,plain,
% 0.20/0.39 ((~![A: $i] : preboolean(finite_subsets(A))) | preboolean(finite_subsets(A!10))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 (preboolean(finite_subsets(A!10))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B))))))) <=> ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (^[A: $i, B: $i] : refl(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (^[A: $i, B: $i] : rewrite(((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | (~(in(tptp_fun_C_11(B, A), B) <=> (subset(tptp_fun_C_11(B, A), A) & finite(tptp_fun_C_11(B, A)))))))) <=> ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | (~(in(tptp_fun_C_11(B, A), B) <=> (subset(tptp_fun_C_11(B, A), A) & finite(tptp_fun_C_11(B, A)))))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) <=> ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))), ((preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> (preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))))), rewrite((preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))), ((preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (![A: $i, B: $i] : (preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C))))) <=> ![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.40 tff(83,axiom,(![A: $i, B: $i] : (preboolean(B) => ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_finsub_1')).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | ((B = finite_subsets(A)) <=> ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.40 tff(86,plain,(
% 0.20/0.40 ![A: $i, B: $i] : ((~preboolean(B)) | (((~(B = finite_subsets(A))) | ![C: $i] : (in(C, B) <=> (subset(C, A) & finite(C)))) & ((B = finite_subsets(A)) | (~(in(tptp_fun_C_11(B, A), B) <=> (subset(tptp_fun_C_11(B, A), A) & finite(tptp_fun_C_11(B, A))))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[85])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))) | (~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 (![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[88, 72])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!10))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!10))) <=> in(C, finite_subsets(A!10)))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | (~preboolean(finite_subsets(A!10))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!10))) <=> in(C, finite_subsets(A!10)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 (((~preboolean(finite_subsets(A!10))) | (~((~((finite_subsets(A!10) = finite_subsets(A!10)) | (((~subset(tptp_fun_C_11(finite_subsets(A!10), A!10), A!10)) | (~finite(tptp_fun_C_11(finite_subsets(A!10), A!10)))) <=> in(tptp_fun_C_11(finite_subsets(A!10), A!10), finite_subsets(A!10))))) | (~((~(finite_subsets(A!10) = finite_subsets(A!10))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!10))) <=> in(C, finite_subsets(A!10))))))))) <=> ((~preboolean(finite_subsets(A!10))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!10))) <=> in(C, finite_subsets(A!10)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!10))) | (~((~((finite_subsets(A!10) = finite_subsets(A!10)) | (((~subset(tptp_fun_C_11(finite_subsets(A!10), A!10), A!10)) | (~finite(tptp_fun_C_11(finite_subsets(A!10), A!10)))) <=> in(tptp_fun_C_11(finite_subsets(A!10), A!10), finite_subsets(A!10))))) | (~((~(finite_subsets(A!10) = finite_subsets(A!10))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!10))) <=> in(C, finite_subsets(A!10)))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!10))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!10))) <=> in(C, finite_subsets(A!10))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 (((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!10))) | (~((~((finite_subsets(A!10) = finite_subsets(A!10)) | (((~subset(tptp_fun_C_11(finite_subsets(A!10), A!10), A!10)) | (~finite(tptp_fun_C_11(finite_subsets(A!10), A!10)))) <=> in(tptp_fun_C_11(finite_subsets(A!10), A!10), finite_subsets(A!10))))) | (~((~(finite_subsets(A!10) = finite_subsets(A!10))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!10))) <=> in(C, finite_subsets(A!10)))))))))) <=> ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | (~preboolean(finite_subsets(A!10))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!10))) <=> in(C, finite_subsets(A!10)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[92, 90])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | ((~preboolean(finite_subsets(A!10))) | (~((~((finite_subsets(A!10) = finite_subsets(A!10)) | (((~subset(tptp_fun_C_11(finite_subsets(A!10), A!10), A!10)) | (~finite(tptp_fun_C_11(finite_subsets(A!10), A!10)))) <=> in(tptp_fun_C_11(finite_subsets(A!10), A!10), finite_subsets(A!10))))) | (~((~(finite_subsets(A!10) = finite_subsets(A!10))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!10))) <=> in(C, finite_subsets(A!10)))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 ((~![A: $i, B: $i] : ((~preboolean(B)) | (~((~((B = finite_subsets(A)) | (((~subset(tptp_fun_C_11(B, A), A)) | (~finite(tptp_fun_C_11(B, A)))) <=> in(tptp_fun_C_11(B, A), B)))) | (~((~(B = finite_subsets(A))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A))) <=> in(C, B))))))))) | (~preboolean(finite_subsets(A!10))) | ![C: $i] : (~(((~finite(C)) | (~subset(C, A!10))) <=> in(C, finite_subsets(A!10))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 (![C: $i] : (~(((~finite(C)) | (~subset(C, A!10))) <=> in(C, finite_subsets(A!10))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[95, 89, 70])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 ((~![C: $i] : (~(((~finite(C)) | (~subset(C, A!10))) <=> in(C, finite_subsets(A!10))))) | (~(((~finite(B!9)) | (~subset(B!9, A!10))) <=> in(B!9, finite_subsets(A!10))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[97, 96, 61])).
% 0.20/0.40 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------