TSTP Solution File: SEU235+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU235+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:28:23 EDT 2022
% Result : Theorem 63.08s 40.73s
% Output : Proof 63.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU235+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 10:50:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 63.08/40.73 % SZS status Theorem
% 63.08/40.73 % SZS output start Proof
% 63.08/40.73 tff(in_type, type, (
% 63.08/40.73 in: ( $i * $i ) > $o)).
% 63.08/40.73 tff(tptp_fun_C_17_type, type, (
% 63.08/40.73 tptp_fun_C_17: $i > $i)).
% 63.08/40.73 tff(tptp_fun_A_15_type, type, (
% 63.08/40.73 tptp_fun_A_15: $i)).
% 63.08/40.73 tff(empty_set_type, type, (
% 63.08/40.73 empty_set: $i)).
% 63.08/40.73 tff(tptp_fun_A_7_type, type, (
% 63.08/40.73 tptp_fun_A_7: $i)).
% 63.08/40.73 tff(empty_type, type, (
% 63.08/40.73 empty: $i > $o)).
% 63.08/40.73 tff(ordinal_type, type, (
% 63.08/40.73 ordinal: $i > $o)).
% 63.08/40.73 tff(epsilon_connected_type, type, (
% 63.08/40.73 epsilon_connected: $i > $o)).
% 63.08/40.73 tff(epsilon_transitive_type, type, (
% 63.08/40.73 epsilon_transitive: $i > $o)).
% 63.08/40.73 tff(one_to_one_type, type, (
% 63.08/40.73 one_to_one: $i > $o)).
% 63.08/40.73 tff(function_type, type, (
% 63.08/40.73 function: $i > $o)).
% 63.08/40.73 tff(relation_type, type, (
% 63.08/40.73 relation: $i > $o)).
% 63.08/40.73 tff(relation_empty_yielding_type, type, (
% 63.08/40.73 relation_empty_yielding: $i > $o)).
% 63.08/40.73 tff(tptp_fun_D_16_type, type, (
% 63.08/40.73 tptp_fun_D_16: $i > $i)).
% 63.08/40.73 tff(tptp_fun_B_1_type, type, (
% 63.08/40.73 tptp_fun_B_1: $i > $i)).
% 63.08/40.73 tff(ordinal_subset_type, type, (
% 63.08/40.73 ordinal_subset: ( $i * $i ) > $o)).
% 63.08/40.73 tff(subset_type, type, (
% 63.08/40.73 subset: ( $i * $i ) > $o)).
% 63.08/40.73 tff(tptp_fun_B_0_type, type, (
% 63.08/40.73 tptp_fun_B_0: $i > $i)).
% 63.08/40.73 tff(tptp_fun_B_14_type, type, (
% 63.08/40.73 tptp_fun_B_14: $i)).
% 63.08/40.73 tff(element_type, type, (
% 63.08/40.73 element: ( $i * $i ) > $o)).
% 63.08/40.73 tff(powerset_type, type, (
% 63.08/40.73 powerset: $i > $i)).
% 63.08/40.73 tff(1,plain,
% 63.08/40.73 (^[A: $i, B: $i] : refl(((A = B) | (~empty(B)) | (~empty(A))) <=> ((A = B) | (~empty(B)) | (~empty(A))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(2,plain,
% 63.08/40.73 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 63.08/40.73 inference(quant_intro,[status(thm)],[1])).
% 63.08/40.73 tff(3,plain,
% 63.08/40.73 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((A = B) | (~empty(B)) | (~empty(A))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((A = B) | (~empty(B)) | (~empty(A))))))), rewrite((~(~((A = B) | (~empty(B)) | (~empty(A))))) <=> ((A = B) | (~empty(B)) | (~empty(A)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((A = B) | (~empty(B)) | (~empty(A)))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(4,plain,
% 63.08/40.73 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 63.08/40.73 inference(quant_intro,[status(thm)],[3])).
% 63.08/40.73 tff(5,plain,
% 63.08/40.73 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 63.08/40.73 inference(rewrite,[status(thm)],[])).
% 63.08/40.73 tff(6,plain,
% 63.08/40.73 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(7,plain,
% 63.08/40.73 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 63.08/40.73 inference(quant_intro,[status(thm)],[6])).
% 63.08/40.73 tff(8,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 63.08/40.73 tff(9,plain,
% 63.08/40.73 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[8, 7])).
% 63.08/40.73 tff(10,plain,
% 63.08/40.73 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[9, 5])).
% 63.08/40.73 tff(11,plain,(
% 63.08/40.73 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 63.08/40.73 inference(skolemize,[status(sab)],[10])).
% 63.08/40.73 tff(12,plain,
% 63.08/40.73 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[11, 4])).
% 63.08/40.73 tff(13,plain,
% 63.08/40.73 (![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[12, 2])).
% 63.08/40.73 tff(14,plain,
% 63.08/40.73 (?[A: $i] : (relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A) & epsilon_connected(A) & ordinal(A)) <=> ?[A: $i] : (relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))),
% 63.08/40.73 inference(rewrite,[status(thm)],[])).
% 63.08/40.73 tff(15,plain,
% 63.08/40.73 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((relation(A) & function(A)) & one_to_one(A)) <=> (relation(A) & function(A) & one_to_one(A))), ((((relation(A) & function(A)) & one_to_one(A)) & empty(A)) <=> ((relation(A) & function(A) & one_to_one(A)) & empty(A)))), rewrite(((relation(A) & function(A) & one_to_one(A)) & empty(A)) <=> (relation(A) & function(A) & one_to_one(A) & empty(A))), ((((relation(A) & function(A)) & one_to_one(A)) & empty(A)) <=> (relation(A) & function(A) & one_to_one(A) & empty(A)))), (((((relation(A) & function(A)) & one_to_one(A)) & empty(A)) & epsilon_transitive(A)) <=> ((relation(A) & function(A) & one_to_one(A) & empty(A)) & epsilon_transitive(A)))), rewrite(((relation(A) & function(A) & one_to_one(A) & empty(A)) & epsilon_transitive(A)) <=> (relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A))), (((((relation(A) & function(A)) & one_to_one(A)) & empty(A)) & epsilon_transitive(A)) <=> (relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A)))), ((((((relation(A) & function(A)) & one_to_one(A)) & empty(A)) & epsilon_transitive(A)) & epsilon_connected(A)) <=> ((relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A)) & epsilon_connected(A)))), rewrite(((relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A)) & epsilon_connected(A)) <=> (relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A) & epsilon_connected(A))), ((((((relation(A) & function(A)) & one_to_one(A)) & empty(A)) & epsilon_transitive(A)) & epsilon_connected(A)) <=> (relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A) & epsilon_connected(A)))), (((((((relation(A) & function(A)) & one_to_one(A)) & empty(A)) & epsilon_transitive(A)) & epsilon_connected(A)) & ordinal(A)) <=> ((relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A) & epsilon_connected(A)) & ordinal(A)))), rewrite(((relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A) & epsilon_connected(A)) & ordinal(A)) <=> (relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))), (((((((relation(A) & function(A)) & one_to_one(A)) & empty(A)) & epsilon_transitive(A)) & epsilon_connected(A)) & ordinal(A)) <=> (relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(16,plain,
% 63.08/40.73 (?[A: $i] : ((((((relation(A) & function(A)) & one_to_one(A)) & empty(A)) & epsilon_transitive(A)) & epsilon_connected(A)) & ordinal(A)) <=> ?[A: $i] : (relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))),
% 63.08/40.73 inference(quant_intro,[status(thm)],[15])).
% 63.08/40.73 tff(17,axiom,(?[A: $i] : ((((((relation(A) & function(A)) & one_to_one(A)) & empty(A)) & epsilon_transitive(A)) & epsilon_connected(A)) & ordinal(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rc2_ordinal1')).
% 63.08/40.73 tff(18,plain,
% 63.08/40.73 (?[A: $i] : (relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[17, 16])).
% 63.08/40.73 tff(19,plain,
% 63.08/40.73 (?[A: $i] : (relation(A) & function(A) & one_to_one(A) & empty(A) & epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[18, 14])).
% 63.08/40.73 tff(20,plain,(
% 63.08/40.73 relation(A!7) & function(A!7) & one_to_one(A!7) & empty(A!7) & epsilon_transitive(A!7) & epsilon_connected(A!7) & ordinal(A!7)),
% 63.08/40.73 inference(skolemize,[status(sab)],[19])).
% 63.08/40.73 tff(21,plain,
% 63.08/40.73 (empty(A!7)),
% 63.08/40.73 inference(and_elim,[status(thm)],[20])).
% 63.08/40.73 tff(22,plain,
% 63.08/40.73 (empty(empty_set) <=> empty(empty_set)),
% 63.08/40.73 inference(rewrite,[status(thm)],[])).
% 63.08/40.73 tff(23,axiom,((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc12_relat_1')).
% 63.08/40.73 tff(24,plain,
% 63.08/40.73 (empty(empty_set) & relation(empty_set)),
% 63.08/40.73 inference(and_elim,[status(thm)],[23])).
% 63.08/40.73 tff(25,plain,
% 63.08/40.73 (empty(empty_set)),
% 63.08/40.73 inference(and_elim,[status(thm)],[24])).
% 63.08/40.73 tff(26,plain,
% 63.08/40.73 (empty(empty_set)),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[25, 22])).
% 63.08/40.73 tff(27,plain,
% 63.08/40.73 (((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((~empty(empty_set)) | (A!7 = empty_set) | (~empty(A!7)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (~empty(empty_set)) | (A!7 = empty_set) | (~empty(A!7)))),
% 63.08/40.73 inference(rewrite,[status(thm)],[])).
% 63.08/40.73 tff(28,plain,
% 63.08/40.73 (((A!7 = empty_set) | (~empty(empty_set)) | (~empty(A!7))) <=> ((~empty(empty_set)) | (A!7 = empty_set) | (~empty(A!7)))),
% 63.08/40.73 inference(rewrite,[status(thm)],[])).
% 63.08/40.73 tff(29,plain,
% 63.08/40.73 (((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((A!7 = empty_set) | (~empty(empty_set)) | (~empty(A!7)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((~empty(empty_set)) | (A!7 = empty_set) | (~empty(A!7))))),
% 63.08/40.73 inference(monotonicity,[status(thm)],[28])).
% 63.08/40.73 tff(30,plain,
% 63.08/40.73 (((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((A!7 = empty_set) | (~empty(empty_set)) | (~empty(A!7)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (~empty(empty_set)) | (A!7 = empty_set) | (~empty(A!7)))),
% 63.08/40.73 inference(transitivity,[status(thm)],[29, 27])).
% 63.08/40.73 tff(31,plain,
% 63.08/40.73 ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((A!7 = empty_set) | (~empty(empty_set)) | (~empty(A!7)))),
% 63.08/40.73 inference(quant_inst,[status(thm)],[])).
% 63.08/40.73 tff(32,plain,
% 63.08/40.73 ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (~empty(empty_set)) | (A!7 = empty_set) | (~empty(A!7))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[31, 30])).
% 63.08/40.73 tff(33,plain,
% 63.08/40.73 (A!7 = empty_set),
% 63.08/40.73 inference(unit_resolution,[status(thm)],[32, 26, 21, 13])).
% 63.08/40.73 tff(34,plain,
% 63.08/40.73 (empty_set = A!7),
% 63.08/40.73 inference(symmetry,[status(thm)],[33])).
% 63.08/40.73 tff(35,plain,
% 63.08/40.73 (in(empty_set, tptp_fun_C_17(A!15)) <=> in(A!7, tptp_fun_C_17(A!15))),
% 63.08/40.73 inference(monotonicity,[status(thm)],[34])).
% 63.08/40.73 tff(36,plain,
% 63.08/40.73 (in(A!7, tptp_fun_C_17(A!15)) <=> in(empty_set, tptp_fun_C_17(A!15))),
% 63.08/40.73 inference(symmetry,[status(thm)],[35])).
% 63.08/40.73 tff(37,assumption,(~(ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (~in(tptp_fun_D_16(empty_set), A!15)))), introduced(assumption)).
% 63.08/40.73 tff(38,plain,
% 63.08/40.73 ((ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (~in(tptp_fun_D_16(empty_set), A!15))) | ordinal(tptp_fun_D_16(empty_set))),
% 63.08/40.73 inference(tautology,[status(thm)],[])).
% 63.08/40.73 tff(39,plain,
% 63.08/40.73 (ordinal(tptp_fun_D_16(empty_set))),
% 63.08/40.73 inference(unit_resolution,[status(thm)],[38, 37])).
% 63.08/40.73 tff(40,plain,
% 63.08/40.73 (^[A: $i] : refl((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(41,plain,
% 63.08/40.73 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 63.08/40.73 inference(quant_intro,[status(thm)],[40])).
% 63.08/40.73 tff(42,plain,
% 63.08/40.73 (^[A: $i] : rewrite((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(43,plain,
% 63.08/40.73 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 63.08/40.73 inference(quant_intro,[status(thm)],[42])).
% 63.08/40.73 tff(44,plain,
% 63.08/40.73 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 63.08/40.73 inference(transitivity,[status(thm)],[43, 41])).
% 63.08/40.73 tff(45,plain,
% 63.08/40.73 (^[A: $i] : trans(monotonicity(rewrite(((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))), rewrite((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(46,plain,
% 63.08/40.73 (![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 63.08/40.73 inference(quant_intro,[status(thm)],[45])).
% 63.08/40.73 tff(47,plain,
% 63.08/40.73 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 63.08/40.73 inference(rewrite,[status(thm)],[])).
% 63.08/40.73 tff(48,plain,
% 63.08/40.73 (^[A: $i] : rewrite((epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(49,plain,
% 63.08/40.73 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 63.08/40.73 inference(quant_intro,[status(thm)],[48])).
% 63.08/40.73 tff(50,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_ordinal1')).
% 63.08/40.73 tff(51,plain,
% 63.08/40.73 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[50, 49])).
% 63.08/40.73 tff(52,plain,
% 63.08/40.73 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[51, 47])).
% 63.08/40.73 tff(53,plain,(
% 63.08/40.73 ![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))),
% 63.08/40.73 inference(skolemize,[status(sab)],[52])).
% 63.08/40.73 tff(54,plain,
% 63.08/40.73 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[53, 46])).
% 63.08/40.73 tff(55,plain,
% 63.08/40.73 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[54, 44])).
% 63.08/40.73 tff(56,plain,
% 63.08/40.73 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(tptp_fun_D_16(empty_set))) | ![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set))))) | (~(epsilon_transitive(tptp_fun_D_16(empty_set)) | (~((~in(tptp_fun_B_0(tptp_fun_D_16(empty_set)), tptp_fun_D_16(empty_set))) | subset(tptp_fun_B_0(tptp_fun_D_16(empty_set)), tptp_fun_D_16(empty_set))))))))),
% 63.08/40.73 inference(quant_inst,[status(thm)],[])).
% 63.08/40.73 tff(57,plain,
% 63.08/40.73 (~((~((~epsilon_transitive(tptp_fun_D_16(empty_set))) | ![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set))))) | (~(epsilon_transitive(tptp_fun_D_16(empty_set)) | (~((~in(tptp_fun_B_0(tptp_fun_D_16(empty_set)), tptp_fun_D_16(empty_set))) | subset(tptp_fun_B_0(tptp_fun_D_16(empty_set)), tptp_fun_D_16(empty_set)))))))),
% 63.08/40.73 inference(unit_resolution,[status(thm)],[56, 55])).
% 63.08/40.73 tff(58,plain,
% 63.08/40.73 (((~((~epsilon_transitive(tptp_fun_D_16(empty_set))) | ![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set))))) | (~(epsilon_transitive(tptp_fun_D_16(empty_set)) | (~((~in(tptp_fun_B_0(tptp_fun_D_16(empty_set)), tptp_fun_D_16(empty_set))) | subset(tptp_fun_B_0(tptp_fun_D_16(empty_set)), tptp_fun_D_16(empty_set))))))) | ((~epsilon_transitive(tptp_fun_D_16(empty_set))) | ![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set))))),
% 63.08/40.73 inference(tautology,[status(thm)],[])).
% 63.08/40.73 tff(59,plain,
% 63.08/40.73 ((~epsilon_transitive(tptp_fun_D_16(empty_set))) | ![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set)))),
% 63.08/40.73 inference(unit_resolution,[status(thm)],[58, 57])).
% 63.08/40.73 tff(60,plain,
% 63.08/40.73 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(61,plain,
% 63.08/40.73 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 63.08/40.73 inference(quant_intro,[status(thm)],[60])).
% 63.08/40.73 tff(62,plain,
% 63.08/40.73 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(63,plain,
% 63.08/40.73 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 63.08/40.73 inference(quant_intro,[status(thm)],[62])).
% 63.08/40.73 tff(64,plain,
% 63.08/40.73 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 63.08/40.73 inference(rewrite,[status(thm)],[])).
% 63.08/40.73 tff(65,plain,
% 63.08/40.73 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(66,plain,
% 63.08/40.73 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 63.08/40.73 inference(quant_intro,[status(thm)],[65])).
% 63.08/40.73 tff(67,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_ordinal1')).
% 63.08/40.73 tff(68,plain,
% 63.08/40.73 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[67, 66])).
% 63.08/40.73 tff(69,plain,
% 63.08/40.73 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[68, 64])).
% 63.08/40.73 tff(70,plain,(
% 63.08/40.73 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 63.08/40.73 inference(skolemize,[status(sab)],[69])).
% 63.08/40.73 tff(71,plain,
% 63.08/40.73 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[70, 63])).
% 63.08/40.73 tff(72,plain,
% 63.08/40.73 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[71, 61])).
% 63.08/40.73 tff(73,plain,
% 63.08/40.73 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(tptp_fun_D_16(empty_set))) | (~((~epsilon_transitive(tptp_fun_D_16(empty_set))) | (~epsilon_connected(tptp_fun_D_16(empty_set))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(tptp_fun_D_16(empty_set))) | (~((~epsilon_transitive(tptp_fun_D_16(empty_set))) | (~epsilon_connected(tptp_fun_D_16(empty_set))))))),
% 63.08/40.73 inference(rewrite,[status(thm)],[])).
% 63.08/40.73 tff(74,plain,
% 63.08/40.73 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(tptp_fun_D_16(empty_set))) | (~((~epsilon_transitive(tptp_fun_D_16(empty_set))) | (~epsilon_connected(tptp_fun_D_16(empty_set))))))),
% 63.08/40.73 inference(quant_inst,[status(thm)],[])).
% 63.08/40.73 tff(75,plain,
% 63.08/40.73 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(tptp_fun_D_16(empty_set))) | (~((~epsilon_transitive(tptp_fun_D_16(empty_set))) | (~epsilon_connected(tptp_fun_D_16(empty_set)))))),
% 63.08/40.73 inference(modus_ponens,[status(thm)],[74, 73])).
% 63.08/40.73 tff(76,plain,
% 63.08/40.73 (~((~epsilon_transitive(tptp_fun_D_16(empty_set))) | (~epsilon_connected(tptp_fun_D_16(empty_set))))),
% 63.08/40.73 inference(unit_resolution,[status(thm)],[75, 72, 39])).
% 63.08/40.73 tff(77,plain,
% 63.08/40.73 (((~epsilon_transitive(tptp_fun_D_16(empty_set))) | (~epsilon_connected(tptp_fun_D_16(empty_set)))) | epsilon_transitive(tptp_fun_D_16(empty_set))),
% 63.08/40.73 inference(tautology,[status(thm)],[])).
% 63.08/40.73 tff(78,plain,
% 63.08/40.73 (epsilon_transitive(tptp_fun_D_16(empty_set))),
% 63.08/40.73 inference(unit_resolution,[status(thm)],[77, 76])).
% 63.08/40.73 tff(79,plain,
% 63.08/40.73 ((~((~epsilon_transitive(tptp_fun_D_16(empty_set))) | ![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set))))) | (~epsilon_transitive(tptp_fun_D_16(empty_set))) | ![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set)))),
% 63.08/40.73 inference(tautology,[status(thm)],[])).
% 63.08/40.73 tff(80,plain,
% 63.08/40.73 ((~((~epsilon_transitive(tptp_fun_D_16(empty_set))) | ![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set)))),
% 63.08/40.73 inference(unit_resolution,[status(thm)],[79, 78])).
% 63.08/40.73 tff(81,plain,
% 63.08/40.73 (![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set)))),
% 63.08/40.73 inference(unit_resolution,[status(thm)],[80, 59])).
% 63.08/40.73 tff(82,plain,
% 63.08/40.73 (^[A: $i, B: $i] : refl(((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(83,plain,
% 63.08/40.73 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 63.08/40.73 inference(quant_intro,[status(thm)],[82])).
% 63.08/40.73 tff(84,plain,
% 63.08/40.73 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> (((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))))), rewrite((((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))))),
% 63.08/40.73 inference(bind,[status(th)],[])).
% 63.08/40.73 tff(85,plain,
% 63.08/40.73 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[84])).
% 63.08/40.74 tff(86,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(87,plain,
% 63.08/40.74 (^[A: $i, B: $i] : rewrite(((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(88,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[87])).
% 63.08/40.74 tff(89,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r1_ordinal1')).
% 63.08/40.74 tff(90,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[89, 88])).
% 63.08/40.74 tff(91,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[90, 86])).
% 63.08/40.74 tff(92,plain,(
% 63.08/40.74 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 63.08/40.74 inference(skolemize,[status(sab)],[91])).
% 63.08/40.74 tff(93,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[92, 85])).
% 63.08/40.74 tff(94,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[93, 83])).
% 63.08/40.74 tff(95,plain,
% 63.08/40.74 (ordinal(empty_set) <=> ordinal(empty_set)),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(96,axiom,(((((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set)) & epsilon_transitive(empty_set)) & epsilon_connected(empty_set)) & ordinal(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc2_ordinal1')).
% 63.08/40.74 tff(97,plain,
% 63.08/40.74 (ordinal(empty_set)),
% 63.08/40.74 inference(and_elim,[status(thm)],[96])).
% 63.08/40.74 tff(98,plain,
% 63.08/40.74 (ordinal(empty_set)),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[97, 95])).
% 63.08/40.74 tff(99,plain,
% 63.08/40.74 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set))))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(100,plain,
% 63.08/40.74 (((ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set))) | (~ordinal(tptp_fun_D_16(empty_set))) | (~ordinal(empty_set))) <=> ((~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set))))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(101,plain,
% 63.08/40.74 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set))) | (~ordinal(tptp_fun_D_16(empty_set))) | (~ordinal(empty_set)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set)))))),
% 63.08/40.74 inference(monotonicity,[status(thm)],[100])).
% 63.08/40.74 tff(102,plain,
% 63.08/40.74 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set))) | (~ordinal(tptp_fun_D_16(empty_set))) | (~ordinal(empty_set)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set))))),
% 63.08/40.74 inference(transitivity,[status(thm)],[101, 99])).
% 63.08/40.74 tff(103,plain,
% 63.08/40.74 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set))) | (~ordinal(tptp_fun_D_16(empty_set))) | (~ordinal(empty_set)))),
% 63.08/40.74 inference(quant_inst,[status(thm)],[])).
% 63.08/40.74 tff(104,plain,
% 63.08/40.74 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[103, 102])).
% 63.08/40.74 tff(105,plain,
% 63.08/40.74 (ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set))),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[104, 98, 94, 39])).
% 63.08/40.74 tff(106,plain,
% 63.08/40.74 ((ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (~in(tptp_fun_D_16(empty_set), A!15))) | (~ordinal_subset(empty_set, tptp_fun_D_16(empty_set)))),
% 63.08/40.74 inference(tautology,[status(thm)],[])).
% 63.08/40.74 tff(107,plain,
% 63.08/40.74 (~ordinal_subset(empty_set, tptp_fun_D_16(empty_set))),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[106, 37])).
% 63.08/40.74 tff(108,plain,
% 63.08/40.74 ((~(ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set)))) | ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) | (~subset(empty_set, tptp_fun_D_16(empty_set)))),
% 63.08/40.74 inference(tautology,[status(thm)],[])).
% 63.08/40.74 tff(109,plain,
% 63.08/40.74 ((~(ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> subset(empty_set, tptp_fun_D_16(empty_set)))) | (~subset(empty_set, tptp_fun_D_16(empty_set)))),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[108, 107])).
% 63.08/40.74 tff(110,plain,
% 63.08/40.74 (~subset(empty_set, tptp_fun_D_16(empty_set))),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[109, 105])).
% 63.08/40.74 tff(111,plain,
% 63.08/40.74 (((~![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set)))) | ((~in(empty_set, tptp_fun_D_16(empty_set))) | subset(empty_set, tptp_fun_D_16(empty_set)))) <=> ((~![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set)))) | (~in(empty_set, tptp_fun_D_16(empty_set))) | subset(empty_set, tptp_fun_D_16(empty_set)))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(112,plain,
% 63.08/40.74 ((~![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set)))) | ((~in(empty_set, tptp_fun_D_16(empty_set))) | subset(empty_set, tptp_fun_D_16(empty_set)))),
% 63.08/40.74 inference(quant_inst,[status(thm)],[])).
% 63.08/40.74 tff(113,plain,
% 63.08/40.74 ((~![B: $i] : ((~in(B, tptp_fun_D_16(empty_set))) | subset(B, tptp_fun_D_16(empty_set)))) | (~in(empty_set, tptp_fun_D_16(empty_set))) | subset(empty_set, tptp_fun_D_16(empty_set))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[112, 111])).
% 63.08/40.74 tff(114,plain,
% 63.08/40.74 (~in(empty_set, tptp_fun_D_16(empty_set))),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[113, 110, 81])).
% 63.08/40.74 tff(115,assumption,(in(tptp_fun_D_16(empty_set), empty_set)), introduced(assumption)).
% 63.08/40.74 tff(116,plain,
% 63.08/40.74 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(117,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[116])).
% 63.08/40.74 tff(118,plain,
% 63.08/40.74 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(119,plain,
% 63.08/40.74 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[118])).
% 63.08/40.74 tff(120,plain,
% 63.08/40.74 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(121,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_boole')).
% 63.08/40.74 tff(122,plain,
% 63.08/40.74 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[121, 120])).
% 63.08/40.74 tff(123,plain,(
% 63.08/40.74 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 63.08/40.74 inference(skolemize,[status(sab)],[122])).
% 63.08/40.74 tff(124,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[123, 119])).
% 63.08/40.74 tff(125,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[124, 117])).
% 63.08/40.74 tff(126,plain,
% 63.08/40.74 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_16(empty_set), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_16(empty_set), empty_set)))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(127,plain,
% 63.08/40.74 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_16(empty_set), empty_set)))),
% 63.08/40.74 inference(quant_inst,[status(thm)],[])).
% 63.08/40.74 tff(128,plain,
% 63.08/40.74 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_16(empty_set), empty_set))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[127, 126])).
% 63.08/40.74 tff(129,plain,
% 63.08/40.74 ($false),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[128, 26, 125, 115])).
% 63.08/40.74 tff(130,plain,(~in(tptp_fun_D_16(empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 63.08/40.74 tff(131,plain,
% 63.08/40.74 (^[A: $i] : refl(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(132,plain,
% 63.08/40.74 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[131])).
% 63.08/40.74 tff(133,plain,
% 63.08/40.74 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(134,plain,
% 63.08/40.74 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[133])).
% 63.08/40.74 tff(135,plain,
% 63.08/40.74 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 63.08/40.74 inference(transitivity,[status(thm)],[134, 132])).
% 63.08/40.74 tff(136,plain,
% 63.08/40.74 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(137,plain,
% 63.08/40.74 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[136])).
% 63.08/40.74 tff(138,plain,
% 63.08/40.74 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(139,plain,
% 63.08/40.74 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))) <=> (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> (ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), rewrite((ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), (![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> (ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), rewrite((ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(140,plain,
% 63.08/40.74 (![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[139])).
% 63.08/40.74 tff(141,axiom,(![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t24_ordinal1')).
% 63.08/40.74 tff(142,plain,
% 63.08/40.74 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[141, 140])).
% 63.08/40.74 tff(143,plain,
% 63.08/40.74 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[142, 138])).
% 63.08/40.74 tff(144,plain,(
% 63.08/40.74 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 63.08/40.74 inference(skolemize,[status(sab)],[143])).
% 63.08/40.74 tff(145,plain,
% 63.08/40.74 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[144, 137])).
% 63.08/40.74 tff(146,plain,
% 63.08/40.74 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[145, 135])).
% 63.08/40.74 tff(147,plain,
% 63.08/40.74 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(empty_set)) | ![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(empty_set)) | ![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B)))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(148,plain,
% 63.08/40.74 (((~ordinal(empty_set)) | ![B: $i] : (in(B, empty_set) | in(empty_set, B) | (empty_set = B) | (~ordinal(B)))) <=> ((~ordinal(empty_set)) | ![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B)))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(149,plain,
% 63.08/40.74 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(empty_set)) | ![B: $i] : (in(B, empty_set) | in(empty_set, B) | (empty_set = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(empty_set)) | ![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))))),
% 63.08/40.74 inference(monotonicity,[status(thm)],[148])).
% 63.08/40.74 tff(150,plain,
% 63.08/40.74 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(empty_set)) | ![B: $i] : (in(B, empty_set) | in(empty_set, B) | (empty_set = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(empty_set)) | ![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B)))),
% 63.08/40.74 inference(transitivity,[status(thm)],[149, 147])).
% 63.08/40.74 tff(151,plain,
% 63.08/40.74 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(empty_set)) | ![B: $i] : (in(B, empty_set) | in(empty_set, B) | (empty_set = B) | (~ordinal(B))))),
% 63.08/40.74 inference(quant_inst,[status(thm)],[])).
% 63.08/40.74 tff(152,plain,
% 63.08/40.74 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(empty_set)) | ![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[151, 150])).
% 63.08/40.74 tff(153,plain,
% 63.08/40.74 (![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[152, 98, 146])).
% 63.08/40.74 tff(154,plain,
% 63.08/40.74 (((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | ((~ordinal(tptp_fun_D_16(empty_set))) | in(empty_set, tptp_fun_D_16(empty_set)) | (empty_set = tptp_fun_D_16(empty_set)) | in(tptp_fun_D_16(empty_set), empty_set))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | (~ordinal(tptp_fun_D_16(empty_set))) | in(empty_set, tptp_fun_D_16(empty_set)) | (empty_set = tptp_fun_D_16(empty_set)) | in(tptp_fun_D_16(empty_set), empty_set))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(155,plain,
% 63.08/40.74 (((~ordinal(tptp_fun_D_16(empty_set))) | in(tptp_fun_D_16(empty_set), empty_set) | in(empty_set, tptp_fun_D_16(empty_set)) | (empty_set = tptp_fun_D_16(empty_set))) <=> ((~ordinal(tptp_fun_D_16(empty_set))) | in(empty_set, tptp_fun_D_16(empty_set)) | (empty_set = tptp_fun_D_16(empty_set)) | in(tptp_fun_D_16(empty_set), empty_set))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(156,plain,
% 63.08/40.74 (((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | ((~ordinal(tptp_fun_D_16(empty_set))) | in(tptp_fun_D_16(empty_set), empty_set) | in(empty_set, tptp_fun_D_16(empty_set)) | (empty_set = tptp_fun_D_16(empty_set)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | ((~ordinal(tptp_fun_D_16(empty_set))) | in(empty_set, tptp_fun_D_16(empty_set)) | (empty_set = tptp_fun_D_16(empty_set)) | in(tptp_fun_D_16(empty_set), empty_set)))),
% 63.08/40.74 inference(monotonicity,[status(thm)],[155])).
% 63.08/40.74 tff(157,plain,
% 63.08/40.74 (((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | ((~ordinal(tptp_fun_D_16(empty_set))) | in(tptp_fun_D_16(empty_set), empty_set) | in(empty_set, tptp_fun_D_16(empty_set)) | (empty_set = tptp_fun_D_16(empty_set)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | (~ordinal(tptp_fun_D_16(empty_set))) | in(empty_set, tptp_fun_D_16(empty_set)) | (empty_set = tptp_fun_D_16(empty_set)) | in(tptp_fun_D_16(empty_set), empty_set))),
% 63.08/40.74 inference(transitivity,[status(thm)],[156, 154])).
% 63.08/40.74 tff(158,plain,
% 63.08/40.74 ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | ((~ordinal(tptp_fun_D_16(empty_set))) | in(tptp_fun_D_16(empty_set), empty_set) | in(empty_set, tptp_fun_D_16(empty_set)) | (empty_set = tptp_fun_D_16(empty_set)))),
% 63.08/40.74 inference(quant_inst,[status(thm)],[])).
% 63.08/40.74 tff(159,plain,
% 63.08/40.74 ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | (~ordinal(tptp_fun_D_16(empty_set))) | in(empty_set, tptp_fun_D_16(empty_set)) | (empty_set = tptp_fun_D_16(empty_set)) | in(tptp_fun_D_16(empty_set), empty_set)),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[158, 157])).
% 63.08/40.74 tff(160,plain,
% 63.08/40.74 ((~ordinal(tptp_fun_D_16(empty_set))) | in(empty_set, tptp_fun_D_16(empty_set)) | (empty_set = tptp_fun_D_16(empty_set))),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[159, 153, 130])).
% 63.08/40.74 tff(161,plain,
% 63.08/40.74 (empty_set = tptp_fun_D_16(empty_set)),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[160, 114, 39])).
% 63.08/40.74 tff(162,plain,
% 63.08/40.74 (tptp_fun_D_16(empty_set) = empty_set),
% 63.08/40.74 inference(symmetry,[status(thm)],[161])).
% 63.08/40.74 tff(163,plain,
% 63.08/40.74 (ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) <=> ordinal_subset(empty_set, empty_set)),
% 63.08/40.74 inference(monotonicity,[status(thm)],[162])).
% 63.08/40.74 tff(164,plain,
% 63.08/40.74 (ordinal_subset(empty_set, empty_set) <=> ordinal_subset(empty_set, tptp_fun_D_16(empty_set))),
% 63.08/40.74 inference(symmetry,[status(thm)],[163])).
% 63.08/40.74 tff(165,plain,
% 63.08/40.74 (^[A: $i, B: $i] : refl((ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A))) <=> (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A))))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(166,plain,
% 63.08/40.74 (![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[165])).
% 63.08/40.74 tff(167,plain,
% 63.08/40.74 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), (((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> (((~ordinal(B)) | (~ordinal(A))) | ordinal_subset(A, A)))), rewrite((((~ordinal(B)) | (~ordinal(A))) | ordinal_subset(A, A)) <=> (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))), (((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(168,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> ![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[167])).
% 63.08/40.74 tff(169,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(170,plain,
% 63.08/40.74 (^[A: $i, B: $i] : rewrite(((ordinal(A) & ordinal(B)) => ordinal_subset(A, A)) <=> ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A)))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(171,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => ordinal_subset(A, A)) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[170])).
% 63.08/40.74 tff(172,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => ordinal_subset(A, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r1_ordinal1')).
% 63.08/40.74 tff(173,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[172, 171])).
% 63.08/40.74 tff(174,plain,
% 63.08/40.74 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[173, 169])).
% 63.08/40.74 tff(175,plain,(
% 63.08/40.74 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | ordinal_subset(A, A))),
% 63.08/40.74 inference(skolemize,[status(sab)],[174])).
% 63.08/40.74 tff(176,plain,
% 63.08/40.74 (![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[175, 168])).
% 63.08/40.74 tff(177,plain,
% 63.08/40.74 (![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[176, 166])).
% 63.08/40.74 tff(178,plain,
% 63.08/40.74 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(empty_set)) | ordinal_subset(empty_set, empty_set))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(empty_set)) | ordinal_subset(empty_set, empty_set))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(179,plain,
% 63.08/40.74 ((ordinal_subset(empty_set, empty_set) | (~ordinal(empty_set)) | (~ordinal(empty_set))) <=> ((~ordinal(empty_set)) | ordinal_subset(empty_set, empty_set))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(180,plain,
% 63.08/40.74 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(empty_set, empty_set) | (~ordinal(empty_set)) | (~ordinal(empty_set)))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(empty_set)) | ordinal_subset(empty_set, empty_set)))),
% 63.08/40.74 inference(monotonicity,[status(thm)],[179])).
% 63.08/40.74 tff(181,plain,
% 63.08/40.74 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(empty_set, empty_set) | (~ordinal(empty_set)) | (~ordinal(empty_set)))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(empty_set)) | ordinal_subset(empty_set, empty_set))),
% 63.08/40.74 inference(transitivity,[status(thm)],[180, 178])).
% 63.08/40.74 tff(182,plain,
% 63.08/40.74 ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(empty_set, empty_set) | (~ordinal(empty_set)) | (~ordinal(empty_set)))),
% 63.08/40.74 inference(quant_inst,[status(thm)],[])).
% 63.08/40.74 tff(183,plain,
% 63.08/40.74 ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(empty_set)) | ordinal_subset(empty_set, empty_set)),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[182, 181])).
% 63.08/40.74 tff(184,plain,
% 63.08/40.74 (ordinal_subset(empty_set, empty_set)),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[183, 98, 177])).
% 63.08/40.74 tff(185,plain,
% 63.08/40.74 (ordinal_subset(empty_set, tptp_fun_D_16(empty_set))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[184, 164])).
% 63.08/40.74 tff(186,plain,
% 63.08/40.74 ($false),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[107, 185])).
% 63.08/40.74 tff(187,plain,(ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (~in(tptp_fun_D_16(empty_set), A!15))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.74 tff(188,plain,
% 63.08/40.74 (^[C: $i] : refl(((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15))))) <=> ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15))))))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(189,plain,
% 63.08/40.74 (![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15))))) <=> ![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[188])).
% 63.08/40.74 tff(190,plain,
% 63.08/40.74 ((ordinal(B!14) & (subset(A!15, B!14) & (~(A!15 = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15))))))) <=> (ordinal(B!14) & subset(A!15, B!14) & (~(A!15 = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15))))))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(191,plain,
% 63.08/40.74 ((subset(A!15, B!14) & (~(A!15 = empty_set)) & ![C: $i] : ((~ordinal(C)) | ((~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15))))))) <=> (subset(A!15, B!14) & (~(A!15 = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15))))))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(192,plain,
% 63.08/40.74 ((~(~ordinal(B!14))) <=> ordinal(B!14)),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(193,plain,
% 63.08/40.74 (((~(~ordinal(B!14))) & (subset(A!15, B!14) & (~(A!15 = empty_set)) & ![C: $i] : ((~ordinal(C)) | ((~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))))) <=> (ordinal(B!14) & (subset(A!15, B!14) & (~(A!15 = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))))),
% 63.08/40.74 inference(monotonicity,[status(thm)],[192, 191])).
% 63.08/40.74 tff(194,plain,
% 63.08/40.74 (((~(~ordinal(B!14))) & (subset(A!15, B!14) & (~(A!15 = empty_set)) & ![C: $i] : ((~ordinal(C)) | ((~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))))) <=> (ordinal(B!14) & subset(A!15, B!14) & (~(A!15 = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15))))))),
% 63.08/40.74 inference(transitivity,[status(thm)],[193, 190])).
% 63.08/40.74 tff(195,plain,
% 63.08/40.74 ((~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))) <=> (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A))))))))))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(196,plain,
% 63.08/40.74 ((~![A: $i, B: $i] : (ordinal(B) => (~((subset(A, B) & (~(A = empty_set))) & ![C: $i] : (ordinal(C) => (~(in(C, A) & ![D: $i] : (ordinal(D) => (in(D, A) => ordinal_subset(C, D)))))))))) <=> (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A))))))))))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(197,axiom,(~![A: $i, B: $i] : (ordinal(B) => (~((subset(A, B) & (~(A = empty_set))) & ![C: $i] : (ordinal(C) => (~(in(C, A) & ![D: $i] : (ordinal(D) => (in(D, A) => ordinal_subset(C, D)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t32_ordinal1')).
% 63.08/40.74 tff(198,plain,
% 63.08/40.74 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[197, 196])).
% 63.08/40.74 tff(199,plain,
% 63.08/40.74 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[198, 195])).
% 63.08/40.74 tff(200,plain,
% 63.08/40.74 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[199, 195])).
% 63.08/40.74 tff(201,plain,
% 63.08/40.74 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[200, 195])).
% 63.08/40.74 tff(202,plain,
% 63.08/40.74 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[201, 195])).
% 63.08/40.74 tff(203,plain,
% 63.08/40.74 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[202, 195])).
% 63.08/40.74 tff(204,plain,
% 63.08/40.74 (~![A: $i, B: $i] : ((~ordinal(B)) | (~(subset(A, B) & (~(A = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~(in(C, A) & ![D: $i] : (ordinal_subset(C, D) | (~ordinal(D)) | (~in(D, A)))))))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[203, 195])).
% 63.08/40.74 tff(205,plain,
% 63.08/40.74 (ordinal(B!14) & subset(A!15, B!14) & (~(A!15 = empty_set)) & ![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[204, 194])).
% 63.08/40.74 tff(206,plain,
% 63.08/40.74 (![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))),
% 63.08/40.74 inference(and_elim,[status(thm)],[205])).
% 63.08/40.74 tff(207,plain,
% 63.08/40.74 (![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[206, 189])).
% 63.08/40.74 tff(208,plain,
% 63.08/40.74 (((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(empty_set)) | (~in(empty_set, A!15)) | (~(ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (~in(tptp_fun_D_16(empty_set), A!15)))))) <=> ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | (~ordinal(empty_set)) | (~in(empty_set, A!15)) | (~(ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (~in(tptp_fun_D_16(empty_set), A!15)))))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(209,plain,
% 63.08/40.74 ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(empty_set)) | (~in(empty_set, A!15)) | (~(ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (~in(tptp_fun_D_16(empty_set), A!15)))))),
% 63.08/40.74 inference(quant_inst,[status(thm)],[])).
% 63.08/40.74 tff(210,plain,
% 63.08/40.74 ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | (~ordinal(empty_set)) | (~in(empty_set, A!15)) | (~(ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (~in(tptp_fun_D_16(empty_set), A!15))))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[209, 208])).
% 63.08/40.74 tff(211,plain,
% 63.08/40.74 ((~in(empty_set, A!15)) | (~(ordinal_subset(empty_set, tptp_fun_D_16(empty_set)) | (~ordinal(tptp_fun_D_16(empty_set))) | (~in(tptp_fun_D_16(empty_set), A!15))))),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[210, 98, 207])).
% 63.08/40.74 tff(212,plain,
% 63.08/40.74 (~in(empty_set, A!15)),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[211, 187])).
% 63.08/40.74 tff(213,assumption,(~in(empty_set, A!15)), introduced(assumption)).
% 63.08/40.74 tff(214,assumption,(empty_set = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), introduced(assumption)).
% 63.08/40.74 tff(215,plain,
% 63.08/40.74 (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))) = empty_set),
% 63.08/40.74 inference(symmetry,[status(thm)],[214])).
% 63.08/40.74 tff(216,plain,
% 63.08/40.74 (in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15) <=> in(empty_set, A!15)),
% 63.08/40.74 inference(monotonicity,[status(thm)],[215])).
% 63.08/40.74 tff(217,plain,
% 63.08/40.74 (in(empty_set, A!15) <=> in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)),
% 63.08/40.74 inference(symmetry,[status(thm)],[216])).
% 63.08/40.74 tff(218,plain,
% 63.08/40.74 ((~in(empty_set, A!15)) <=> (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15))),
% 63.08/40.74 inference(monotonicity,[status(thm)],[217])).
% 63.08/40.74 tff(219,plain,
% 63.08/40.74 (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[213, 218])).
% 63.08/40.74 tff(220,assumption,(empty(A!15)), introduced(assumption)).
% 63.08/40.74 tff(221,plain,
% 63.08/40.74 (~(A!15 = empty_set)),
% 63.08/40.74 inference(and_elim,[status(thm)],[205])).
% 63.08/40.74 tff(222,plain,
% 63.08/40.74 (((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((A!15 = empty_set) | (~empty(empty_set)) | (~empty(A!15)))) <=> ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (A!15 = empty_set) | (~empty(empty_set)) | (~empty(A!15)))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(223,plain,
% 63.08/40.74 ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | ((A!15 = empty_set) | (~empty(empty_set)) | (~empty(A!15)))),
% 63.08/40.74 inference(quant_inst,[status(thm)],[])).
% 63.08/40.74 tff(224,plain,
% 63.08/40.74 ((~![A: $i, B: $i] : ((A = B) | (~empty(B)) | (~empty(A)))) | (A!15 = empty_set) | (~empty(empty_set)) | (~empty(A!15))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[223, 222])).
% 63.08/40.74 tff(225,plain,
% 63.08/40.74 ($false),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[224, 26, 221, 13, 220])).
% 63.08/40.74 tff(226,plain,(~empty(A!15)), inference(lemma,lemma(discharge,[]))).
% 63.08/40.74 tff(227,plain,
% 63.08/40.74 (![A: $i] : ?[B: $i] : element(B, A) <=> ![A: $i] : ?[B: $i] : element(B, A)),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(228,axiom,(![A: $i] : ?[B: $i] : element(B, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','existence_m1_subset_1')).
% 63.08/40.74 tff(229,plain,
% 63.08/40.74 (![A: $i] : ?[B: $i] : element(B, A)),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[228, 227])).
% 63.08/40.74 tff(230,plain,(
% 63.08/40.74 ![A: $i] : element(tptp_fun_B_1(A), A)),
% 63.08/40.74 inference(skolemize,[status(sab)],[229])).
% 63.08/40.74 tff(231,plain,
% 63.08/40.74 ((~![A: $i] : element(tptp_fun_B_1(A), A)) | element(tptp_fun_B_1(A!15), A!15)),
% 63.08/40.74 inference(quant_inst,[status(thm)],[])).
% 63.08/40.74 tff(232,plain,
% 63.08/40.74 (element(tptp_fun_B_1(A!15), A!15)),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[231, 230])).
% 63.08/40.74 tff(233,plain,
% 63.08/40.74 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(234,plain,
% 63.08/40.74 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[233])).
% 63.08/40.74 tff(235,plain,
% 63.08/40.74 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(236,plain,
% 63.08/40.74 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(237,plain,
% 63.08/40.74 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[236])).
% 63.08/40.74 tff(238,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 63.08/40.74 tff(239,plain,
% 63.08/40.74 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[238, 237])).
% 63.08/40.74 tff(240,plain,
% 63.08/40.74 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[239, 235])).
% 63.08/40.74 tff(241,plain,(
% 63.08/40.74 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 63.08/40.74 inference(skolemize,[status(sab)],[240])).
% 63.08/40.74 tff(242,plain,
% 63.08/40.74 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[241, 234])).
% 63.08/40.74 tff(243,plain,
% 63.08/40.74 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!15) | in(tptp_fun_B_1(A!15), A!15) | (~element(tptp_fun_B_1(A!15), A!15)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!15) | in(tptp_fun_B_1(A!15), A!15) | (~element(tptp_fun_B_1(A!15), A!15)))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(244,plain,
% 63.08/40.74 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!15) | in(tptp_fun_B_1(A!15), A!15) | (~element(tptp_fun_B_1(A!15), A!15)))),
% 63.08/40.74 inference(quant_inst,[status(thm)],[])).
% 63.08/40.74 tff(245,plain,
% 63.08/40.74 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!15) | in(tptp_fun_B_1(A!15), A!15) | (~element(tptp_fun_B_1(A!15), A!15))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[244, 243])).
% 63.08/40.74 tff(246,plain,
% 63.08/40.74 (empty(A!15) | in(tptp_fun_B_1(A!15), A!15)),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[245, 242, 232])).
% 63.08/40.74 tff(247,plain,
% 63.08/40.74 (in(tptp_fun_B_1(A!15), A!15)),
% 63.08/40.74 inference(unit_resolution,[status(thm)],[246, 226])).
% 63.08/40.74 tff(248,plain,
% 63.08/40.74 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 63.08/40.74 inference(bind,[status(th)],[])).
% 63.08/40.74 tff(249,plain,
% 63.08/40.74 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 63.08/40.74 inference(quant_intro,[status(thm)],[248])).
% 63.08/40.74 tff(250,plain,
% 63.08/40.74 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 63.08/40.74 inference(rewrite,[status(thm)],[])).
% 63.08/40.74 tff(251,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_subset')).
% 63.08/40.74 tff(252,plain,
% 63.08/40.74 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 63.08/40.74 inference(modus_ponens,[status(thm)],[251, 250])).
% 63.08/40.74 tff(253,plain,(
% 63.08/40.74 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 63.08/40.75 inference(skolemize,[status(sab)],[252])).
% 63.08/40.75 tff(254,plain,
% 63.08/40.75 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[253, 249])).
% 63.08/40.75 tff(255,plain,
% 63.08/40.75 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(A!15, powerset(B!14)) <=> subset(A!15, B!14))),
% 63.08/40.75 inference(quant_inst,[status(thm)],[])).
% 63.08/40.75 tff(256,plain,
% 63.08/40.75 (element(A!15, powerset(B!14)) <=> subset(A!15, B!14)),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[255, 254])).
% 63.08/40.75 tff(257,plain,
% 63.08/40.75 (subset(A!15, B!14)),
% 63.08/40.75 inference(and_elim,[status(thm)],[205])).
% 63.08/40.75 tff(258,plain,
% 63.08/40.75 ((~(element(A!15, powerset(B!14)) <=> subset(A!15, B!14))) | element(A!15, powerset(B!14)) | (~subset(A!15, B!14))),
% 63.08/40.75 inference(tautology,[status(thm)],[])).
% 63.08/40.75 tff(259,plain,
% 63.08/40.75 ((~(element(A!15, powerset(B!14)) <=> subset(A!15, B!14))) | element(A!15, powerset(B!14))),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[258, 257])).
% 63.08/40.75 tff(260,plain,
% 63.08/40.75 (element(A!15, powerset(B!14))),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[259, 256])).
% 63.08/40.75 tff(261,plain,
% 63.08/40.75 (^[A: $i, B: $i, C: $i] : refl((element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 63.08/40.75 inference(bind,[status(th)],[])).
% 63.08/40.75 tff(262,plain,
% 63.08/40.75 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 63.08/40.75 inference(quant_intro,[status(thm)],[261])).
% 63.08/40.75 tff(263,plain,
% 63.08/40.75 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C))) <=> (~((~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)))) <=> (~(~((~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)))) <=> ((~in(A, B)) | (~element(B, powerset(C)))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)))), rewrite((((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 63.08/40.75 inference(bind,[status(th)],[])).
% 63.08/40.75 tff(264,plain,
% 63.08/40.75 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 63.08/40.75 inference(quant_intro,[status(thm)],[263])).
% 63.08/40.75 tff(265,plain,
% 63.08/40.75 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(266,plain,
% 63.08/40.75 (^[A: $i, B: $i, C: $i] : rewrite(((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)))),
% 63.08/40.75 inference(bind,[status(th)],[])).
% 63.08/40.75 tff(267,plain,
% 63.08/40.75 (![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 63.08/40.75 inference(quant_intro,[status(thm)],[266])).
% 63.08/40.75 tff(268,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_subset')).
% 63.08/40.75 tff(269,plain,
% 63.08/40.75 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[268, 267])).
% 63.08/40.75 tff(270,plain,
% 63.08/40.75 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[269, 265])).
% 63.08/40.75 tff(271,plain,(
% 63.08/40.75 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 63.08/40.75 inference(skolemize,[status(sab)],[270])).
% 63.08/40.75 tff(272,plain,
% 63.08/40.75 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[271, 264])).
% 63.08/40.75 tff(273,plain,
% 63.08/40.75 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[272, 262])).
% 63.08/40.75 tff(274,plain,
% 63.08/40.75 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(A!15, powerset(B!14))) | (~in(tptp_fun_B_1(A!15), A!15)) | element(tptp_fun_B_1(A!15), B!14))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(A!15, powerset(B!14))) | (~in(tptp_fun_B_1(A!15), A!15)) | element(tptp_fun_B_1(A!15), B!14))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(275,plain,
% 63.08/40.75 ((element(tptp_fun_B_1(A!15), B!14) | (~in(tptp_fun_B_1(A!15), A!15)) | (~element(A!15, powerset(B!14)))) <=> ((~element(A!15, powerset(B!14))) | (~in(tptp_fun_B_1(A!15), A!15)) | element(tptp_fun_B_1(A!15), B!14))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(276,plain,
% 63.08/40.75 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_1(A!15), B!14) | (~in(tptp_fun_B_1(A!15), A!15)) | (~element(A!15, powerset(B!14))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(A!15, powerset(B!14))) | (~in(tptp_fun_B_1(A!15), A!15)) | element(tptp_fun_B_1(A!15), B!14)))),
% 63.08/40.75 inference(monotonicity,[status(thm)],[275])).
% 63.08/40.75 tff(277,plain,
% 63.08/40.75 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_1(A!15), B!14) | (~in(tptp_fun_B_1(A!15), A!15)) | (~element(A!15, powerset(B!14))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(A!15, powerset(B!14))) | (~in(tptp_fun_B_1(A!15), A!15)) | element(tptp_fun_B_1(A!15), B!14))),
% 63.08/40.75 inference(transitivity,[status(thm)],[276, 274])).
% 63.08/40.75 tff(278,plain,
% 63.08/40.75 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_1(A!15), B!14) | (~in(tptp_fun_B_1(A!15), A!15)) | (~element(A!15, powerset(B!14))))),
% 63.08/40.75 inference(quant_inst,[status(thm)],[])).
% 63.08/40.75 tff(279,plain,
% 63.08/40.75 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(A!15, powerset(B!14))) | (~in(tptp_fun_B_1(A!15), A!15)) | element(tptp_fun_B_1(A!15), B!14)),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[278, 277])).
% 63.08/40.75 tff(280,plain,
% 63.08/40.75 (element(tptp_fun_B_1(A!15), B!14)),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[279, 273, 260, 247])).
% 63.08/40.75 tff(281,plain,
% 63.08/40.75 (^[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)))))),
% 63.08/40.75 inference(bind,[status(th)],[])).
% 63.08/40.75 tff(282,plain,
% 63.08/40.75 (![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))))),
% 63.08/40.75 inference(quant_intro,[status(thm)],[281])).
% 63.08/40.75 tff(283,plain,
% 63.08/40.75 (^[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))))))),
% 63.08/40.75 inference(bind,[status(th)],[])).
% 63.08/40.75 tff(284,plain,
% 63.08/40.75 (![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))))),
% 63.08/40.75 inference(quant_intro,[status(thm)],[283])).
% 63.08/40.75 tff(285,plain,
% 63.08/40.75 (![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)))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(286,plain,
% 63.08/40.75 (^[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))))),
% 63.08/40.75 inference(bind,[status(th)],[])).
% 63.08/40.75 tff(287,plain,
% 63.08/40.75 (![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)))),
% 63.08/40.75 inference(quant_intro,[status(thm)],[286])).
% 63.08/40.75 tff(288,axiom,(![A: $i, B: $i, C: $i] : (~((in(A, B) & element(B, powerset(C))) & empty(C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_subset')).
% 63.08/40.75 tff(289,plain,
% 63.08/40.75 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[288, 287])).
% 63.08/40.75 tff(290,plain,
% 63.08/40.75 (![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[289, 285])).
% 63.08/40.75 tff(291,plain,(
% 63.08/40.75 ![A: $i, B: $i, C: $i] : (~(in(A, B) & element(B, powerset(C)) & empty(C)))),
% 63.08/40.75 inference(skolemize,[status(sab)],[290])).
% 63.08/40.75 tff(292,plain,
% 63.08/40.75 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[291, 284])).
% 63.08/40.75 tff(293,plain,
% 63.08/40.75 (![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[292, 282])).
% 63.08/40.75 tff(294,plain,
% 63.08/40.75 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!14)) | (~element(A!15, powerset(B!14))) | (~in(tptp_fun_B_1(A!15), A!15)))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(B!14)) | (~element(A!15, powerset(B!14))) | (~in(tptp_fun_B_1(A!15), A!15)))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(295,plain,
% 63.08/40.75 (((~empty(B!14)) | (~in(tptp_fun_B_1(A!15), A!15)) | (~element(A!15, powerset(B!14)))) <=> ((~empty(B!14)) | (~element(A!15, powerset(B!14))) | (~in(tptp_fun_B_1(A!15), A!15)))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(296,plain,
% 63.08/40.75 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!14)) | (~in(tptp_fun_B_1(A!15), A!15)) | (~element(A!15, powerset(B!14))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!14)) | (~element(A!15, powerset(B!14))) | (~in(tptp_fun_B_1(A!15), A!15))))),
% 63.08/40.75 inference(monotonicity,[status(thm)],[295])).
% 63.08/40.75 tff(297,plain,
% 63.08/40.75 (((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!14)) | (~in(tptp_fun_B_1(A!15), A!15)) | (~element(A!15, powerset(B!14))))) <=> ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(B!14)) | (~element(A!15, powerset(B!14))) | (~in(tptp_fun_B_1(A!15), A!15)))),
% 63.08/40.75 inference(transitivity,[status(thm)],[296, 294])).
% 63.08/40.75 tff(298,plain,
% 63.08/40.75 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~empty(B!14)) | (~in(tptp_fun_B_1(A!15), A!15)) | (~element(A!15, powerset(B!14))))),
% 63.08/40.75 inference(quant_inst,[status(thm)],[])).
% 63.08/40.75 tff(299,plain,
% 63.08/40.75 ((~![A: $i, B: $i, C: $i] : ((~empty(C)) | (~in(A, B)) | (~element(B, powerset(C))))) | (~empty(B!14)) | (~element(A!15, powerset(B!14))) | (~in(tptp_fun_B_1(A!15), A!15))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[298, 297])).
% 63.08/40.75 tff(300,plain,
% 63.08/40.75 (~empty(B!14)),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[299, 293, 260, 247])).
% 63.08/40.75 tff(301,plain,
% 63.08/40.75 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | (~element(tptp_fun_B_1(A!15), B!14)) | in(tptp_fun_B_1(A!15), B!14))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(B!14) | (~element(tptp_fun_B_1(A!15), B!14)) | in(tptp_fun_B_1(A!15), B!14))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(302,plain,
% 63.08/40.75 ((empty(B!14) | in(tptp_fun_B_1(A!15), B!14) | (~element(tptp_fun_B_1(A!15), B!14))) <=> (empty(B!14) | (~element(tptp_fun_B_1(A!15), B!14)) | in(tptp_fun_B_1(A!15), B!14))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(303,plain,
% 63.08/40.75 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | in(tptp_fun_B_1(A!15), B!14) | (~element(tptp_fun_B_1(A!15), B!14)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | (~element(tptp_fun_B_1(A!15), B!14)) | in(tptp_fun_B_1(A!15), B!14)))),
% 63.08/40.75 inference(monotonicity,[status(thm)],[302])).
% 63.08/40.75 tff(304,plain,
% 63.08/40.75 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | in(tptp_fun_B_1(A!15), B!14) | (~element(tptp_fun_B_1(A!15), B!14)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(B!14) | (~element(tptp_fun_B_1(A!15), B!14)) | in(tptp_fun_B_1(A!15), B!14))),
% 63.08/40.75 inference(transitivity,[status(thm)],[303, 301])).
% 63.08/40.75 tff(305,plain,
% 63.08/40.75 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | in(tptp_fun_B_1(A!15), B!14) | (~element(tptp_fun_B_1(A!15), B!14)))),
% 63.08/40.75 inference(quant_inst,[status(thm)],[])).
% 63.08/40.75 tff(306,plain,
% 63.08/40.75 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(B!14) | (~element(tptp_fun_B_1(A!15), B!14)) | in(tptp_fun_B_1(A!15), B!14)),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[305, 304])).
% 63.08/40.75 tff(307,plain,
% 63.08/40.75 (in(tptp_fun_B_1(A!15), B!14)),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[306, 242, 300, 280])).
% 63.08/40.75 tff(308,plain,
% 63.08/40.75 (ordinal(B!14)),
% 63.08/40.75 inference(and_elim,[status(thm)],[205])).
% 63.08/40.75 tff(309,plain,
% 63.08/40.75 (^[A: $i, B: $i] : refl((ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B))))),
% 63.08/40.75 inference(bind,[status(th)],[])).
% 63.08/40.75 tff(310,plain,
% 63.08/40.75 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 63.08/40.75 inference(quant_intro,[status(thm)],[309])).
% 63.08/40.75 tff(311,plain,
% 63.08/40.75 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(312,plain,
% 63.08/40.75 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) => ordinal(A)) <=> (ordinal(A) | (~in(A, B)))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> (ordinal(B) => (ordinal(A) | (~in(A, B)))))), rewrite((ordinal(B) => (ordinal(A) | (~in(A, B)))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B)))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B)))))),
% 63.08/40.75 inference(bind,[status(th)],[])).
% 63.08/40.75 tff(313,plain,
% 63.08/40.75 (![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 63.08/40.75 inference(quant_intro,[status(thm)],[312])).
% 63.08/40.75 tff(314,axiom,(![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_ordinal1')).
% 63.08/40.75 tff(315,plain,
% 63.08/40.75 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[314, 313])).
% 63.08/40.75 tff(316,plain,
% 63.08/40.75 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[315, 311])).
% 63.08/40.75 tff(317,plain,(
% 63.08/40.75 ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 63.08/40.75 inference(skolemize,[status(sab)],[316])).
% 63.08/40.75 tff(318,plain,
% 63.08/40.75 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[317, 310])).
% 63.08/40.75 tff(319,plain,
% 63.08/40.75 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(B!14)) | ordinal(tptp_fun_B_1(A!15)) | (~in(tptp_fun_B_1(A!15), B!14)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!14)) | ordinal(tptp_fun_B_1(A!15)) | (~in(tptp_fun_B_1(A!15), B!14)))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(320,plain,
% 63.08/40.75 ((ordinal(tptp_fun_B_1(A!15)) | (~in(tptp_fun_B_1(A!15), B!14)) | (~ordinal(B!14))) <=> ((~ordinal(B!14)) | ordinal(tptp_fun_B_1(A!15)) | (~in(tptp_fun_B_1(A!15), B!14)))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(321,plain,
% 63.08/40.75 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_B_1(A!15)) | (~in(tptp_fun_B_1(A!15), B!14)) | (~ordinal(B!14)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(B!14)) | ordinal(tptp_fun_B_1(A!15)) | (~in(tptp_fun_B_1(A!15), B!14))))),
% 63.08/40.75 inference(monotonicity,[status(thm)],[320])).
% 63.08/40.75 tff(322,plain,
% 63.08/40.75 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_B_1(A!15)) | (~in(tptp_fun_B_1(A!15), B!14)) | (~ordinal(B!14)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!14)) | ordinal(tptp_fun_B_1(A!15)) | (~in(tptp_fun_B_1(A!15), B!14)))),
% 63.08/40.75 inference(transitivity,[status(thm)],[321, 319])).
% 63.08/40.75 tff(323,plain,
% 63.08/40.75 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_B_1(A!15)) | (~in(tptp_fun_B_1(A!15), B!14)) | (~ordinal(B!14)))),
% 63.08/40.75 inference(quant_inst,[status(thm)],[])).
% 63.08/40.75 tff(324,plain,
% 63.08/40.75 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!14)) | ordinal(tptp_fun_B_1(A!15)) | (~in(tptp_fun_B_1(A!15), B!14))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[323, 322])).
% 63.08/40.75 tff(325,plain,
% 63.08/40.75 (ordinal(tptp_fun_B_1(A!15))),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[324, 318, 308, 307])).
% 63.08/40.75 tff(326,plain,
% 63.08/40.75 (((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_B_1(A!15))) | (~in(tptp_fun_B_1(A!15), A!15)) | (~((~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | (~ordinal(tptp_fun_B_1(A!15))) | (~in(tptp_fun_B_1(A!15), A!15)) | (~((~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(327,plain,
% 63.08/40.75 (((~ordinal(tptp_fun_B_1(A!15))) | (~in(tptp_fun_B_1(A!15), A!15)) | (~(ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15))))) <=> ((~ordinal(tptp_fun_B_1(A!15))) | (~in(tptp_fun_B_1(A!15), A!15)) | (~((~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(328,plain,
% 63.08/40.75 (((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_B_1(A!15))) | (~in(tptp_fun_B_1(A!15), A!15)) | (~(ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)))))) <=> ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_B_1(A!15))) | (~in(tptp_fun_B_1(A!15), A!15)) | (~((~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.75 inference(monotonicity,[status(thm)],[327])).
% 63.08/40.75 tff(329,plain,
% 63.08/40.75 (((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_B_1(A!15))) | (~in(tptp_fun_B_1(A!15), A!15)) | (~(ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)))))) <=> ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | (~ordinal(tptp_fun_B_1(A!15))) | (~in(tptp_fun_B_1(A!15), A!15)) | (~((~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.75 inference(transitivity,[status(thm)],[328, 326])).
% 63.08/40.75 tff(330,plain,
% 63.08/40.75 ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_B_1(A!15))) | (~in(tptp_fun_B_1(A!15), A!15)) | (~(ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)))))),
% 63.08/40.75 inference(quant_inst,[status(thm)],[])).
% 63.08/40.75 tff(331,plain,
% 63.08/40.75 ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | (~ordinal(tptp_fun_B_1(A!15))) | (~in(tptp_fun_B_1(A!15), A!15)) | (~((~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[330, 329])).
% 63.08/40.75 tff(332,plain,
% 63.08/40.75 ((~ordinal(tptp_fun_B_1(A!15))) | (~((~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[331, 207, 247])).
% 63.08/40.75 tff(333,plain,
% 63.08/40.75 (~((~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[332, 325])).
% 63.08/40.75 tff(334,plain,
% 63.08/40.75 (((~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.75 inference(tautology,[status(thm)],[])).
% 63.08/40.75 tff(335,plain,
% 63.08/40.75 (ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[334, 333])).
% 63.08/40.75 tff(336,plain,
% 63.08/40.75 (((~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_B_1(A!15), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)),
% 63.08/40.75 inference(tautology,[status(thm)],[])).
% 63.08/40.75 tff(337,plain,
% 63.08/40.75 (in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[336, 333])).
% 63.08/40.75 tff(338,plain,
% 63.08/40.75 (((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))) <=> ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(339,plain,
% 63.08/40.75 (((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~(ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15))))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(340,plain,
% 63.08/40.75 (((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~(ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)))))) <=> ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))))),
% 63.08/40.75 inference(monotonicity,[status(thm)],[339])).
% 63.08/40.75 tff(341,plain,
% 63.08/40.75 (((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~(ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)))))) <=> ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))),
% 63.08/40.75 inference(transitivity,[status(thm)],[340, 338])).
% 63.08/40.75 tff(342,plain,
% 63.08/40.75 ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~(ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)))))),
% 63.08/40.75 inference(quant_inst,[status(thm)],[])).
% 63.08/40.75 tff(343,plain,
% 63.08/40.75 ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), A!15)) | (~((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[342, 341])).
% 63.08/40.75 tff(344,plain,
% 63.08/40.75 (~((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[343, 207, 337, 335])).
% 63.08/40.75 tff(345,plain,
% 63.08/40.75 (((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)),
% 63.08/40.75 inference(tautology,[status(thm)],[])).
% 63.08/40.75 tff(346,plain,
% 63.08/40.75 (in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[345, 344])).
% 63.08/40.75 tff(347,plain,
% 63.08/40.75 ($false),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[346, 219])).
% 63.08/40.75 tff(348,plain,((~(empty_set = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(empty_set, A!15)), inference(lemma,lemma(discharge,[]))).
% 63.08/40.75 tff(349,plain,
% 63.08/40.75 (~(empty_set = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[348, 213])).
% 63.08/40.75 tff(350,assumption,(in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set)), introduced(assumption)).
% 63.08/40.75 tff(351,plain,
% 63.08/40.75 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set)))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(352,plain,
% 63.08/40.75 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set)))),
% 63.08/40.75 inference(quant_inst,[status(thm)],[])).
% 63.08/40.75 tff(353,plain,
% 63.08/40.75 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[352, 351])).
% 63.08/40.75 tff(354,plain,
% 63.08/40.75 ($false),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[353, 26, 125, 350])).
% 63.08/40.75 tff(355,plain,(~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set)), inference(lemma,lemma(discharge,[]))).
% 63.08/40.75 tff(356,plain,
% 63.08/40.75 (((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.75 inference(tautology,[status(thm)],[])).
% 63.08/40.75 tff(357,plain,
% 63.08/40.75 (ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[356, 344])).
% 63.08/40.75 tff(358,plain,
% 63.08/40.75 (((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set) | in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (empty_set = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set) | in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (empty_set = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(359,plain,
% 63.08/40.75 ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set) | in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (empty_set = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.75 inference(quant_inst,[status(thm)],[])).
% 63.08/40.75 tff(360,plain,
% 63.08/40.75 ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set) | in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (empty_set = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[359, 358])).
% 63.08/40.75 tff(361,plain,
% 63.08/40.75 (in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set) | in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (empty_set = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[360, 153, 357])).
% 63.08/40.75 tff(362,plain,
% 63.08/40.75 (in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (empty_set = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[361, 355])).
% 63.08/40.75 tff(363,plain,
% 63.08/40.75 (in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.75 inference(unit_resolution,[status(thm)],[362, 349])).
% 63.08/40.75 tff(364,assumption,(in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))), introduced(assumption)).
% 63.08/40.75 tff(365,assumption,(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), introduced(assumption)).
% 63.08/40.75 tff(366,plain,
% 63.08/40.75 (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.75 inference(monotonicity,[status(thm)],[365])).
% 63.08/40.75 tff(367,plain,
% 63.08/40.75 (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.75 inference(symmetry,[status(thm)],[366])).
% 63.08/40.75 tff(368,plain,
% 63.08/40.75 (^[A: $i, B: $i] : refl(((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B)))))))) <=> ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B)))))))))),
% 63.08/40.75 inference(bind,[status(th)],[])).
% 63.08/40.75 tff(369,plain,
% 63.08/40.75 (![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B)))))))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))),
% 63.08/40.75 inference(quant_intro,[status(thm)],[368])).
% 63.08/40.75 tff(370,plain,
% 63.08/40.75 (^[A: $i, B: $i] : rewrite(((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B)))))))) <=> ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B)))))))))),
% 63.08/40.75 inference(bind,[status(th)],[])).
% 63.08/40.75 tff(371,plain,
% 63.08/40.75 (![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B)))))))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))),
% 63.08/40.75 inference(quant_intro,[status(thm)],[370])).
% 63.08/40.75 tff(372,plain,
% 63.08/40.75 (![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B)))))))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))),
% 63.08/40.75 inference(transitivity,[status(thm)],[371, 369])).
% 63.08/40.75 tff(373,plain,
% 63.08/40.75 (^[A: $i, B: $i] : rewrite(((~in(A, B)) | (in(tptp_fun_C_17(B), B) & ![D: $i] : (~(in(D, B) & in(D, tptp_fun_C_17(B)))))) <=> ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B)))))))))),
% 63.08/40.75 inference(bind,[status(th)],[])).
% 63.08/40.75 tff(374,plain,
% 63.08/40.75 (![A: $i, B: $i] : ((~in(A, B)) | (in(tptp_fun_C_17(B), B) & ![D: $i] : (~(in(D, B) & in(D, tptp_fun_C_17(B)))))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))),
% 63.08/40.75 inference(quant_intro,[status(thm)],[373])).
% 63.08/40.75 tff(375,plain,
% 63.08/40.75 (![A: $i, B: $i] : (~(in(A, B) & ![C: $i] : (~(in(C, B) & ![D: $i] : (~(in(D, B) & in(D, C))))))) <=> ![A: $i, B: $i] : (~(in(A, B) & ![C: $i] : (~(in(C, B) & ![D: $i] : (~(in(D, B) & in(D, C)))))))),
% 63.08/40.75 inference(rewrite,[status(thm)],[])).
% 63.08/40.75 tff(376,axiom,(![A: $i, B: $i] : (~(in(A, B) & ![C: $i] : (~(in(C, B) & ![D: $i] : (~(in(D, B) & in(D, C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_tarski')).
% 63.08/40.75 tff(377,plain,
% 63.08/40.75 (![A: $i, B: $i] : (~(in(A, B) & ![C: $i] : (~(in(C, B) & ![D: $i] : (~(in(D, B) & in(D, C)))))))),
% 63.08/40.75 inference(modus_ponens,[status(thm)],[376, 375])).
% 63.08/40.75 tff(378,plain,(
% 63.08/40.75 ![A: $i, B: $i] : ((~in(A, B)) | (in(tptp_fun_C_17(B), B) & ![D: $i] : (~(in(D, B) & in(D, tptp_fun_C_17(B))))))),
% 63.08/40.75 inference(skolemize,[status(sab)],[377])).
% 63.08/40.75 tff(379,plain,
% 63.08/40.75 (![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[378, 374])).
% 63.08/40.76 tff(380,plain,
% 63.08/40.76 (![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[379, 372])).
% 63.08/40.76 tff(381,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | ((~in(tptp_fun_B_1(A!15), B!14)) | (~((~in(tptp_fun_C_17(B!14), B!14)) | (~![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14))))))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | (~in(tptp_fun_B_1(A!15), B!14)) | (~((~in(tptp_fun_C_17(B!14), B!14)) | (~![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14))))))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(382,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | ((~in(tptp_fun_B_1(A!15), B!14)) | (~((~in(tptp_fun_C_17(B!14), B!14)) | (~![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14))))))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(383,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | (~in(tptp_fun_B_1(A!15), B!14)) | (~((~in(tptp_fun_C_17(B!14), B!14)) | (~![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14)))))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[382, 381])).
% 63.08/40.76 tff(384,plain,
% 63.08/40.76 (~((~in(tptp_fun_C_17(B!14), B!14)) | (~![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14))))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[383, 380, 307])).
% 63.08/40.76 tff(385,plain,
% 63.08/40.76 (((~in(tptp_fun_C_17(B!14), B!14)) | (~![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14)))))) | in(tptp_fun_C_17(B!14), B!14)),
% 63.08/40.76 inference(tautology,[status(thm)],[])).
% 63.08/40.76 tff(386,plain,
% 63.08/40.76 (in(tptp_fun_C_17(B!14), B!14)),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[385, 384])).
% 63.08/40.76 tff(387,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(B!14)) | (~in(tptp_fun_C_17(B!14), B!14)) | ordinal(tptp_fun_C_17(B!14)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!14)) | (~in(tptp_fun_C_17(B!14), B!14)) | ordinal(tptp_fun_C_17(B!14)))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(388,plain,
% 63.08/40.76 ((ordinal(tptp_fun_C_17(B!14)) | (~in(tptp_fun_C_17(B!14), B!14)) | (~ordinal(B!14))) <=> ((~ordinal(B!14)) | (~in(tptp_fun_C_17(B!14), B!14)) | ordinal(tptp_fun_C_17(B!14)))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(389,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_17(B!14)) | (~in(tptp_fun_C_17(B!14), B!14)) | (~ordinal(B!14)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(B!14)) | (~in(tptp_fun_C_17(B!14), B!14)) | ordinal(tptp_fun_C_17(B!14))))),
% 63.08/40.76 inference(monotonicity,[status(thm)],[388])).
% 63.08/40.76 tff(390,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_17(B!14)) | (~in(tptp_fun_C_17(B!14), B!14)) | (~ordinal(B!14)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!14)) | (~in(tptp_fun_C_17(B!14), B!14)) | ordinal(tptp_fun_C_17(B!14)))),
% 63.08/40.76 inference(transitivity,[status(thm)],[389, 387])).
% 63.08/40.76 tff(391,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_17(B!14)) | (~in(tptp_fun_C_17(B!14), B!14)) | (~ordinal(B!14)))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(392,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!14)) | (~in(tptp_fun_C_17(B!14), B!14)) | ordinal(tptp_fun_C_17(B!14))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[391, 390])).
% 63.08/40.76 tff(393,plain,
% 63.08/40.76 (ordinal(tptp_fun_C_17(B!14))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[392, 318, 308, 386])).
% 63.08/40.76 tff(394,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_C_17(B!14))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_17(B!14))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(395,plain,
% 63.08/40.76 ((ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_C_17(B!14))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~ordinal(tptp_fun_C_17(B!14))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(396,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_C_17(B!14))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_C_17(B!14))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(monotonicity,[status(thm)],[395])).
% 63.08/40.76 tff(397,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_C_17(B!14))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_17(B!14))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(transitivity,[status(thm)],[396, 394])).
% 63.08/40.76 tff(398,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_C_17(B!14))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(399,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_17(B!14))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[398, 397])).
% 63.08/40.76 tff(400,plain,
% 63.08/40.76 (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[399, 177, 393, 357])).
% 63.08/40.76 tff(401,plain,
% 63.08/40.76 (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[400, 367])).
% 63.08/40.76 tff(402,plain,
% 63.08/40.76 (((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | (~(ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), A!15)))))) <=> ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | (~(ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), A!15)))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(403,plain,
% 63.08/40.76 ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | (~(ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), A!15)))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(404,plain,
% 63.08/40.76 ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | (~(ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), A!15))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[403, 402])).
% 63.08/40.76 tff(405,plain,
% 63.08/40.76 (~(ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), A!15)))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[404, 207, 346, 357])).
% 63.08/40.76 tff(406,plain,
% 63.08/40.76 ((ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), A!15))) | (~ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(tautology,[status(thm)],[])).
% 63.08/40.76 tff(407,plain,
% 63.08/40.76 (~ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[406, 405])).
% 63.08/40.76 tff(408,plain,
% 63.08/40.76 ($false),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[407, 401])).
% 63.08/40.76 tff(409,plain,(~(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.76 tff(410,plain,
% 63.08/40.76 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) | (~(epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~((~in(tptp_fun_B_0(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(tptp_fun_B_0(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(411,plain,
% 63.08/40.76 (~((~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) | (~(epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~((~in(tptp_fun_B_0(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(tptp_fun_B_0(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[410, 55])).
% 63.08/40.76 tff(412,plain,
% 63.08/40.76 (((~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) | (~(epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~((~in(tptp_fun_B_0(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(tptp_fun_B_0(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))))) | ((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.76 inference(tautology,[status(thm)],[])).
% 63.08/40.76 tff(413,plain,
% 63.08/40.76 ((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[412, 411])).
% 63.08/40.76 tff(414,plain,
% 63.08/40.76 ((ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), A!15))) | ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(tautology,[status(thm)],[])).
% 63.08/40.76 tff(415,plain,
% 63.08/40.76 (ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[414, 405])).
% 63.08/40.76 tff(416,plain,
% 63.08/40.76 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~epsilon_connected(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~epsilon_connected(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(417,plain,
% 63.08/40.76 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~epsilon_connected(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(418,plain,
% 63.08/40.76 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~epsilon_connected(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[417, 416])).
% 63.08/40.76 tff(419,plain,
% 63.08/40.76 (~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~epsilon_connected(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[418, 72, 415])).
% 63.08/40.76 tff(420,plain,
% 63.08/40.76 (((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~epsilon_connected(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(tautology,[status(thm)],[])).
% 63.08/40.76 tff(421,plain,
% 63.08/40.76 (epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[420, 419])).
% 63.08/40.76 tff(422,plain,
% 63.08/40.76 ((~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) | (~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(tautology,[status(thm)],[])).
% 63.08/40.76 tff(423,plain,
% 63.08/40.76 ((~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[422, 421])).
% 63.08/40.76 tff(424,plain,
% 63.08/40.76 (![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[423, 413])).
% 63.08/40.76 tff(425,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(426,plain,
% 63.08/40.76 (((ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(427,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))),
% 63.08/40.76 inference(monotonicity,[status(thm)],[426])).
% 63.08/40.76 tff(428,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.76 inference(transitivity,[status(thm)],[427, 425])).
% 63.08/40.76 tff(429,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(430,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[429, 428])).
% 63.08/40.76 tff(431,plain,
% 63.08/40.76 (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[430, 94, 357, 415])).
% 63.08/40.76 tff(432,plain,
% 63.08/40.76 ((~(ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(tautology,[status(thm)],[])).
% 63.08/40.76 tff(433,plain,
% 63.08/40.76 ((~(ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | (~subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[432, 407])).
% 63.08/40.76 tff(434,plain,
% 63.08/40.76 (~subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[433, 431])).
% 63.08/40.76 tff(435,plain,
% 63.08/40.76 (((~![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | ((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(436,plain,
% 63.08/40.76 ((~![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | ((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(437,plain,
% 63.08/40.76 ((~![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[436, 435])).
% 63.08/40.76 tff(438,plain,
% 63.08/40.76 (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[437, 434, 424])).
% 63.08/40.76 tff(439,plain,
% 63.08/40.76 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B)))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(440,plain,
% 63.08/40.76 (((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : (in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B)))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(441,plain,
% 63.08/40.76 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : (in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))))),
% 63.08/40.76 inference(monotonicity,[status(thm)],[440])).
% 63.08/40.76 tff(442,plain,
% 63.08/40.76 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : (in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B)))),
% 63.08/40.76 inference(transitivity,[status(thm)],[441, 439])).
% 63.08/40.76 tff(443,plain,
% 63.08/40.76 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : (in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B) | (~ordinal(B))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(444,plain,
% 63.08/40.76 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[443, 442])).
% 63.08/40.76 tff(445,plain,
% 63.08/40.76 (![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[444, 146, 415])).
% 63.08/40.76 tff(446,plain,
% 63.08/40.76 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(447,plain,
% 63.08/40.76 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(448,plain,
% 63.08/40.76 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[447, 446])).
% 63.08/40.76 tff(449,plain,
% 63.08/40.76 (in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[448, 357, 445])).
% 63.08/40.76 tff(450,plain,
% 63.08/40.76 (in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[449, 438])).
% 63.08/40.76 tff(451,plain,
% 63.08/40.76 (in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[450, 409])).
% 63.08/40.76 tff(452,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | ((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(453,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | ((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(454,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[453, 452])).
% 63.08/40.76 tff(455,plain,
% 63.08/40.76 (~((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[454, 380, 451])).
% 63.08/40.76 tff(456,plain,
% 63.08/40.76 (((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))) | ![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.76 inference(tautology,[status(thm)],[])).
% 63.08/40.76 tff(457,plain,
% 63.08/40.76 (![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[456, 455])).
% 63.08/40.76 tff(458,assumption,(in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))), introduced(assumption)).
% 63.08/40.76 tff(459,plain,
% 63.08/40.76 (((~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) | ((~in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) | (~in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(460,plain,
% 63.08/40.76 ((~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) | ((~in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(461,plain,
% 63.08/40.76 ((~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) | (~in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[460, 459])).
% 63.08/40.76 tff(462,plain,
% 63.08/40.76 ($false),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[461, 458, 457, 364])).
% 63.08/40.76 tff(463,plain,((~in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.76 tff(464,plain,
% 63.08/40.76 (~in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[463, 363])).
% 63.08/40.76 tff(465,assumption,(in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set)), introduced(assumption)).
% 63.08/40.76 tff(466,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set)))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(467,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set)))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(468,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[467, 466])).
% 63.08/40.76 tff(469,plain,
% 63.08/40.76 ($false),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[468, 26, 125, 465])).
% 63.08/40.76 tff(470,plain,(~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set)), inference(lemma,lemma(discharge,[]))).
% 63.08/40.76 tff(471,plain,
% 63.08/40.76 (((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.76 inference(tautology,[status(thm)],[])).
% 63.08/40.76 tff(472,plain,
% 63.08/40.76 (in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[471, 455])).
% 63.08/40.76 tff(473,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(474,plain,
% 63.08/40.76 ((ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(475,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.76 inference(monotonicity,[status(thm)],[474])).
% 63.08/40.76 tff(476,plain,
% 63.08/40.76 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(transitivity,[status(thm)],[475, 473])).
% 63.08/40.76 tff(477,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(478,plain,
% 63.08/40.76 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[477, 476])).
% 63.08/40.76 tff(479,plain,
% 63.08/40.76 (ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[478, 318, 357, 472])).
% 63.08/40.76 tff(480,plain,
% 63.08/40.76 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B)))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(481,plain,
% 63.08/40.76 (((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : (in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B)))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.76 tff(482,plain,
% 63.08/40.76 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : (in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))))),
% 63.08/40.76 inference(monotonicity,[status(thm)],[481])).
% 63.08/40.76 tff(483,plain,
% 63.08/40.76 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : (in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B)))),
% 63.08/40.76 inference(transitivity,[status(thm)],[482, 480])).
% 63.08/40.76 tff(484,plain,
% 63.08/40.76 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : (in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B) | (~ordinal(B))))),
% 63.08/40.76 inference(quant_inst,[status(thm)],[])).
% 63.08/40.76 tff(485,plain,
% 63.08/40.76 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))),
% 63.08/40.76 inference(modus_ponens,[status(thm)],[484, 483])).
% 63.08/40.76 tff(486,plain,
% 63.08/40.76 (![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))),
% 63.08/40.76 inference(unit_resolution,[status(thm)],[485, 146, 479])).
% 63.08/40.76 tff(487,plain,
% 63.08/40.76 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | ((~ordinal(empty_set)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set) | in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | (~ordinal(empty_set)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set) | in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set))),
% 63.08/40.76 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(488,plain,
% 63.08/40.77 (((~ordinal(empty_set)) | in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set)) <=> ((~ordinal(empty_set)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set) | in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(489,plain,
% 63.08/40.77 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | ((~ordinal(empty_set)) | in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | ((~ordinal(empty_set)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set) | in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set)))),
% 63.08/40.77 inference(monotonicity,[status(thm)],[488])).
% 63.08/40.77 tff(490,plain,
% 63.08/40.77 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | ((~ordinal(empty_set)) | in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | (~ordinal(empty_set)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set) | in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set))),
% 63.08/40.77 inference(transitivity,[status(thm)],[489, 487])).
% 63.08/40.77 tff(491,plain,
% 63.08/40.77 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | ((~ordinal(empty_set)) | in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(492,plain,
% 63.08/40.77 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | (~ordinal(empty_set)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set) | in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set)),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[491, 490])).
% 63.08/40.77 tff(493,plain,
% 63.08/40.77 (in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), empty_set) | in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set)),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[492, 98, 486])).
% 63.08/40.77 tff(494,plain,
% 63.08/40.77 (in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set)),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[493, 470])).
% 63.08/40.77 tff(495,plain,
% 63.08/40.77 (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[494, 464])).
% 63.08/40.77 tff(496,assumption,(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_C_17(A!15)), introduced(assumption)).
% 63.08/40.77 tff(497,plain,
% 63.08/40.77 (tptp_fun_C_17(A!15) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(symmetry,[status(thm)],[496])).
% 63.08/40.77 tff(498,plain,
% 63.08/40.77 (tptp_fun_C_17(A!15) = empty_set),
% 63.08/40.77 inference(transitivity,[status(thm)],[497, 495])).
% 63.08/40.77 tff(499,plain,
% 63.08/40.77 (in(tptp_fun_C_17(A!15), A!15) <=> in(empty_set, A!15)),
% 63.08/40.77 inference(monotonicity,[status(thm)],[498])).
% 63.08/40.77 tff(500,plain,
% 63.08/40.77 (in(empty_set, A!15) <=> in(tptp_fun_C_17(A!15), A!15)),
% 63.08/40.77 inference(symmetry,[status(thm)],[499])).
% 63.08/40.77 tff(501,plain,
% 63.08/40.77 ((~in(empty_set, A!15)) <=> (~in(tptp_fun_C_17(A!15), A!15))),
% 63.08/40.77 inference(monotonicity,[status(thm)],[500])).
% 63.08/40.77 tff(502,plain,
% 63.08/40.77 (~in(tptp_fun_C_17(A!15), A!15)),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[213, 501])).
% 63.08/40.77 tff(503,assumption,(~in(tptp_fun_C_17(A!15), A!15)), introduced(assumption)).
% 63.08/40.77 tff(504,plain,
% 63.08/40.77 (((~in(tptp_fun_C_17(A!15), A!15)) | (~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15)))))) | in(tptp_fun_C_17(A!15), A!15)),
% 63.08/40.77 inference(tautology,[status(thm)],[])).
% 63.08/40.77 tff(505,plain,
% 63.08/40.77 ((~in(tptp_fun_C_17(A!15), A!15)) | (~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15)))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[504, 503])).
% 63.08/40.77 tff(506,assumption,(in(tptp_fun_B_1(A!15), A!15)), introduced(assumption)).
% 63.08/40.77 tff(507,plain,
% 63.08/40.77 (((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | ((~in(tptp_fun_B_1(A!15), A!15)) | (~((~in(tptp_fun_C_17(A!15), A!15)) | (~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | (~in(tptp_fun_B_1(A!15), A!15)) | (~((~in(tptp_fun_C_17(A!15), A!15)) | (~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))))))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(508,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | ((~in(tptp_fun_B_1(A!15), A!15)) | (~((~in(tptp_fun_C_17(A!15), A!15)) | (~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))))))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(509,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | (~in(tptp_fun_B_1(A!15), A!15)) | (~((~in(tptp_fun_C_17(A!15), A!15)) | (~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15)))))))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[508, 507])).
% 63.08/40.77 tff(510,plain,
% 63.08/40.77 ($false),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[509, 380, 506, 505])).
% 63.08/40.77 tff(511,plain,((~in(tptp_fun_B_1(A!15), A!15)) | in(tptp_fun_C_17(A!15), A!15)), inference(lemma,lemma(discharge,[]))).
% 63.08/40.77 tff(512,plain,
% 63.08/40.77 (in(tptp_fun_C_17(A!15), A!15)),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[511, 247])).
% 63.08/40.77 tff(513,plain,
% 63.08/40.77 ($false),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[512, 502])).
% 63.08/40.77 tff(514,plain,((~(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_C_17(A!15))) | in(empty_set, A!15)), inference(lemma,lemma(discharge,[]))).
% 63.08/40.77 tff(515,plain,
% 63.08/40.77 (~(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_C_17(A!15))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[514, 212])).
% 63.08/40.77 tff(516,plain,
% 63.08/40.77 (empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> empty(empty_set)),
% 63.08/40.77 inference(monotonicity,[status(thm)],[215])).
% 63.08/40.77 tff(517,plain,
% 63.08/40.77 (empty(empty_set) <=> empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(symmetry,[status(thm)],[516])).
% 63.08/40.77 tff(518,plain,
% 63.08/40.77 (empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[26, 517])).
% 63.08/40.77 tff(519,plain,
% 63.08/40.77 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(520,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(521,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[520, 519])).
% 63.08/40.77 tff(522,plain,
% 63.08/40.77 (~empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[521, 125, 451])).
% 63.08/40.77 tff(523,plain,
% 63.08/40.77 ($false),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[522, 518])).
% 63.08/40.77 tff(524,plain,(~(empty_set = tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.77 tff(525,plain,
% 63.08/40.77 (in(empty_set, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[362, 524])).
% 63.08/40.77 tff(526,plain,
% 63.08/40.77 (~in(empty_set, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[463, 525])).
% 63.08/40.77 tff(527,plain,
% 63.08/40.77 (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[494, 526])).
% 63.08/40.77 tff(528,assumption,(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set), introduced(assumption)).
% 63.08/40.77 tff(529,plain,
% 63.08/40.77 (empty_set = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(symmetry,[status(thm)],[528])).
% 63.08/40.77 tff(530,assumption,(B!14 = empty_set), introduced(assumption)).
% 63.08/40.77 tff(531,plain,
% 63.08/40.77 (empty(B!14) <=> empty(empty_set)),
% 63.08/40.77 inference(monotonicity,[status(thm)],[530])).
% 63.08/40.77 tff(532,plain,
% 63.08/40.77 (empty(empty_set) <=> empty(B!14)),
% 63.08/40.77 inference(symmetry,[status(thm)],[531])).
% 63.08/40.77 tff(533,plain,
% 63.08/40.77 (empty(B!14)),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[26, 532])).
% 63.08/40.77 tff(534,plain,
% 63.08/40.77 ($false),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[300, 533])).
% 63.08/40.77 tff(535,plain,(~(B!14 = empty_set)), inference(lemma,lemma(discharge,[]))).
% 63.08/40.77 tff(536,assumption,(in(B!14, empty_set)), introduced(assumption)).
% 63.08/40.77 tff(537,plain,
% 63.08/40.77 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(B!14, empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(B!14, empty_set)))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(538,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(B!14, empty_set)))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(539,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(B!14, empty_set))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[538, 537])).
% 63.08/40.77 tff(540,plain,
% 63.08/40.77 ($false),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[539, 26, 125, 536])).
% 63.08/40.77 tff(541,plain,(~in(B!14, empty_set)), inference(lemma,lemma(discharge,[]))).
% 63.08/40.77 tff(542,plain,
% 63.08/40.77 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B)))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(543,plain,
% 63.08/40.77 (((~ordinal(B!14)) | ![B: $i] : (in(B, B!14) | in(B!14, B) | (B!14 = B) | (~ordinal(B)))) <=> ((~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B)))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(544,plain,
% 63.08/40.77 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : (in(B, B!14) | in(B!14, B) | (B!14 = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))))),
% 63.08/40.77 inference(monotonicity,[status(thm)],[543])).
% 63.08/40.77 tff(545,plain,
% 63.08/40.77 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : (in(B, B!14) | in(B!14, B) | (B!14 = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B)))),
% 63.08/40.77 inference(transitivity,[status(thm)],[544, 542])).
% 63.08/40.77 tff(546,plain,
% 63.08/40.77 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(B!14)) | ![B: $i] : (in(B, B!14) | in(B!14, B) | (B!14 = B) | (~ordinal(B))))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(547,plain,
% 63.08/40.77 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(B!14)) | ![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[546, 545])).
% 63.08/40.77 tff(548,plain,
% 63.08/40.77 (![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[547, 146, 308])).
% 63.08/40.77 tff(549,plain,
% 63.08/40.77 (((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | ((~ordinal(empty_set)) | in(empty_set, B!14) | in(B!14, empty_set) | (B!14 = empty_set))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | (~ordinal(empty_set)) | in(empty_set, B!14) | in(B!14, empty_set) | (B!14 = empty_set))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(550,plain,
% 63.08/40.77 ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | ((~ordinal(empty_set)) | in(empty_set, B!14) | in(B!14, empty_set) | (B!14 = empty_set))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(551,plain,
% 63.08/40.77 ((~![B: $i] : ((~ordinal(B)) | in(B, B!14) | in(B!14, B) | (B!14 = B))) | (~ordinal(empty_set)) | in(empty_set, B!14) | in(B!14, empty_set) | (B!14 = empty_set)),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[550, 549])).
% 63.08/40.77 tff(552,plain,
% 63.08/40.77 (in(empty_set, B!14) | in(B!14, empty_set) | (B!14 = empty_set)),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[551, 98, 548])).
% 63.08/40.77 tff(553,plain,
% 63.08/40.77 (in(empty_set, B!14) | (B!14 = empty_set)),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[552, 541])).
% 63.08/40.77 tff(554,plain,
% 63.08/40.77 (in(empty_set, B!14)),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[553, 535])).
% 63.08/40.77 tff(555,plain,
% 63.08/40.77 (((~in(tptp_fun_C_17(B!14), B!14)) | (~![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14)))))) | ![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14))))),
% 63.08/40.77 inference(tautology,[status(thm)],[])).
% 63.08/40.77 tff(556,plain,
% 63.08/40.77 (![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[555, 384])).
% 63.08/40.77 tff(557,assumption,(in(empty_set, tptp_fun_C_17(B!14))), introduced(assumption)).
% 63.08/40.77 tff(558,assumption,(in(empty_set, B!14)), introduced(assumption)).
% 63.08/40.77 tff(559,plain,
% 63.08/40.77 (((~![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14))))) | ((~in(empty_set, B!14)) | (~in(empty_set, tptp_fun_C_17(B!14))))) <=> ((~![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14))))) | (~in(empty_set, B!14)) | (~in(empty_set, tptp_fun_C_17(B!14))))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(560,plain,
% 63.08/40.77 ((~![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14))))) | ((~in(empty_set, B!14)) | (~in(empty_set, tptp_fun_C_17(B!14))))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(561,plain,
% 63.08/40.77 ((~![D: $i] : ((~in(D, B!14)) | (~in(D, tptp_fun_C_17(B!14))))) | (~in(empty_set, B!14)) | (~in(empty_set, tptp_fun_C_17(B!14)))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[560, 559])).
% 63.08/40.77 tff(562,plain,
% 63.08/40.77 ($false),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[561, 558, 557, 556])).
% 63.08/40.77 tff(563,plain,((~in(empty_set, B!14)) | (~in(empty_set, tptp_fun_C_17(B!14)))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.77 tff(564,plain,
% 63.08/40.77 (~in(empty_set, tptp_fun_C_17(B!14))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[563, 554])).
% 63.08/40.77 tff(565,assumption,(in(tptp_fun_C_17(B!14), empty_set)), introduced(assumption)).
% 63.08/40.77 tff(566,plain,
% 63.08/40.77 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_17(B!14), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_17(B!14), empty_set)))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(567,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_17(B!14), empty_set)))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(568,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_17(B!14), empty_set))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[567, 566])).
% 63.08/40.77 tff(569,plain,
% 63.08/40.77 ($false),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[568, 26, 125, 565])).
% 63.08/40.77 tff(570,plain,(~in(tptp_fun_C_17(B!14), empty_set)), inference(lemma,lemma(discharge,[]))).
% 63.08/40.77 tff(571,plain,
% 63.08/40.77 (((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | (in(empty_set, tptp_fun_C_17(B!14)) | (~ordinal(tptp_fun_C_17(B!14))) | in(tptp_fun_C_17(B!14), empty_set) | (empty_set = tptp_fun_C_17(B!14)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | in(empty_set, tptp_fun_C_17(B!14)) | (~ordinal(tptp_fun_C_17(B!14))) | in(tptp_fun_C_17(B!14), empty_set) | (empty_set = tptp_fun_C_17(B!14)))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(572,plain,
% 63.08/40.77 (((~ordinal(tptp_fun_C_17(B!14))) | in(tptp_fun_C_17(B!14), empty_set) | in(empty_set, tptp_fun_C_17(B!14)) | (empty_set = tptp_fun_C_17(B!14))) <=> (in(empty_set, tptp_fun_C_17(B!14)) | (~ordinal(tptp_fun_C_17(B!14))) | in(tptp_fun_C_17(B!14), empty_set) | (empty_set = tptp_fun_C_17(B!14)))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(573,plain,
% 63.08/40.77 (((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | ((~ordinal(tptp_fun_C_17(B!14))) | in(tptp_fun_C_17(B!14), empty_set) | in(empty_set, tptp_fun_C_17(B!14)) | (empty_set = tptp_fun_C_17(B!14)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | (in(empty_set, tptp_fun_C_17(B!14)) | (~ordinal(tptp_fun_C_17(B!14))) | in(tptp_fun_C_17(B!14), empty_set) | (empty_set = tptp_fun_C_17(B!14))))),
% 63.08/40.77 inference(monotonicity,[status(thm)],[572])).
% 63.08/40.77 tff(574,plain,
% 63.08/40.77 (((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | ((~ordinal(tptp_fun_C_17(B!14))) | in(tptp_fun_C_17(B!14), empty_set) | in(empty_set, tptp_fun_C_17(B!14)) | (empty_set = tptp_fun_C_17(B!14)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | in(empty_set, tptp_fun_C_17(B!14)) | (~ordinal(tptp_fun_C_17(B!14))) | in(tptp_fun_C_17(B!14), empty_set) | (empty_set = tptp_fun_C_17(B!14)))),
% 63.08/40.77 inference(transitivity,[status(thm)],[573, 571])).
% 63.08/40.77 tff(575,plain,
% 63.08/40.77 ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | ((~ordinal(tptp_fun_C_17(B!14))) | in(tptp_fun_C_17(B!14), empty_set) | in(empty_set, tptp_fun_C_17(B!14)) | (empty_set = tptp_fun_C_17(B!14)))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(576,plain,
% 63.08/40.77 ((~![B: $i] : ((~ordinal(B)) | in(B, empty_set) | in(empty_set, B) | (empty_set = B))) | in(empty_set, tptp_fun_C_17(B!14)) | (~ordinal(tptp_fun_C_17(B!14))) | in(tptp_fun_C_17(B!14), empty_set) | (empty_set = tptp_fun_C_17(B!14))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[575, 574])).
% 63.08/40.77 tff(577,plain,
% 63.08/40.77 (in(empty_set, tptp_fun_C_17(B!14)) | (~ordinal(tptp_fun_C_17(B!14))) | (empty_set = tptp_fun_C_17(B!14))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[576, 153, 570])).
% 63.08/40.77 tff(578,plain,
% 63.08/40.77 (in(empty_set, tptp_fun_C_17(B!14)) | (empty_set = tptp_fun_C_17(B!14))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[577, 393])).
% 63.08/40.77 tff(579,plain,
% 63.08/40.77 (empty_set = tptp_fun_C_17(B!14)),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[578, 564])).
% 63.08/40.77 tff(580,plain,
% 63.08/40.77 (tptp_fun_C_17(B!14) = empty_set),
% 63.08/40.77 inference(symmetry,[status(thm)],[579])).
% 63.08/40.77 tff(581,plain,
% 63.08/40.77 (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_C_17(B!14)),
% 63.08/40.77 inference(transitivity,[status(thm)],[528, 579])).
% 63.08/40.77 tff(582,plain,
% 63.08/40.77 (in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(monotonicity,[status(thm)],[581])).
% 63.08/40.77 tff(583,plain,
% 63.08/40.77 ((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> (~in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.77 inference(monotonicity,[status(thm)],[582])).
% 63.08/40.77 tff(584,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(585,plain,
% 63.08/40.77 (element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[584, 254])).
% 63.08/40.77 tff(586,plain,
% 63.08/40.77 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(587,plain,
% 63.08/40.77 (((ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(588,plain,
% 63.08/40.77 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.77 inference(monotonicity,[status(thm)],[587])).
% 63.08/40.77 tff(589,plain,
% 63.08/40.77 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.77 inference(transitivity,[status(thm)],[588, 586])).
% 63.08/40.77 tff(590,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(591,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[590, 589])).
% 63.08/40.77 tff(592,plain,
% 63.08/40.77 (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[591, 94, 357, 415])).
% 63.08/40.77 tff(593,plain,
% 63.08/40.77 (^[A: $i, B: $i] : refl((ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A))))),
% 63.08/40.77 inference(bind,[status(th)],[])).
% 63.08/40.77 tff(594,plain,
% 63.08/40.77 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 63.08/40.77 inference(quant_intro,[status(thm)],[593])).
% 63.08/40.77 tff(595,plain,
% 63.08/40.77 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), ((ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | ((~ordinal(B)) | (~ordinal(A)))))), rewrite((ordinal_subset(B, A) | ordinal_subset(A, B) | ((~ordinal(B)) | (~ordinal(A)))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))), ((ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))))),
% 63.08/40.77 inference(bind,[status(th)],[])).
% 63.08/40.77 tff(596,plain,
% 63.08/40.77 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 63.08/40.77 inference(quant_intro,[status(thm)],[595])).
% 63.08/40.77 tff(597,plain,
% 63.08/40.77 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B)))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(598,plain,
% 63.08/40.77 (^[A: $i, B: $i] : trans(monotonicity(rewrite((ordinal_subset(A, B) | ordinal_subset(B, A)) <=> (ordinal_subset(B, A) | ordinal_subset(A, B))), (((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A))) <=> ((ordinal(A) & ordinal(B)) => (ordinal_subset(B, A) | ordinal_subset(A, B))))), rewrite(((ordinal(A) & ordinal(B)) => (ordinal_subset(B, A) | ordinal_subset(A, B))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))), (((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A))) <=> (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))))),
% 63.08/40.77 inference(bind,[status(th)],[])).
% 63.08/40.77 tff(599,plain,
% 63.08/40.77 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A))) <=> ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 63.08/40.77 inference(quant_intro,[status(thm)],[598])).
% 63.08/40.77 tff(600,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) | ordinal_subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','connectedness_r1_ordinal1')).
% 63.08/40.77 tff(601,plain,
% 63.08/40.77 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[600, 599])).
% 63.08/40.77 tff(602,plain,
% 63.08/40.77 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[601, 597])).
% 63.08/40.77 tff(603,plain,(
% 63.08/40.77 ![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~(ordinal(A) & ordinal(B))))),
% 63.08/40.77 inference(skolemize,[status(sab)],[602])).
% 63.08/40.77 tff(604,plain,
% 63.08/40.77 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[603, 596])).
% 63.08/40.77 tff(605,plain,
% 63.08/40.77 (![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[604, 594])).
% 63.08/40.77 tff(606,plain,
% 63.08/40.77 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(607,plain,
% 63.08/40.77 ((ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(608,plain,
% 63.08/40.77 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.77 inference(monotonicity,[status(thm)],[607])).
% 63.08/40.77 tff(609,plain,
% 63.08/40.77 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.77 inference(transitivity,[status(thm)],[608, 606])).
% 63.08/40.77 tff(610,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(611,plain,
% 63.08/40.77 ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[610, 609])).
% 63.08/40.77 tff(612,plain,
% 63.08/40.77 (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[611, 605, 357, 407, 415])).
% 63.08/40.77 tff(613,plain,
% 63.08/40.77 ((~(ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(tautology,[status(thm)],[])).
% 63.08/40.77 tff(614,plain,
% 63.08/40.77 ((~(ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[613, 612])).
% 63.08/40.77 tff(615,plain,
% 63.08/40.77 (subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[614, 592])).
% 63.08/40.77 tff(616,plain,
% 63.08/40.77 ((~(element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.77 inference(tautology,[status(thm)],[])).
% 63.08/40.77 tff(617,plain,
% 63.08/40.77 ((~(element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[616, 615])).
% 63.08/40.77 tff(618,plain,
% 63.08/40.77 (element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[617, 585])).
% 63.08/40.77 tff(619,plain,
% 63.08/40.77 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | (~(epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~((~in(tptp_fun_B_0(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(tptp_fun_B_0(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(620,plain,
% 63.08/40.77 (~((~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | (~(epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~((~in(tptp_fun_B_0(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(tptp_fun_B_0(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[619, 55])).
% 63.08/40.77 tff(621,plain,
% 63.08/40.77 (((~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | (~(epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~((~in(tptp_fun_B_0(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(tptp_fun_B_0(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))) | ((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.77 inference(tautology,[status(thm)],[])).
% 63.08/40.77 tff(622,plain,
% 63.08/40.77 ((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[621, 620])).
% 63.08/40.77 tff(623,plain,
% 63.08/40.77 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~epsilon_connected(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~epsilon_connected(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))),
% 63.08/40.77 inference(rewrite,[status(thm)],[])).
% 63.08/40.77 tff(624,plain,
% 63.08/40.77 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~epsilon_connected(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))),
% 63.08/40.77 inference(quant_inst,[status(thm)],[])).
% 63.08/40.77 tff(625,plain,
% 63.08/40.77 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~epsilon_connected(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.77 inference(modus_ponens,[status(thm)],[624, 623])).
% 63.08/40.77 tff(626,plain,
% 63.08/40.77 (~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~epsilon_connected(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[625, 72, 357])).
% 63.08/40.77 tff(627,plain,
% 63.08/40.77 (((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~epsilon_connected(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(tautology,[status(thm)],[])).
% 63.08/40.77 tff(628,plain,
% 63.08/40.77 (epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.77 inference(unit_resolution,[status(thm)],[627, 626])).
% 63.08/40.77 tff(629,plain,
% 63.08/40.77 ((~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | (~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(tautology,[status(thm)],[])).
% 63.08/40.78 tff(630,plain,
% 63.08/40.78 ((~((~epsilon_transitive(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | ![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[629, 628])).
% 63.08/40.78 tff(631,plain,
% 63.08/40.78 (![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[630, 622])).
% 63.08/40.78 tff(632,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(633,plain,
% 63.08/40.78 (((ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(634,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(monotonicity,[status(thm)],[633])).
% 63.08/40.78 tff(635,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(transitivity,[status(thm)],[634, 632])).
% 63.08/40.78 tff(636,plain,
% 63.08/40.78 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(quant_inst,[status(thm)],[])).
% 63.08/40.78 tff(637,plain,
% 63.08/40.78 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(modus_ponens,[status(thm)],[636, 635])).
% 63.08/40.78 tff(638,plain,
% 63.08/40.78 (ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[637, 94, 335, 357])).
% 63.08/40.78 tff(639,plain,
% 63.08/40.78 (((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), A!15)) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(tautology,[status(thm)],[])).
% 63.08/40.78 tff(640,plain,
% 63.08/40.78 (~ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[639, 344])).
% 63.08/40.78 tff(641,plain,
% 63.08/40.78 ((~(ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(tautology,[status(thm)],[])).
% 63.08/40.78 tff(642,plain,
% 63.08/40.78 ((~(ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[641, 640])).
% 63.08/40.78 tff(643,plain,
% 63.08/40.78 (~subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[642, 638])).
% 63.08/40.78 tff(644,plain,
% 63.08/40.78 (((~![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ((~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(645,plain,
% 63.08/40.78 ((~![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ((~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(quant_inst,[status(thm)],[])).
% 63.08/40.78 tff(646,plain,
% 63.08/40.78 ((~![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(modus_ponens,[status(thm)],[645, 644])).
% 63.08/40.78 tff(647,plain,
% 63.08/40.78 (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[646, 643, 631])).
% 63.08/40.78 tff(648,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(649,plain,
% 63.08/40.78 ((empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> (in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(650,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(monotonicity,[status(thm)],[649])).
% 63.08/40.78 tff(651,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(transitivity,[status(thm)],[650, 648])).
% 63.08/40.78 tff(652,plain,
% 63.08/40.78 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(quant_inst,[status(thm)],[])).
% 63.08/40.78 tff(653,plain,
% 63.08/40.78 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(modus_ponens,[status(thm)],[652, 651])).
% 63.08/40.78 tff(654,plain,
% 63.08/40.78 (empty(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[653, 242, 647])).
% 63.08/40.78 tff(655,plain,
% 63.08/40.78 (~element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[654, 522])).
% 63.08/40.78 tff(656,assumption,(in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))), introduced(assumption)).
% 63.08/40.78 tff(657,plain,
% 63.08/40.78 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(658,plain,
% 63.08/40.78 ((element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> (element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(659,plain,
% 63.08/40.78 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))),
% 63.08/40.78 inference(monotonicity,[status(thm)],[658])).
% 63.08/40.78 tff(660,plain,
% 63.08/40.78 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(transitivity,[status(thm)],[659, 657])).
% 63.08/40.78 tff(661,plain,
% 63.08/40.78 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(quant_inst,[status(thm)],[])).
% 63.08/40.78 tff(662,plain,
% 63.08/40.78 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(modus_ponens,[status(thm)],[661, 660])).
% 63.08/40.78 tff(663,plain,
% 63.08/40.78 ($false),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[662, 273, 656, 655, 618])).
% 63.08/40.78 tff(664,plain,(~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.78 tff(665,assumption,(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15))), introduced(assumption)).
% 63.08/40.78 tff(666,plain,
% 63.08/40.78 (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.78 inference(monotonicity,[status(thm)],[665])).
% 63.08/40.78 tff(667,plain,
% 63.08/40.78 (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15))) <=> ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(symmetry,[status(thm)],[666])).
% 63.08/40.78 tff(668,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(669,plain,
% 63.08/40.78 ((ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(670,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(monotonicity,[status(thm)],[669])).
% 63.08/40.78 tff(671,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(transitivity,[status(thm)],[670, 668])).
% 63.08/40.78 tff(672,plain,
% 63.08/40.78 ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(quant_inst,[status(thm)],[])).
% 63.08/40.78 tff(673,plain,
% 63.08/40.78 ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.78 inference(modus_ponens,[status(thm)],[672, 671])).
% 63.08/40.78 tff(674,plain,
% 63.08/40.78 (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[673, 605, 335, 640, 357])).
% 63.08/40.78 tff(675,plain,
% 63.08/40.78 (ordinal_subset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(modus_ponens,[status(thm)],[674, 667])).
% 63.08/40.78 tff(676,plain,
% 63.08/40.78 ($false),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[407, 675])).
% 63.08/40.78 tff(677,plain,(~(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15)))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.78 tff(678,plain,
% 63.08/40.78 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(679,plain,
% 63.08/40.78 (((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(680,plain,
% 63.08/40.78 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(monotonicity,[status(thm)],[679])).
% 63.08/40.78 tff(681,plain,
% 63.08/40.78 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(transitivity,[status(thm)],[680, 678])).
% 63.08/40.78 tff(682,plain,
% 63.08/40.78 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(quant_inst,[status(thm)],[])).
% 63.08/40.78 tff(683,plain,
% 63.08/40.78 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), B) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = B))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(modus_ponens,[status(thm)],[682, 681])).
% 63.08/40.78 tff(684,plain,
% 63.08/40.78 (in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | (tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_D_16(tptp_fun_B_1(A!15))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[683, 335, 445])).
% 63.08/40.78 tff(685,plain,
% 63.08/40.78 (in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[684, 677])).
% 63.08/40.78 tff(686,plain,
% 63.08/40.78 (in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[685, 664])).
% 63.08/40.78 tff(687,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | ((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(688,plain,
% 63.08/40.78 ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | ((~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))))),
% 63.08/40.78 inference(quant_inst,[status(thm)],[])).
% 63.08/40.78 tff(689,plain,
% 63.08/40.78 ((~![A: $i, B: $i] : ((~in(A, B)) | (~((~in(tptp_fun_C_17(B), B)) | (~![D: $i] : ((~in(D, B)) | (~in(D, tptp_fun_C_17(B))))))))) | (~in(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))))),
% 63.08/40.78 inference(modus_ponens,[status(thm)],[688, 687])).
% 63.08/40.78 tff(690,plain,
% 63.08/40.78 (~((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[689, 380, 686])).
% 63.08/40.78 tff(691,plain,
% 63.08/40.78 (((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) | ![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(tautology,[status(thm)],[])).
% 63.08/40.78 tff(692,plain,
% 63.08/40.78 (![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[691, 690])).
% 63.08/40.78 tff(693,assumption,(in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))), introduced(assumption)).
% 63.08/40.78 tff(694,plain,
% 63.08/40.78 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(quant_inst,[status(thm)],[])).
% 63.08/40.78 tff(695,plain,
% 63.08/40.78 (element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[694, 254])).
% 63.08/40.78 tff(696,plain,
% 63.08/40.78 (((~![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(697,plain,
% 63.08/40.78 ((~![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(quant_inst,[status(thm)],[])).
% 63.08/40.78 tff(698,plain,
% 63.08/40.78 ((~![B: $i] : ((~in(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(B, tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(modus_ponens,[status(thm)],[697, 696])).
% 63.08/40.78 tff(699,plain,
% 63.08/40.78 (subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[698, 631, 472])).
% 63.08/40.78 tff(700,plain,
% 63.08/40.78 ((~(element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(tautology,[status(thm)],[])).
% 63.08/40.78 tff(701,plain,
% 63.08/40.78 ((~(element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[700, 699])).
% 63.08/40.78 tff(702,plain,
% 63.08/40.78 (element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[701, 695])).
% 63.08/40.78 tff(703,plain,
% 63.08/40.78 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(704,plain,
% 63.08/40.78 ((element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> (element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(705,plain,
% 63.08/40.78 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))))),
% 63.08/40.78 inference(monotonicity,[status(thm)],[704])).
% 63.08/40.78 tff(706,plain,
% 63.08/40.78 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(transitivity,[status(thm)],[705, 703])).
% 63.08/40.78 tff(707,plain,
% 63.08/40.78 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(quant_inst,[status(thm)],[])).
% 63.08/40.78 tff(708,plain,
% 63.08/40.78 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~element(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), powerset(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(modus_ponens,[status(thm)],[707, 706])).
% 63.08/40.78 tff(709,plain,
% 63.08/40.78 ($false),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[708, 273, 655, 702, 693])).
% 63.08/40.78 tff(710,plain,(~in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.78 tff(711,assumption,(tptp_fun_D_16(tptp_fun_B_1(A!15)) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))), introduced(assumption)).
% 63.08/40.78 tff(712,plain,
% 63.08/40.78 (ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(monotonicity,[status(thm)],[711])).
% 63.08/40.78 tff(713,plain,
% 63.08/40.78 (ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(symmetry,[status(thm)],[712])).
% 63.08/40.78 tff(714,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(715,plain,
% 63.08/40.78 (((ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(rewrite,[status(thm)],[])).
% 63.08/40.78 tff(716,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(monotonicity,[status(thm)],[715])).
% 63.08/40.78 tff(717,plain,
% 63.08/40.78 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.78 inference(transitivity,[status(thm)],[716, 714])).
% 63.08/40.78 tff(718,plain,
% 63.08/40.78 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))),
% 63.08/40.78 inference(quant_inst,[status(thm)],[])).
% 63.08/40.78 tff(719,plain,
% 63.08/40.78 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.78 inference(modus_ponens,[status(thm)],[718, 717])).
% 63.08/40.78 tff(720,plain,
% 63.08/40.78 (ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.78 inference(unit_resolution,[status(thm)],[719, 94, 357, 479])).
% 63.08/40.78 tff(721,plain,
% 63.08/40.78 ((~(ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.79 inference(tautology,[status(thm)],[])).
% 63.08/40.79 tff(722,plain,
% 63.08/40.79 ((~(ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[721, 699])).
% 63.08/40.79 tff(723,plain,
% 63.08/40.79 (ordinal_subset(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[722, 720])).
% 63.08/40.79 tff(724,plain,
% 63.08/40.79 (ordinal_subset(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[723, 713])).
% 63.08/40.79 tff(725,plain,
% 63.08/40.79 ($false),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[640, 724])).
% 63.08/40.79 tff(726,plain,(~(tptp_fun_D_16(tptp_fun_B_1(A!15)) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.79 tff(727,plain,
% 63.08/40.79 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ![B: $i] : ((~ordinal(B)) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | in(B, tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ![B: $i] : ((~ordinal(B)) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | in(B, tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(728,plain,
% 63.08/40.79 (((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ![B: $i] : (in(B, tptp_fun_D_16(tptp_fun_B_1(A!15))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ![B: $i] : ((~ordinal(B)) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | in(B, tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(729,plain,
% 63.08/40.79 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ![B: $i] : (in(B, tptp_fun_D_16(tptp_fun_B_1(A!15))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ![B: $i] : ((~ordinal(B)) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | in(B, tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[728])).
% 63.08/40.79 tff(730,plain,
% 63.08/40.79 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ![B: $i] : (in(B, tptp_fun_D_16(tptp_fun_B_1(A!15))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ![B: $i] : ((~ordinal(B)) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | in(B, tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.79 inference(transitivity,[status(thm)],[729, 727])).
% 63.08/40.79 tff(731,plain,
% 63.08/40.79 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ![B: $i] : (in(B, tptp_fun_D_16(tptp_fun_B_1(A!15))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | (~ordinal(B))))),
% 63.08/40.79 inference(quant_inst,[status(thm)],[])).
% 63.08/40.79 tff(732,plain,
% 63.08/40.79 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ![B: $i] : ((~ordinal(B)) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | in(B, tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[731, 730])).
% 63.08/40.79 tff(733,plain,
% 63.08/40.79 (![B: $i] : ((~ordinal(B)) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | in(B, tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[732, 146, 335])).
% 63.08/40.79 tff(734,plain,
% 63.08/40.79 (((~![B: $i] : ((~ordinal(B)) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | in(B, tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> ((~![B: $i] : ((~ordinal(B)) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | in(B, tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(735,plain,
% 63.08/40.79 ((~![B: $i] : ((~ordinal(B)) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | in(B, tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(quant_inst,[status(thm)],[])).
% 63.08/40.79 tff(736,plain,
% 63.08/40.79 ((~![B: $i] : ((~ordinal(B)) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = B) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), B) | in(B, tptp_fun_D_16(tptp_fun_B_1(A!15))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) | (tptp_fun_D_16(tptp_fun_B_1(A!15)) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[735, 734])).
% 63.08/40.79 tff(737,plain,
% 63.08/40.79 ((tptp_fun_D_16(tptp_fun_B_1(A!15)) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_D_16(tptp_fun_B_1(A!15)), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[736, 733, 479])).
% 63.08/40.79 tff(738,plain,
% 63.08/40.79 (in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[737, 726, 710])).
% 63.08/40.79 tff(739,plain,
% 63.08/40.79 (((~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | ((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) <=> ((~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(740,plain,
% 63.08/40.79 ((~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | ((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.79 inference(quant_inst,[status(thm)],[])).
% 63.08/40.79 tff(741,plain,
% 63.08/40.79 ((~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[740, 739])).
% 63.08/40.79 tff(742,plain,
% 63.08/40.79 (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[741, 738, 692])).
% 63.08/40.79 tff(743,plain,
% 63.08/40.79 (~in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[742, 583])).
% 63.08/40.79 tff(744,plain,
% 63.08/40.79 (in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set) <=> in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[579])).
% 63.08/40.79 tff(745,plain,
% 63.08/40.79 ((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set)) <=> (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14)))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[744])).
% 63.08/40.79 tff(746,assumption,(in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set)), introduced(assumption)).
% 63.08/40.79 tff(747,plain,
% 63.08/40.79 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set)))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(748,plain,
% 63.08/40.79 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set)))),
% 63.08/40.79 inference(quant_inst,[status(thm)],[])).
% 63.08/40.79 tff(749,plain,
% 63.08/40.79 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[748, 747])).
% 63.08/40.79 tff(750,plain,
% 63.08/40.79 ($false),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[749, 26, 125, 746])).
% 63.08/40.79 tff(751,plain,(~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), empty_set)), inference(lemma,lemma(discharge,[]))).
% 63.08/40.79 tff(752,plain,
% 63.08/40.79 (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[751, 745])).
% 63.08/40.79 tff(753,plain,
% 63.08/40.79 (((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~![D: $i] : ((~in(D, tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(D, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.79 inference(tautology,[status(thm)],[])).
% 63.08/40.79 tff(754,plain,
% 63.08/40.79 (in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[753, 690])).
% 63.08/40.79 tff(755,plain,
% 63.08/40.79 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(756,plain,
% 63.08/40.79 ((ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(757,plain,
% 63.08/40.79 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[756])).
% 63.08/40.79 tff(758,plain,
% 63.08/40.79 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.79 inference(transitivity,[status(thm)],[757, 755])).
% 63.08/40.79 tff(759,plain,
% 63.08/40.79 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.79 inference(quant_inst,[status(thm)],[])).
% 63.08/40.79 tff(760,plain,
% 63.08/40.79 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_D_16(tptp_fun_B_1(A!15)))) | ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[759, 758])).
% 63.08/40.79 tff(761,plain,
% 63.08/40.79 (ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[760, 318, 335, 754])).
% 63.08/40.79 tff(762,plain,
% 63.08/40.79 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(B!14))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_17(B!14))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B)))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(763,plain,
% 63.08/40.79 (((~ordinal(tptp_fun_C_17(B!14))) | ![B: $i] : (in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_C_17(B!14))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B)))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(764,plain,
% 63.08/40.79 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(B!14))) | ![B: $i] : (in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(B!14))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B))))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[763])).
% 63.08/40.79 tff(765,plain,
% 63.08/40.79 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(B!14))) | ![B: $i] : (in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_17(B!14))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B)))),
% 63.08/40.79 inference(transitivity,[status(thm)],[764, 762])).
% 63.08/40.79 tff(766,plain,
% 63.08/40.79 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(B!14))) | ![B: $i] : (in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B) | (~ordinal(B))))),
% 63.08/40.79 inference(quant_inst,[status(thm)],[])).
% 63.08/40.79 tff(767,plain,
% 63.08/40.79 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_17(B!14))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[766, 765])).
% 63.08/40.79 tff(768,plain,
% 63.08/40.79 (![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[767, 146, 393])).
% 63.08/40.79 tff(769,plain,
% 63.08/40.79 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B))) | ((tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B))) | (tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14)))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(770,plain,
% 63.08/40.79 (((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> ((tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14)))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(771,plain,
% 63.08/40.79 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B))) | ((tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14))))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[770])).
% 63.08/40.79 tff(772,plain,
% 63.08/40.79 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B))) | (tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14)))),
% 63.08/40.79 inference(transitivity,[status(thm)],[771, 769])).
% 63.08/40.79 tff(773,plain,
% 63.08/40.79 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.79 inference(quant_inst,[status(thm)],[])).
% 63.08/40.79 tff(774,plain,
% 63.08/40.79 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(B!14)) | in(tptp_fun_C_17(B!14), B) | (tptp_fun_C_17(B!14) = B))) | (tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[773, 772])).
% 63.08/40.79 tff(775,plain,
% 63.08/40.79 ((tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(B!14))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[774, 768, 761])).
% 63.08/40.79 tff(776,plain,
% 63.08/40.79 ((tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[775, 752])).
% 63.08/40.79 tff(777,plain,
% 63.08/40.79 (tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[776, 743])).
% 63.08/40.79 tff(778,plain,
% 63.08/40.79 (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(B!14)),
% 63.08/40.79 inference(symmetry,[status(thm)],[777])).
% 63.08/40.79 tff(779,plain,
% 63.08/40.79 (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(transitivity,[status(thm)],[778, 580, 529])).
% 63.08/40.79 tff(780,plain,
% 63.08/40.79 ((tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) <=> (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_C_17(A!15))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[779])).
% 63.08/40.79 tff(781,plain,
% 63.08/40.79 ((tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_C_17(A!15)) <=> (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15))),
% 63.08/40.79 inference(symmetry,[status(thm)],[780])).
% 63.08/40.79 tff(782,plain,
% 63.08/40.79 ((~(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_C_17(A!15))) <=> (~(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[781])).
% 63.08/40.79 tff(783,assumption,(~(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_C_17(A!15))), introduced(assumption)).
% 63.08/40.79 tff(784,plain,
% 63.08/40.79 (~(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[783, 782])).
% 63.08/40.79 tff(785,assumption,(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)), introduced(assumption)).
% 63.08/40.79 tff(786,plain,
% 63.08/40.79 ($false),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[785, 784])).
% 63.08/40.79 tff(787,plain,((~(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_C_17(A!15)) | (~(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = empty_set))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.79 tff(788,plain,
% 63.08/40.79 ((~(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_C_17(A!15))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[787, 527])).
% 63.08/40.79 tff(789,plain,
% 63.08/40.79 (~(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[788, 515])).
% 63.08/40.79 tff(790,plain,
% 63.08/40.79 (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))) = tptp_fun_C_17(B!14)),
% 63.08/40.79 inference(transitivity,[status(thm)],[527, 579])).
% 63.08/40.79 tff(791,plain,
% 63.08/40.79 (in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[790])).
% 63.08/40.79 tff(792,plain,
% 63.08/40.79 ((~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_D_16(tptp_fun_B_1(A!15)))), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) <=> (~in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[791])).
% 63.08/40.79 tff(793,plain,
% 63.08/40.79 (~in(tptp_fun_C_17(B!14), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[742, 792])).
% 63.08/40.79 tff(794,plain,
% 63.08/40.79 (tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[776, 793])).
% 63.08/40.79 tff(795,assumption,(tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))), introduced(assumption)).
% 63.08/40.79 tff(796,plain,
% 63.08/40.79 (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(B!14)),
% 63.08/40.79 inference(symmetry,[status(thm)],[795])).
% 63.08/40.79 tff(797,plain,
% 63.08/40.79 (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = empty_set),
% 63.08/40.79 inference(transitivity,[status(thm)],[796, 580])).
% 63.08/40.79 tff(798,plain,
% 63.08/40.79 (in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) <=> in(tptp_fun_C_17(A!15), empty_set)),
% 63.08/40.79 inference(monotonicity,[status(thm)],[797])).
% 63.08/40.79 tff(799,plain,
% 63.08/40.79 (in(tptp_fun_C_17(A!15), empty_set) <=> in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(symmetry,[status(thm)],[798])).
% 63.08/40.79 tff(800,plain,
% 63.08/40.79 ((~in(tptp_fun_C_17(A!15), empty_set)) <=> (~in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[799])).
% 63.08/40.79 tff(801,assumption,(in(tptp_fun_C_17(A!15), empty_set)), introduced(assumption)).
% 63.08/40.79 tff(802,plain,
% 63.08/40.79 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_17(A!15), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_17(A!15), empty_set)))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(803,plain,
% 63.08/40.79 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_C_17(A!15), empty_set)))),
% 63.08/40.79 inference(quant_inst,[status(thm)],[])).
% 63.08/40.79 tff(804,plain,
% 63.08/40.79 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_C_17(A!15), empty_set))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[803, 802])).
% 63.08/40.79 tff(805,plain,
% 63.08/40.79 ($false),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[804, 26, 125, 801])).
% 63.08/40.79 tff(806,plain,(~in(tptp_fun_C_17(A!15), empty_set)), inference(lemma,lemma(discharge,[]))).
% 63.08/40.79 tff(807,plain,
% 63.08/40.79 (~in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[806, 800])).
% 63.08/40.79 tff(808,assumption,(~(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15))), introduced(assumption)).
% 63.08/40.79 tff(809,plain,
% 63.08/40.79 (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = A!7),
% 63.08/40.79 inference(transitivity,[status(thm)],[796, 580, 34])).
% 63.08/40.79 tff(810,plain,
% 63.08/40.79 (in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15)) <=> in(A!7, tptp_fun_C_17(A!15))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[809])).
% 63.08/40.79 tff(811,plain,
% 63.08/40.79 (in(A!7, tptp_fun_C_17(A!15)) <=> in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15))),
% 63.08/40.79 inference(symmetry,[status(thm)],[810])).
% 63.08/40.79 tff(812,plain,
% 63.08/40.79 ((~in(A!7, tptp_fun_C_17(A!15))) <=> (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15)))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[811])).
% 63.08/40.79 tff(813,assumption,(~in(A!7, tptp_fun_C_17(A!15))), introduced(assumption)).
% 63.08/40.79 tff(814,plain,
% 63.08/40.79 (~in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[813, 812])).
% 63.08/40.79 tff(815,assumption,(~ordinal(tptp_fun_C_17(A!15))), introduced(assumption)).
% 63.08/40.79 tff(816,assumption,(in(tptp_fun_C_17(A!15), B!14)), introduced(assumption)).
% 63.08/40.79 tff(817,plain,
% 63.08/40.79 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(B!14)) | ordinal(tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), B!14)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!14)) | ordinal(tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), B!14)))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(818,plain,
% 63.08/40.79 ((ordinal(tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), B!14)) | (~ordinal(B!14))) <=> ((~ordinal(B!14)) | ordinal(tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), B!14)))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(819,plain,
% 63.08/40.79 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), B!14)) | (~ordinal(B!14)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(B!14)) | ordinal(tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), B!14))))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[818])).
% 63.08/40.79 tff(820,plain,
% 63.08/40.79 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), B!14)) | (~ordinal(B!14)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!14)) | ordinal(tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), B!14)))),
% 63.08/40.79 inference(transitivity,[status(thm)],[819, 817])).
% 63.08/40.79 tff(821,plain,
% 63.08/40.79 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), B!14)) | (~ordinal(B!14)))),
% 63.08/40.79 inference(quant_inst,[status(thm)],[])).
% 63.08/40.79 tff(822,plain,
% 63.08/40.79 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(B!14)) | ordinal(tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), B!14))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[821, 820])).
% 63.08/40.79 tff(823,plain,
% 63.08/40.79 ($false),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[822, 318, 308, 815, 816])).
% 63.08/40.79 tff(824,plain,((~in(tptp_fun_C_17(A!15), B!14)) | ordinal(tptp_fun_C_17(A!15))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.79 tff(825,plain,
% 63.08/40.79 (~in(tptp_fun_C_17(A!15), B!14)),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[824, 815])).
% 63.08/40.79 tff(826,plain,
% 63.08/40.79 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(A!15, powerset(B!14))) | (~in(tptp_fun_C_17(A!15), A!15)) | element(tptp_fun_C_17(A!15), B!14))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(A!15, powerset(B!14))) | (~in(tptp_fun_C_17(A!15), A!15)) | element(tptp_fun_C_17(A!15), B!14))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(827,plain,
% 63.08/40.79 ((element(tptp_fun_C_17(A!15), B!14) | (~in(tptp_fun_C_17(A!15), A!15)) | (~element(A!15, powerset(B!14)))) <=> ((~element(A!15, powerset(B!14))) | (~in(tptp_fun_C_17(A!15), A!15)) | element(tptp_fun_C_17(A!15), B!14))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(828,plain,
% 63.08/40.79 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_17(A!15), B!14) | (~in(tptp_fun_C_17(A!15), A!15)) | (~element(A!15, powerset(B!14))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | ((~element(A!15, powerset(B!14))) | (~in(tptp_fun_C_17(A!15), A!15)) | element(tptp_fun_C_17(A!15), B!14)))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[827])).
% 63.08/40.79 tff(829,plain,
% 63.08/40.79 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_17(A!15), B!14) | (~in(tptp_fun_C_17(A!15), A!15)) | (~element(A!15, powerset(B!14))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(A!15, powerset(B!14))) | (~in(tptp_fun_C_17(A!15), A!15)) | element(tptp_fun_C_17(A!15), B!14))),
% 63.08/40.79 inference(transitivity,[status(thm)],[828, 826])).
% 63.08/40.79 tff(830,plain,
% 63.08/40.79 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_17(A!15), B!14) | (~in(tptp_fun_C_17(A!15), A!15)) | (~element(A!15, powerset(B!14))))),
% 63.08/40.79 inference(quant_inst,[status(thm)],[])).
% 63.08/40.79 tff(831,plain,
% 63.08/40.79 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (~element(A!15, powerset(B!14))) | (~in(tptp_fun_C_17(A!15), A!15)) | element(tptp_fun_C_17(A!15), B!14)),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[830, 829])).
% 63.08/40.79 tff(832,plain,
% 63.08/40.79 (element(tptp_fun_C_17(A!15), B!14)),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[831, 273, 260, 512])).
% 63.08/40.79 tff(833,plain,
% 63.08/40.79 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | (~element(tptp_fun_C_17(A!15), B!14)) | in(tptp_fun_C_17(A!15), B!14))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(B!14) | (~element(tptp_fun_C_17(A!15), B!14)) | in(tptp_fun_C_17(A!15), B!14))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(834,plain,
% 63.08/40.79 ((empty(B!14) | in(tptp_fun_C_17(A!15), B!14) | (~element(tptp_fun_C_17(A!15), B!14))) <=> (empty(B!14) | (~element(tptp_fun_C_17(A!15), B!14)) | in(tptp_fun_C_17(A!15), B!14))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(835,plain,
% 63.08/40.79 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | in(tptp_fun_C_17(A!15), B!14) | (~element(tptp_fun_C_17(A!15), B!14)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | (~element(tptp_fun_C_17(A!15), B!14)) | in(tptp_fun_C_17(A!15), B!14)))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[834])).
% 63.08/40.79 tff(836,plain,
% 63.08/40.79 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | in(tptp_fun_C_17(A!15), B!14) | (~element(tptp_fun_C_17(A!15), B!14)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(B!14) | (~element(tptp_fun_C_17(A!15), B!14)) | in(tptp_fun_C_17(A!15), B!14))),
% 63.08/40.79 inference(transitivity,[status(thm)],[835, 833])).
% 63.08/40.79 tff(837,plain,
% 63.08/40.79 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(B!14) | in(tptp_fun_C_17(A!15), B!14) | (~element(tptp_fun_C_17(A!15), B!14)))),
% 63.08/40.79 inference(quant_inst,[status(thm)],[])).
% 63.08/40.79 tff(838,plain,
% 63.08/40.79 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(B!14) | (~element(tptp_fun_C_17(A!15), B!14)) | in(tptp_fun_C_17(A!15), B!14)),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[837, 836])).
% 63.08/40.79 tff(839,plain,
% 63.08/40.79 ($false),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[838, 242, 300, 832, 825])).
% 63.08/40.79 tff(840,plain,(ordinal(tptp_fun_C_17(A!15))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.79 tff(841,plain,
% 63.08/40.79 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B)))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(842,plain,
% 63.08/40.79 (((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : (in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B)))),
% 63.08/40.79 inference(rewrite,[status(thm)],[])).
% 63.08/40.79 tff(843,plain,
% 63.08/40.79 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : (in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B))))),
% 63.08/40.79 inference(monotonicity,[status(thm)],[842])).
% 63.08/40.79 tff(844,plain,
% 63.08/40.79 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : (in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B)))),
% 63.08/40.79 inference(transitivity,[status(thm)],[843, 841])).
% 63.08/40.79 tff(845,plain,
% 63.08/40.79 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : (in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | (~ordinal(B))))),
% 63.08/40.79 inference(quant_inst,[status(thm)],[])).
% 63.08/40.79 tff(846,plain,
% 63.08/40.79 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B))),
% 63.08/40.79 inference(modus_ponens,[status(thm)],[845, 844])).
% 63.08/40.79 tff(847,plain,
% 63.08/40.79 (![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B))),
% 63.08/40.79 inference(unit_resolution,[status(thm)],[846, 146, 761])).
% 63.08/40.79 tff(848,plain,
% 63.08/40.79 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B))) | ((~ordinal(tptp_fun_C_17(A!15))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B))) | (~ordinal(tptp_fun_C_17(A!15))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(849,plain,
% 63.08/40.80 (((~ordinal(tptp_fun_C_17(A!15))) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15))) <=> ((~ordinal(tptp_fun_C_17(A!15))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(850,plain,
% 63.08/40.80 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B))) | ((~ordinal(tptp_fun_C_17(A!15))) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B))) | ((~ordinal(tptp_fun_C_17(A!15))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))))),
% 63.08/40.80 inference(monotonicity,[status(thm)],[849])).
% 63.08/40.80 tff(851,plain,
% 63.08/40.80 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B))) | ((~ordinal(tptp_fun_C_17(A!15))) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B))) | (~ordinal(tptp_fun_C_17(A!15))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))))),
% 63.08/40.80 inference(transitivity,[status(thm)],[850, 848])).
% 63.08/40.80 tff(852,plain,
% 63.08/40.80 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B))) | ((~ordinal(tptp_fun_C_17(A!15))) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(quant_inst,[status(thm)],[])).
% 63.08/40.80 tff(853,plain,
% 63.08/40.80 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15)))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = B) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), B))) | (~ordinal(tptp_fun_C_17(A!15))) | (tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[852, 851])).
% 63.08/40.80 tff(854,plain,
% 63.08/40.80 ((tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))), tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[853, 847, 840])).
% 63.08/40.80 tff(855,plain,
% 63.08/40.80 ($false),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[854, 814, 808, 807])).
% 63.08/40.80 tff(856,plain,((tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | (~(tptp_fun_C_17(B!14) = tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))))) | in(A!7, tptp_fun_C_17(A!15))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.80 tff(857,plain,
% 63.08/40.80 ((tptp_fun_C_17(tptp_fun_D_16(tptp_fun_B_1(A!15))) = tptp_fun_C_17(A!15)) | in(A!7, tptp_fun_C_17(A!15))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[856, 794])).
% 63.08/40.80 tff(858,plain,
% 63.08/40.80 (in(A!7, tptp_fun_C_17(A!15))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[857, 789])).
% 63.08/40.80 tff(859,plain,
% 63.08/40.80 (in(empty_set, tptp_fun_C_17(A!15))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[858, 36])).
% 63.08/40.80 tff(860,assumption,(~in(empty_set, tptp_fun_C_17(A!15))), introduced(assumption)).
% 63.08/40.80 tff(861,plain,
% 63.08/40.80 ($false),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[860, 859])).
% 63.08/40.80 tff(862,plain,(in(empty_set, tptp_fun_C_17(A!15))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.80 tff(863,assumption,(in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))), introduced(assumption)).
% 63.08/40.80 tff(864,assumption,(ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15))), introduced(assumption)).
% 63.08/40.80 tff(865,plain,
% 63.08/40.80 (((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_C_17(A!15))) | (~in(tptp_fun_C_17(A!15), A!15)) | (~(ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15)))))) <=> ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | (~ordinal(tptp_fun_C_17(A!15))) | (~in(tptp_fun_C_17(A!15), A!15)) | (~(ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15)))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(866,plain,
% 63.08/40.80 ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | ((~ordinal(tptp_fun_C_17(A!15))) | (~in(tptp_fun_C_17(A!15), A!15)) | (~(ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15)))))),
% 63.08/40.80 inference(quant_inst,[status(thm)],[])).
% 63.08/40.80 tff(867,plain,
% 63.08/40.80 ((~![C: $i] : ((~ordinal(C)) | (~in(C, A!15)) | (~(ordinal_subset(C, tptp_fun_D_16(C)) | (~ordinal(tptp_fun_D_16(C))) | (~in(tptp_fun_D_16(C), A!15)))))) | (~ordinal(tptp_fun_C_17(A!15))) | (~in(tptp_fun_C_17(A!15), A!15)) | (~(ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15))))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[866, 865])).
% 63.08/40.80 tff(868,plain,
% 63.08/40.80 ($false),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[867, 207, 512, 840, 864])).
% 63.08/40.80 tff(869,plain,(~(ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15)))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.80 tff(870,plain,
% 63.08/40.80 ((ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15))) | in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15)),
% 63.08/40.80 inference(tautology,[status(thm)],[])).
% 63.08/40.80 tff(871,plain,
% 63.08/40.80 (in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15)),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[870, 869])).
% 63.08/40.80 tff(872,plain,
% 63.08/40.80 (~((~in(tptp_fun_C_17(A!15), A!15)) | (~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[509, 380, 247])).
% 63.08/40.80 tff(873,plain,
% 63.08/40.80 (((~in(tptp_fun_C_17(A!15), A!15)) | (~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15)))))) | ![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(tautology,[status(thm)],[])).
% 63.08/40.80 tff(874,plain,
% 63.08/40.80 (![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[873, 872])).
% 63.08/40.80 tff(875,plain,
% 63.08/40.80 (((~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))) | ((~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15)) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))))) <=> ((~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15)) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(876,plain,
% 63.08/40.80 ((~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))) | ((~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15)) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(quant_inst,[status(thm)],[])).
% 63.08/40.80 tff(877,plain,
% 63.08/40.80 ((~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15)) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[876, 875])).
% 63.08/40.80 tff(878,plain,
% 63.08/40.80 ($false),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[877, 874, 871, 863])).
% 63.08/40.80 tff(879,plain,(~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.80 tff(880,assumption,(~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))), introduced(assumption)).
% 63.08/40.80 tff(881,plain,
% 63.08/40.80 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(A!15))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_17(A!15))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B)))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(882,plain,
% 63.08/40.80 (((~ordinal(tptp_fun_C_17(A!15))) | ![B: $i] : (in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_C_17(A!15))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B)))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(883,plain,
% 63.08/40.80 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(A!15))) | ![B: $i] : (in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(A!15))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B))))),
% 63.08/40.80 inference(monotonicity,[status(thm)],[882])).
% 63.08/40.80 tff(884,plain,
% 63.08/40.80 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(A!15))) | ![B: $i] : (in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_17(A!15))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B)))),
% 63.08/40.80 inference(transitivity,[status(thm)],[883, 881])).
% 63.08/40.80 tff(885,plain,
% 63.08/40.80 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_17(A!15))) | ![B: $i] : (in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B) | (~ordinal(B))))),
% 63.08/40.80 inference(quant_inst,[status(thm)],[])).
% 63.08/40.80 tff(886,plain,
% 63.08/40.80 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_17(A!15))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[885, 884])).
% 63.08/40.80 tff(887,plain,
% 63.08/40.80 (![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[886, 146, 840])).
% 63.08/40.80 tff(888,assumption,(tptp_fun_C_17(A!15) = tptp_fun_D_16(tptp_fun_C_17(A!15))), introduced(assumption)).
% 63.08/40.80 tff(889,plain,
% 63.08/40.80 (ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) <=> ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(monotonicity,[status(thm)],[888])).
% 63.08/40.80 tff(890,plain,
% 63.08/40.80 (ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15))) <=> ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(symmetry,[status(thm)],[889])).
% 63.08/40.80 tff(891,plain,
% 63.08/40.80 ((ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15))) | ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(tautology,[status(thm)],[])).
% 63.08/40.80 tff(892,plain,
% 63.08/40.80 (ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[891, 869])).
% 63.08/40.80 tff(893,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(894,plain,
% 63.08/40.80 ((ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15))))) <=> ((~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(895,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15)))))),
% 63.08/40.80 inference(monotonicity,[status(thm)],[894])).
% 63.08/40.80 tff(896,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(transitivity,[status(thm)],[895, 893])).
% 63.08/40.80 tff(897,plain,
% 63.08/40.80 ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))))),
% 63.08/40.80 inference(quant_inst,[status(thm)],[])).
% 63.08/40.80 tff(898,plain,
% 63.08/40.80 ((~![A: $i, B: $i] : (ordinal_subset(A, A) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(empty_set)) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[897, 896])).
% 63.08/40.80 tff(899,plain,
% 63.08/40.80 (ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_D_16(tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[898, 98, 177, 892])).
% 63.08/40.80 tff(900,plain,
% 63.08/40.80 (ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[899, 890])).
% 63.08/40.80 tff(901,plain,
% 63.08/40.80 ((ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~in(tptp_fun_D_16(tptp_fun_C_17(A!15)), A!15))) | (~ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(tautology,[status(thm)],[])).
% 63.08/40.80 tff(902,plain,
% 63.08/40.80 (~ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[901, 869])).
% 63.08/40.80 tff(903,plain,
% 63.08/40.80 ($false),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[902, 900])).
% 63.08/40.80 tff(904,plain,(~(tptp_fun_C_17(A!15) = tptp_fun_D_16(tptp_fun_C_17(A!15)))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.80 tff(905,plain,
% 63.08/40.80 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | (tptp_fun_C_17(A!15) = tptp_fun_D_16(tptp_fun_C_17(A!15))) | in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | (tptp_fun_C_17(A!15) = tptp_fun_D_16(tptp_fun_C_17(A!15))) | in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(906,plain,
% 63.08/40.80 (((~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (tptp_fun_C_17(A!15) = tptp_fun_D_16(tptp_fun_C_17(A!15)))) <=> ((~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | (tptp_fun_C_17(A!15) = tptp_fun_D_16(tptp_fun_C_17(A!15))) | in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(907,plain,
% 63.08/40.80 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (tptp_fun_C_17(A!15) = tptp_fun_D_16(tptp_fun_C_17(A!15))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | (tptp_fun_C_17(A!15) = tptp_fun_D_16(tptp_fun_C_17(A!15))) | in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15)))))),
% 63.08/40.80 inference(monotonicity,[status(thm)],[906])).
% 63.08/40.80 tff(908,plain,
% 63.08/40.80 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (tptp_fun_C_17(A!15) = tptp_fun_D_16(tptp_fun_C_17(A!15))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | (tptp_fun_C_17(A!15) = tptp_fun_D_16(tptp_fun_C_17(A!15))) | in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(transitivity,[status(thm)],[907, 905])).
% 63.08/40.80 tff(909,plain,
% 63.08/40.80 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B))) | ((~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (tptp_fun_C_17(A!15) = tptp_fun_D_16(tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(quant_inst,[status(thm)],[])).
% 63.08/40.80 tff(910,plain,
% 63.08/40.80 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), B) | (tptp_fun_C_17(A!15) = B))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | (tptp_fun_C_17(A!15) = tptp_fun_D_16(tptp_fun_C_17(A!15))) | in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[909, 908])).
% 63.08/40.80 tff(911,plain,
% 63.08/40.80 (in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[910, 892, 904, 887, 880])).
% 63.08/40.80 tff(912,assumption,(~empty(tptp_fun_C_17(A!15))), introduced(assumption)).
% 63.08/40.80 tff(913,plain,
% 63.08/40.80 (((~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))) | ((~in(tptp_fun_C_17(A!15), A!15)) | (~in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15))))) <=> ((~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))) | (~in(tptp_fun_C_17(A!15), A!15)) | (~in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(914,plain,
% 63.08/40.80 ((~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))) | ((~in(tptp_fun_C_17(A!15), A!15)) | (~in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(quant_inst,[status(thm)],[])).
% 63.08/40.80 tff(915,plain,
% 63.08/40.80 ((~![D: $i] : ((~in(D, A!15)) | (~in(D, tptp_fun_C_17(A!15))))) | (~in(tptp_fun_C_17(A!15), A!15)) | (~in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[914, 913])).
% 63.08/40.80 tff(916,plain,
% 63.08/40.80 (~in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[915, 512, 874])).
% 63.08/40.80 tff(917,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | empty(tptp_fun_C_17(A!15)) | (~element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | empty(tptp_fun_C_17(A!15)) | (~element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(918,plain,
% 63.08/40.80 ((empty(tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | (~element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)))) <=> (in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | empty(tptp_fun_C_17(A!15)) | (~element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(919,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | (~element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | empty(tptp_fun_C_17(A!15)) | (~element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)))))),
% 63.08/40.80 inference(monotonicity,[status(thm)],[918])).
% 63.08/40.80 tff(920,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | (~element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | empty(tptp_fun_C_17(A!15)) | (~element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(transitivity,[status(thm)],[919, 917])).
% 63.08/40.80 tff(921,plain,
% 63.08/40.80 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(tptp_fun_C_17(A!15)) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | (~element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(quant_inst,[status(thm)],[])).
% 63.08/40.80 tff(922,plain,
% 63.08/40.80 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | in(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | empty(tptp_fun_C_17(A!15)) | (~element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[921, 920])).
% 63.08/40.80 tff(923,plain,
% 63.08/40.80 (~element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[922, 242, 916, 912])).
% 63.08/40.80 tff(924,assumption,(~ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))), introduced(assumption)).
% 63.08/40.80 tff(925,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_C_17(A!15))) | ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_17(A!15))) | ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(926,plain,
% 63.08/40.80 ((ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | (~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15))))) <=> ((~ordinal(tptp_fun_C_17(A!15))) | ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(927,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | (~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_C_17(A!15))) | ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(monotonicity,[status(thm)],[926])).
% 63.08/40.80 tff(928,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | (~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))))) <=> ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_17(A!15))) | ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(transitivity,[status(thm)],[927, 925])).
% 63.08/40.80 tff(929,plain,
% 63.08/40.80 ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | (~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))))),
% 63.08/40.80 inference(quant_inst,[status(thm)],[])).
% 63.08/40.80 tff(930,plain,
% 63.08/40.80 ((~![A: $i, B: $i] : (ordinal_subset(B, A) | ordinal_subset(A, B) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_17(A!15))) | ordinal_subset(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[929, 928])).
% 63.08/40.80 tff(931,plain,
% 63.08/40.80 ($false),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[930, 605, 840, 902, 892, 924])).
% 63.08/40.80 tff(932,plain,(ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.80 tff(933,assumption,(~(ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))), introduced(assumption)).
% 63.08/40.80 tff(934,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(935,plain,
% 63.08/40.80 (((ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15))))) <=> ((~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(936,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))))),
% 63.08/40.80 inference(monotonicity,[status(thm)],[935])).
% 63.08/40.80 tff(937,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(transitivity,[status(thm)],[936, 934])).
% 63.08/40.80 tff(938,plain,
% 63.08/40.80 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))))),
% 63.08/40.80 inference(quant_inst,[status(thm)],[])).
% 63.08/40.80 tff(939,plain,
% 63.08/40.80 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(tptp_fun_C_17(A!15))) | (~ordinal(tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[938, 937])).
% 63.08/40.80 tff(940,plain,
% 63.08/40.80 ($false),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[939, 94, 840, 892, 933])).
% 63.08/40.80 tff(941,plain,(ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.80 tff(942,plain,
% 63.08/40.80 ((~(ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))) | (~ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))) | subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))),
% 63.08/40.80 inference(tautology,[status(thm)],[])).
% 63.08/40.80 tff(943,plain,
% 63.08/40.80 ((~ordinal_subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))) | subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[942, 941])).
% 63.08/40.80 tff(944,plain,
% 63.08/40.80 (subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[943, 932])).
% 63.08/40.80 tff(945,assumption,(~(element(tptp_fun_D_16(tptp_fun_C_17(A!15)), powerset(tptp_fun_C_17(A!15))) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))), introduced(assumption)).
% 63.08/40.80 tff(946,plain,
% 63.08/40.80 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(tptp_fun_D_16(tptp_fun_C_17(A!15)), powerset(tptp_fun_C_17(A!15))) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(quant_inst,[status(thm)],[])).
% 63.08/40.80 tff(947,plain,
% 63.08/40.80 ($false),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[946, 254, 945])).
% 63.08/40.80 tff(948,plain,(element(tptp_fun_D_16(tptp_fun_C_17(A!15)), powerset(tptp_fun_C_17(A!15))) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.80 tff(949,plain,
% 63.08/40.80 ((~(element(tptp_fun_D_16(tptp_fun_C_17(A!15)), powerset(tptp_fun_C_17(A!15))) <=> subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))) | element(tptp_fun_D_16(tptp_fun_C_17(A!15)), powerset(tptp_fun_C_17(A!15))) | (~subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(tautology,[status(thm)],[])).
% 63.08/40.80 tff(950,plain,
% 63.08/40.80 (element(tptp_fun_D_16(tptp_fun_C_17(A!15)), powerset(tptp_fun_C_17(A!15))) | (~subset(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[949, 948])).
% 63.08/40.80 tff(951,plain,
% 63.08/40.80 (element(tptp_fun_D_16(tptp_fun_C_17(A!15)), powerset(tptp_fun_C_17(A!15)))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[950, 944])).
% 63.08/40.80 tff(952,plain,
% 63.08/40.80 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_C_17(A!15)), powerset(tptp_fun_C_17(A!15)))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_C_17(A!15)), powerset(tptp_fun_C_17(A!15)))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(953,plain,
% 63.08/40.80 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_C_17(A!15)), powerset(tptp_fun_C_17(A!15)))))),
% 63.08/40.80 inference(quant_inst,[status(thm)],[])).
% 63.08/40.80 tff(954,plain,
% 63.08/40.80 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_C_17(A!15), tptp_fun_C_17(A!15)) | (~in(tptp_fun_C_17(A!15), tptp_fun_D_16(tptp_fun_C_17(A!15)))) | (~element(tptp_fun_D_16(tptp_fun_C_17(A!15)), powerset(tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(modus_ponens,[status(thm)],[953, 952])).
% 63.08/40.80 tff(955,plain,
% 63.08/40.80 ($false),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[954, 273, 951, 923, 911])).
% 63.08/40.80 tff(956,plain,(in(tptp_fun_D_16(tptp_fun_C_17(A!15)), tptp_fun_C_17(A!15)) | empty(tptp_fun_C_17(A!15))), inference(lemma,lemma(discharge,[]))).
% 63.08/40.80 tff(957,plain,
% 63.08/40.80 (empty(tptp_fun_C_17(A!15))),
% 63.08/40.80 inference(unit_resolution,[status(thm)],[956, 879])).
% 63.08/40.80 tff(958,plain,
% 63.08/40.80 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(tptp_fun_C_17(A!15))) | (~in(empty_set, tptp_fun_C_17(A!15))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(tptp_fun_C_17(A!15))) | (~in(empty_set, tptp_fun_C_17(A!15))))),
% 63.08/40.80 inference(rewrite,[status(thm)],[])).
% 63.08/40.80 tff(959,plain,
% 63.08/40.80 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(tptp_fun_C_17(A!15))) | (~in(empty_set, tptp_fun_C_17(A!15))))),
% 63.08/40.81 inference(quant_inst,[status(thm)],[])).
% 63.08/40.81 tff(960,plain,
% 63.08/40.81 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(tptp_fun_C_17(A!15))) | (~in(empty_set, tptp_fun_C_17(A!15)))),
% 63.08/40.81 inference(modus_ponens,[status(thm)],[959, 958])).
% 63.08/40.81 tff(961,plain,
% 63.08/40.81 ($false),
% 63.08/40.81 inference(unit_resolution,[status(thm)],[960, 125, 957, 862])).
% 63.08/40.81 % SZS output end Proof
%------------------------------------------------------------------------------