%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU238+3 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:21 AM UTC 2025
% Result : Theorem 0.20s 0.52s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU238+3 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:28:11 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.52 % SZS status Theorem
% 0.20/0.52 % SZS output start Proof
% 0.20/0.52 tff(in_type, type, (
% 0.20/0.52 in: ( $i * $i ) > $o)).
% 0.20/0.52 tff(tptp_fun_A_15_type, type, (
% 0.20/0.52 tptp_fun_A_15: $i)).
% 0.20/0.52 tff(succ_type, type, (
% 0.20/0.52 succ: $i > $i)).
% 0.20/0.52 tff(tptp_fun_B_16_type, type, (
% 0.20/0.52 tptp_fun_B_16: $i)).
% 0.20/0.52 tff(ordinal_type, type, (
% 0.20/0.52 ordinal: $i > $o)).
% 0.20/0.52 tff(being_limit_ordinal_type, type, (
% 0.20/0.52 being_limit_ordinal: $i > $o)).
% 0.20/0.52 tff(proper_subset_type, type, (
% 0.20/0.52 proper_subset: ( $i * $i ) > $o)).
% 0.20/0.52 tff(set_union2_type, type, (
% 0.20/0.52 set_union2: ( $i * $i ) > $i)).
% 0.20/0.52 tff(singleton_type, type, (
% 0.20/0.52 singleton: $i > $i)).
% 0.20/0.52 tff(tptp_fun_B_14_type, type, (
% 0.20/0.52 tptp_fun_B_14: $i > $i)).
% 0.20/0.52 tff(subset_type, type, (
% 0.20/0.52 subset: ( $i * $i ) > $o)).
% 0.20/0.52 tff(ordinal_subset_type, type, (
% 0.20/0.52 ordinal_subset: ( $i * $i ) > $o)).
% 0.20/0.52 tff(epsilon_connected_type, type, (
% 0.20/0.52 epsilon_connected: $i > $o)).
% 0.20/0.52 tff(epsilon_transitive_type, type, (
% 0.20/0.52 epsilon_transitive: $i > $o)).
% 0.20/0.52 tff(empty_type, type, (
% 0.20/0.52 empty: $i > $o)).
% 0.20/0.52 tff(1,plain,
% 0.20/0.52 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(2,plain,
% 0.20/0.52 (![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.52 tff(3,plain,
% 0.20/0.52 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & (~(A = B))) <=> (~((~subset(A, B)) | (A = B)))), ((proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> (proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))))), rewrite((proper_subset(A, B) <=> (~((~subset(A, B)) | (A = B)))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))), ((proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))))), rewrite((~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))), ((proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(4,plain,
% 0.20/0.52 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.52 tff(5,plain,
% 0.20/0.52 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B)))) <=> ![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(6,axiom,(![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d8_xboole_0')).
% 0.20/0.52 tff(7,plain,
% 0.20/0.52 (![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.52 tff(8,plain,(
% 0.20/0.52 ![A: $i, B: $i] : (proper_subset(A, B) <=> (subset(A, B) & (~(A = B))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[7])).
% 0.20/0.52 tff(9,plain,
% 0.20/0.52 (![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.52 tff(10,plain,
% 0.20/0.52 (![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.52 tff(11,plain,
% 0.20/0.52 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (A = B)) <=> proper_subset(A, B)))) | (~(((~subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | (set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = A!15)) <=> proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(12,plain,
% 0.20/0.52 (~(((~subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | (set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = A!15)) <=> proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.52 tff(13,plain,
% 0.20/0.52 (^[A: $i] : refl((succ(A) = set_union2(A, singleton(A))) <=> (succ(A) = set_union2(A, singleton(A))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(14,plain,
% 0.20/0.52 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.52 tff(15,plain,
% 0.20/0.52 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(16,axiom,(![A: $i] : (succ(A) = set_union2(A, singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_ordinal1')).
% 0.20/0.52 tff(17,plain,
% 0.20/0.52 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.52 tff(18,plain,(
% 0.20/0.52 ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.20/0.52 inference(skolemize,[status(sab)],[17])).
% 0.20/0.52 tff(19,plain,
% 0.20/0.52 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.52 tff(20,plain,
% 0.20/0.52 ((~![A: $i] : (succ(A) = set_union2(A, singleton(A)))) | (succ(tptp_fun_B_14(A!15)) = set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(21,plain,
% 0.20/0.52 (succ(tptp_fun_B_14(A!15)) = set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.52 tff(22,plain,
% 0.20/0.52 (set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = succ(tptp_fun_B_14(A!15))),
% 0.20/0.52 inference(symmetry,[status(thm)],[21])).
% 0.20/0.52 tff(23,plain,
% 0.20/0.52 (ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15)))) <=> ordinal(succ(tptp_fun_B_14(A!15)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.52 tff(24,plain,
% 0.20/0.52 (ordinal(succ(tptp_fun_B_14(A!15))) <=> ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))),
% 0.20/0.52 inference(symmetry,[status(thm)],[23])).
% 0.20/0.52 tff(25,assumption,(~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))), introduced(assumption)).
% 0.20/0.52 tff(26,plain,
% 0.20/0.52 ((being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B)))))) | (~being_limit_ordinal(A!15))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(27,plain,
% 0.20/0.52 (~being_limit_ordinal(A!15)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.20/0.52 tff(28,plain,
% 0.20/0.52 ((ordinal(A!15) & (((~being_limit_ordinal(A!15)) & ![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))) | ((ordinal(B!16) & (A!15 = succ(B!16))) & being_limit_ordinal(A!15)))) <=> (ordinal(A!15) & (((~being_limit_ordinal(A!15)) & ![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))) | (ordinal(B!16) & (A!15 = succ(B!16)) & being_limit_ordinal(A!15))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(29,plain,
% 0.20/0.52 ((~![A: $i] : ((~ordinal(A)) | ((~((~being_limit_ordinal(A)) & ![B: $i] : ((~ordinal(B)) | (~(A = succ(B)))))) & (~(?[B: $i] : (ordinal(B) & (A = succ(B))) & being_limit_ordinal(A)))))) <=> (~![A: $i] : ((~ordinal(A)) | ((~((~being_limit_ordinal(A)) & ![B: $i] : ((~ordinal(B)) | (~(A = succ(B)))))) & (~(?[B: $i] : (ordinal(B) & (A = succ(B))) & being_limit_ordinal(A))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(30,plain,
% 0.20/0.52 ((~![A: $i] : (ordinal(A) => ((~((~being_limit_ordinal(A)) & ![B: $i] : (ordinal(B) => (~(A = succ(B)))))) & (~(?[B: $i] : (ordinal(B) & (A = succ(B))) & being_limit_ordinal(A)))))) <=> (~![A: $i] : ((~ordinal(A)) | ((~((~being_limit_ordinal(A)) & ![B: $i] : ((~ordinal(B)) | (~(A = succ(B)))))) & (~(?[B: $i] : (ordinal(B) & (A = succ(B))) & being_limit_ordinal(A))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(31,axiom,(~![A: $i] : (ordinal(A) => ((~((~being_limit_ordinal(A)) & ![B: $i] : (ordinal(B) => (~(A = succ(B)))))) & (~(?[B: $i] : (ordinal(B) & (A = succ(B))) & being_limit_ordinal(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t42_ordinal1')).
% 0.20/0.52 tff(32,plain,
% 0.20/0.52 (~![A: $i] : ((~ordinal(A)) | ((~((~being_limit_ordinal(A)) & ![B: $i] : ((~ordinal(B)) | (~(A = succ(B)))))) & (~(?[B: $i] : (ordinal(B) & (A = succ(B))) & being_limit_ordinal(A)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.52 tff(33,plain,
% 0.20/0.52 (~![A: $i] : ((~ordinal(A)) | ((~((~being_limit_ordinal(A)) & ![B: $i] : ((~ordinal(B)) | (~(A = succ(B)))))) & (~(?[B: $i] : (ordinal(B) & (A = succ(B))) & being_limit_ordinal(A)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.20/0.52 tff(34,plain,
% 0.20/0.52 (~![A: $i] : ((~ordinal(A)) | ((~((~being_limit_ordinal(A)) & ![B: $i] : ((~ordinal(B)) | (~(A = succ(B)))))) & (~(?[B: $i] : (ordinal(B) & (A = succ(B))) & being_limit_ordinal(A)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.52 tff(35,plain,
% 0.20/0.52 (~![A: $i] : ((~ordinal(A)) | ((~((~being_limit_ordinal(A)) & ![B: $i] : ((~ordinal(B)) | (~(A = succ(B)))))) & (~(?[B: $i] : (ordinal(B) & (A = succ(B))) & being_limit_ordinal(A)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.20/0.52 tff(36,plain,
% 0.20/0.52 (ordinal(A!15) & (((~being_limit_ordinal(A!15)) & ![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))) | (ordinal(B!16) & (A!15 = succ(B!16)) & being_limit_ordinal(A!15)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.20/0.52 tff(37,plain,
% 0.20/0.52 (ordinal(A!15)),
% 0.20/0.52 inference(and_elim,[status(thm)],[36])).
% 0.20/0.52 tff(38,plain,
% 0.20/0.52 (^[A: $i] : refl(((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A)))))))))) <=> ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A)))))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(39,plain,
% 0.20/0.52 (![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A)))))))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.52 tff(40,plain,
% 0.20/0.52 (^[A: $i] : rewrite(((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A)))))))))) <=> ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A)))))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(41,plain,
% 0.20/0.52 (![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A)))))))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.52 tff(42,plain,
% 0.20/0.52 (![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A)))))))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[41, 39])).
% 0.20/0.52 tff(43,plain,
% 0.20/0.52 (^[A: $i] : rewrite(((~ordinal(A)) | (((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B)))) & (being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A)))))))) <=> ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A)))))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(44,plain,
% 0.20/0.52 (![A: $i] : ((~ordinal(A)) | (((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B)))) & (being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A)))))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.52 tff(45,plain,
% 0.20/0.52 (![A: $i] : ((~ordinal(A)) | (being_limit_ordinal(A) <=> ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) <=> ![A: $i] : ((~ordinal(A)) | (being_limit_ordinal(A) <=> ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(46,plain,
% 0.20/0.52 (^[A: $i] : trans(monotonicity(rewrite((being_limit_ordinal(A) <=> ![B: $i] : (ordinal(B) => (in(B, A) => in(succ(B), A)))) <=> (being_limit_ordinal(A) <=> ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))), ((ordinal(A) => (being_limit_ordinal(A) <=> ![B: $i] : (ordinal(B) => (in(B, A) => in(succ(B), A))))) <=> (ordinal(A) => (being_limit_ordinal(A) <=> ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))))), rewrite((ordinal(A) => (being_limit_ordinal(A) <=> ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) <=> ((~ordinal(A)) | (being_limit_ordinal(A) <=> ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B)))))), ((ordinal(A) => (being_limit_ordinal(A) <=> ![B: $i] : (ordinal(B) => (in(B, A) => in(succ(B), A))))) <=> ((~ordinal(A)) | (being_limit_ordinal(A) <=> ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(47,plain,
% 0.20/0.52 (![A: $i] : (ordinal(A) => (being_limit_ordinal(A) <=> ![B: $i] : (ordinal(B) => (in(B, A) => in(succ(B), A))))) <=> ![A: $i] : ((~ordinal(A)) | (being_limit_ordinal(A) <=> ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.52 tff(48,axiom,(![A: $i] : (ordinal(A) => (being_limit_ordinal(A) <=> ![B: $i] : (ordinal(B) => (in(B, A) => in(succ(B), A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t41_ordinal1')).
% 0.20/0.52 tff(49,plain,
% 0.20/0.52 (![A: $i] : ((~ordinal(A)) | (being_limit_ordinal(A) <=> ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.52 tff(50,plain,
% 0.20/0.52 (![A: $i] : ((~ordinal(A)) | (being_limit_ordinal(A) <=> ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.20/0.52 tff(51,plain,(
% 0.20/0.52 ![A: $i] : ((~ordinal(A)) | (((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B)))) & (being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[50])).
% 0.20/0.52 tff(52,plain,
% 0.20/0.52 (![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.20/0.52 tff(53,plain,
% 0.20/0.52 (![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.20/0.52 tff(54,plain,
% 0.20/0.52 (((~![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))) | ((~ordinal(A!15)) | (~((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15)))) | (~(being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15)))))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))) | (~ordinal(A!15)) | (~((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15)))) | (~(being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15)))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(55,plain,
% 0.20/0.52 (((~ordinal(A!15)) | (~((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~in(B, A!15)) | in(succ(B), A!15) | (~ordinal(B))))) | (~(being_limit_ordinal(A!15) | (~((~in(tptp_fun_B_14(A!15), A!15)) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~ordinal(tptp_fun_B_14(A!15)))))))))) <=> ((~ordinal(A!15)) | (~((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15)))) | (~(being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15)))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(56,plain,
% 0.20/0.52 (((~![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))) | ((~ordinal(A!15)) | (~((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~in(B, A!15)) | in(succ(B), A!15) | (~ordinal(B))))) | (~(being_limit_ordinal(A!15) | (~((~in(tptp_fun_B_14(A!15), A!15)) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~ordinal(tptp_fun_B_14(A!15))))))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))) | ((~ordinal(A!15)) | (~((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15)))) | (~(being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15))))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[55])).
% 0.20/0.52 tff(57,plain,
% 0.20/0.52 (((~![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))) | ((~ordinal(A!15)) | (~((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~in(B, A!15)) | in(succ(B), A!15) | (~ordinal(B))))) | (~(being_limit_ordinal(A!15) | (~((~in(tptp_fun_B_14(A!15), A!15)) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~ordinal(tptp_fun_B_14(A!15))))))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))) | (~ordinal(A!15)) | (~((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15)))) | (~(being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15)))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[56, 54])).
% 0.20/0.52 tff(58,plain,
% 0.20/0.52 ((~![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))) | ((~ordinal(A!15)) | (~((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~in(B, A!15)) | in(succ(B), A!15) | (~ordinal(B))))) | (~(being_limit_ordinal(A!15) | (~((~in(tptp_fun_B_14(A!15), A!15)) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~ordinal(tptp_fun_B_14(A!15))))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(59,plain,
% 0.20/0.52 ((~![A: $i] : ((~ordinal(A)) | (~((~((~being_limit_ordinal(A)) | ![B: $i] : ((~in(B, A)) | in(succ(B), A) | (~ordinal(B))))) | (~(being_limit_ordinal(A) | (~((~in(tptp_fun_B_14(A), A)) | in(succ(tptp_fun_B_14(A)), A) | (~ordinal(tptp_fun_B_14(A))))))))))) | (~ordinal(A!15)) | (~((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15)))) | (~(being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.52 tff(60,plain,
% 0.20/0.52 (~((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15)))) | (~(being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15)))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[59, 53, 37])).
% 0.20/0.52 tff(61,plain,
% 0.20/0.52 (((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15)))) | (~(being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15))))))) | (being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15)))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(62,plain,
% 0.20/0.52 (being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.52 tff(63,plain,
% 0.20/0.52 ((~(being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15)))))) | being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(64,plain,
% 0.20/0.52 (being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.20/0.52 tff(65,plain,
% 0.20/0.52 (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[64, 27])).
% 0.20/0.52 tff(66,plain,
% 0.20/0.52 (((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15))) | ordinal(tptp_fun_B_14(A!15))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(67,plain,
% 0.20/0.52 (ordinal(tptp_fun_B_14(A!15))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.20/0.52 tff(68,plain,
% 0.20/0.52 (^[A: $i] : refl(((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A)))))) <=> ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(69,plain,
% 0.20/0.52 (![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A)))))) <=> ![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.52 tff(70,plain,
% 0.20/0.52 (^[A: $i] : rewrite(((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))) <=> ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(71,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))) <=> ![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.53 tff(72,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))) <=> ![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(73,plain,
% 0.20/0.53 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) <=> ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)))), (((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) & ordinal(succ(A))) <=> (((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A))) & ordinal(succ(A))))), rewrite((((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A))) & ordinal(succ(A))) <=> ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))), (((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) & ordinal(succ(A))) <=> ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))), ((ordinal(A) => ((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) & ordinal(succ(A)))) <=> (ordinal(A) => ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))))), rewrite((ordinal(A) => ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))) <=> ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))), ((ordinal(A) => ((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) & ordinal(succ(A)))) <=> ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(74,plain,
% 0.20/0.53 (![A: $i] : (ordinal(A) => ((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) & ordinal(succ(A)))) <=> ![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.53 tff(75,axiom,(![A: $i] : (ordinal(A) => ((((~empty(succ(A))) & epsilon_transitive(succ(A))) & epsilon_connected(succ(A))) & ordinal(succ(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc3_ordinal1')).
% 0.20/0.53 tff(76,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.53 tff(77,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.20/0.53 tff(78,plain,(
% 0.20/0.53 ![A: $i] : ((~ordinal(A)) | ((~empty(succ(A))) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[77])).
% 0.20/0.53 tff(79,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.20/0.53 tff(80,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[79, 69])).
% 0.20/0.53 tff(81,plain,
% 0.20/0.53 (((~![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))) | ((~ordinal(tptp_fun_B_14(A!15))) | (~(empty(succ(tptp_fun_B_14(A!15))) | (~epsilon_transitive(succ(tptp_fun_B_14(A!15)))) | (~epsilon_connected(succ(tptp_fun_B_14(A!15)))) | (~ordinal(succ(tptp_fun_B_14(A!15)))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))) | (~ordinal(tptp_fun_B_14(A!15))) | (~(empty(succ(tptp_fun_B_14(A!15))) | (~epsilon_transitive(succ(tptp_fun_B_14(A!15)))) | (~epsilon_connected(succ(tptp_fun_B_14(A!15)))) | (~ordinal(succ(tptp_fun_B_14(A!15)))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(82,plain,
% 0.20/0.53 ((~![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))) | ((~ordinal(tptp_fun_B_14(A!15))) | (~(empty(succ(tptp_fun_B_14(A!15))) | (~epsilon_transitive(succ(tptp_fun_B_14(A!15)))) | (~epsilon_connected(succ(tptp_fun_B_14(A!15)))) | (~ordinal(succ(tptp_fun_B_14(A!15)))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(83,plain,
% 0.20/0.53 ((~![A: $i] : ((~ordinal(A)) | (~(empty(succ(A)) | (~epsilon_transitive(succ(A))) | (~epsilon_connected(succ(A))) | (~ordinal(succ(A))))))) | (~ordinal(tptp_fun_B_14(A!15))) | (~(empty(succ(tptp_fun_B_14(A!15))) | (~epsilon_transitive(succ(tptp_fun_B_14(A!15)))) | (~epsilon_connected(succ(tptp_fun_B_14(A!15)))) | (~ordinal(succ(tptp_fun_B_14(A!15))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.53 tff(84,plain,
% 0.20/0.53 (~(empty(succ(tptp_fun_B_14(A!15))) | (~epsilon_transitive(succ(tptp_fun_B_14(A!15)))) | (~epsilon_connected(succ(tptp_fun_B_14(A!15)))) | (~ordinal(succ(tptp_fun_B_14(A!15)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[83, 80, 67])).
% 0.20/0.53 tff(85,plain,
% 0.20/0.53 ((empty(succ(tptp_fun_B_14(A!15))) | (~epsilon_transitive(succ(tptp_fun_B_14(A!15)))) | (~epsilon_connected(succ(tptp_fun_B_14(A!15)))) | (~ordinal(succ(tptp_fun_B_14(A!15))))) | ordinal(succ(tptp_fun_B_14(A!15)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(86,plain,
% 0.20/0.53 (ordinal(succ(tptp_fun_B_14(A!15)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.20/0.53 tff(87,plain,
% 0.20/0.53 (ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[86, 24])).
% 0.20/0.53 tff(88,plain,
% 0.20/0.53 (^[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))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(89,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.53 tff(90,plain,
% 0.20/0.53 (^[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)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(91,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.53 tff(92,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(93,plain,
% 0.20/0.53 (^[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))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(94,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.53 tff(95,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_r1_ordinal1')).
% 0.20/0.53 tff(96,plain,
% 0.20/0.53 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.53 tff(97,plain,
% 0.20/0.53 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.20/0.53 tff(98,plain,(
% 0.20/0.53 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[97])).
% 0.20/0.53 tff(99,plain,
% 0.20/0.53 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.20/0.53 tff(100,plain,
% 0.20/0.53 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.20/0.53 tff(101,plain,
% 0.20/0.53 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!15)) | (~ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | (ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!15)) | (~ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | (ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(102,plain,
% 0.20/0.53 (((ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | (~ordinal(A!15)) | (~ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15)))))) <=> ((~ordinal(A!15)) | (~ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | (ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(103,plain,
% 0.20/0.53 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | (~ordinal(A!15)) | (~ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!15)) | (~ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | (ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.53 tff(104,plain,
% 0.20/0.53 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | (~ordinal(A!15)) | (~ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!15)) | (~ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | (ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.53 tff(105,plain,
% 0.20/0.53 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | (~ordinal(A!15)) | (~ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(106,plain,
% 0.20/0.53 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!15)) | (~ordinal(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | (ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.53 tff(107,plain,
% 0.20/0.53 (ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[106, 100, 37, 87])).
% 0.20/0.53 tff(108,plain,
% 0.20/0.53 (ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), A!15)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.53 tff(109,plain,
% 0.20/0.53 (ordinal_subset(succ(tptp_fun_B_14(A!15)), A!15) <=> ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)),
% 0.20/0.53 inference(symmetry,[status(thm)],[108])).
% 0.20/0.53 tff(110,plain,
% 0.20/0.53 (^[A: $i] : refl(((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B)))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(111,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.53 tff(112,plain,
% 0.20/0.53 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B)))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(113,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.53 tff(114,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[113, 111])).
% 0.20/0.53 tff(115,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(116,plain,
% 0.20/0.53 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((ordinal(B) => (in(A, B) <=> ordinal_subset(succ(A), B))) <=> ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))), (![B: $i] : (ordinal(B) => (in(A, B) <=> ordinal_subset(succ(A), B))) <=> ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (in(A, B) <=> ordinal_subset(succ(A), B)))) <=> (ordinal(A) => ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B)))))), rewrite((ordinal(A) => ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B)))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (in(A, B) <=> ordinal_subset(succ(A), B)))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(117,plain,
% 0.20/0.53 (![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (in(A, B) <=> ordinal_subset(succ(A), B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.53 tff(118,axiom,(![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (in(A, B) <=> ordinal_subset(succ(A), B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t33_ordinal1')).
% 0.20/0.53 tff(119,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.53 tff(120,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.20/0.53 tff(121,plain,(
% 0.20/0.53 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[120])).
% 0.20/0.53 tff(122,plain,
% 0.20/0.53 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.20/0.53 tff(123,plain,
% 0.20/0.53 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))) | ((~ordinal(tptp_fun_B_14(A!15))) | ![B: $i] : ((~ordinal(B)) | (in(tptp_fun_B_14(A!15), B) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))) | (~ordinal(tptp_fun_B_14(A!15))) | ![B: $i] : ((~ordinal(B)) | (in(tptp_fun_B_14(A!15), B) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), B))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(124,plain,
% 0.20/0.53 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))) | ((~ordinal(tptp_fun_B_14(A!15))) | ![B: $i] : ((~ordinal(B)) | (in(tptp_fun_B_14(A!15), B) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), B))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(125,plain,
% 0.20/0.53 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, B) <=> ordinal_subset(succ(A), B))))) | (~ordinal(tptp_fun_B_14(A!15))) | ![B: $i] : ((~ordinal(B)) | (in(tptp_fun_B_14(A!15), B) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), B)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.53 tff(126,plain,
% 0.20/0.53 (![B: $i] : ((~ordinal(B)) | (in(tptp_fun_B_14(A!15), B) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), B)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[125, 122, 67])).
% 0.20/0.53 tff(127,plain,
% 0.20/0.53 (((~![B: $i] : ((~ordinal(B)) | (in(tptp_fun_B_14(A!15), B) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), B)))) | ((~ordinal(A!15)) | (in(tptp_fun_B_14(A!15), A!15) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), A!15)))) <=> ((~![B: $i] : ((~ordinal(B)) | (in(tptp_fun_B_14(A!15), B) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), B)))) | (~ordinal(A!15)) | (in(tptp_fun_B_14(A!15), A!15) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), A!15)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(128,plain,
% 0.20/0.53 ((~![B: $i] : ((~ordinal(B)) | (in(tptp_fun_B_14(A!15), B) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), B)))) | ((~ordinal(A!15)) | (in(tptp_fun_B_14(A!15), A!15) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), A!15)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(129,plain,
% 0.20/0.53 ((~![B: $i] : ((~ordinal(B)) | (in(tptp_fun_B_14(A!15), B) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), B)))) | (~ordinal(A!15)) | (in(tptp_fun_B_14(A!15), A!15) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), A!15))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.53 tff(130,plain,
% 0.20/0.53 (in(tptp_fun_B_14(A!15), A!15) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), A!15)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[129, 37, 126])).
% 0.20/0.53 tff(131,plain,
% 0.20/0.53 (((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15))) | in(tptp_fun_B_14(A!15), A!15)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(132,plain,
% 0.20/0.53 (in(tptp_fun_B_14(A!15), A!15)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[131, 65])).
% 0.20/0.53 tff(133,plain,
% 0.20/0.53 ((~(in(tptp_fun_B_14(A!15), A!15) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), A!15))) | (~in(tptp_fun_B_14(A!15), A!15)) | ordinal_subset(succ(tptp_fun_B_14(A!15)), A!15)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(134,plain,
% 0.20/0.53 ((~(in(tptp_fun_B_14(A!15), A!15) <=> ordinal_subset(succ(tptp_fun_B_14(A!15)), A!15))) | ordinal_subset(succ(tptp_fun_B_14(A!15)), A!15)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.20/0.53 tff(135,plain,
% 0.20/0.53 (ordinal_subset(succ(tptp_fun_B_14(A!15)), A!15)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[134, 130])).
% 0.20/0.53 tff(136,plain,
% 0.20/0.53 (ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[135, 109])).
% 0.20/0.53 tff(137,plain,
% 0.20/0.53 ((~(ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15))) | (~ordinal_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(138,plain,
% 0.20/0.53 (subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[137, 136, 107])).
% 0.20/0.53 tff(139,plain,
% 0.20/0.53 ((succ(tptp_fun_B_14(A!15)) = A!15) <=> (A!15 = succ(tptp_fun_B_14(A!15)))),
% 0.20/0.53 inference(commutativity,[status(thm)],[])).
% 0.20/0.53 tff(140,plain,
% 0.20/0.53 ((set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = A!15) <=> (succ(tptp_fun_B_14(A!15)) = A!15)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.53 tff(141,plain,
% 0.20/0.53 ((set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = A!15) <=> (A!15 = succ(tptp_fun_B_14(A!15)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[140, 139])).
% 0.20/0.53 tff(142,plain,
% 0.20/0.53 ((A!15 = succ(tptp_fun_B_14(A!15))) <=> (set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = A!15)),
% 0.20/0.53 inference(symmetry,[status(thm)],[141])).
% 0.20/0.53 tff(143,plain,
% 0.20/0.53 ((~(A!15 = succ(tptp_fun_B_14(A!15)))) <=> (~(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = A!15))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.53 tff(144,plain,
% 0.20/0.53 ((being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B)))))) | ![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(145,plain,
% 0.20/0.53 (![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[144, 25])).
% 0.20/0.53 tff(146,plain,
% 0.20/0.53 (((~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))) | ((~ordinal(tptp_fun_B_14(A!15))) | (~(A!15 = succ(tptp_fun_B_14(A!15)))))) <=> ((~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))) | (~ordinal(tptp_fun_B_14(A!15))) | (~(A!15 = succ(tptp_fun_B_14(A!15)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(147,plain,
% 0.20/0.53 ((~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))) | ((~ordinal(tptp_fun_B_14(A!15))) | (~(A!15 = succ(tptp_fun_B_14(A!15)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(148,plain,
% 0.20/0.53 ((~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))) | (~ordinal(tptp_fun_B_14(A!15))) | (~(A!15 = succ(tptp_fun_B_14(A!15))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.53 tff(149,plain,
% 0.20/0.53 (~(A!15 = succ(tptp_fun_B_14(A!15)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[148, 145, 67])).
% 0.20/0.53 tff(150,plain,
% 0.20/0.53 (~(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = A!15)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[149, 143])).
% 0.20/0.53 tff(151,plain,
% 0.20/0.53 ((~((~subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | (set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = A!15))) | (~subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | (set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = A!15)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(152,plain,
% 0.20/0.53 (~((~subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | (set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = A!15))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[151, 150, 138])).
% 0.20/0.53 tff(153,plain,
% 0.20/0.53 (in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) <=> in(succ(tptp_fun_B_14(A!15)), A!15)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.53 tff(154,plain,
% 0.20/0.53 (in(succ(tptp_fun_B_14(A!15)), A!15) <=> in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)),
% 0.20/0.53 inference(symmetry,[status(thm)],[153])).
% 0.20/0.53 tff(155,plain,
% 0.20/0.53 ((~in(succ(tptp_fun_B_14(A!15)), A!15)) <=> (~in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[154])).
% 0.20/0.53 tff(156,plain,
% 0.20/0.53 (((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15))) | (~in(succ(tptp_fun_B_14(A!15)), A!15))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(157,plain,
% 0.20/0.53 (~in(succ(tptp_fun_B_14(A!15)), A!15)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[156, 65])).
% 0.20/0.53 tff(158,plain,
% 0.20/0.53 (~in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[157, 155])).
% 0.20/0.53 tff(159,plain,
% 0.20/0.53 (epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15)))) <=> epsilon_transitive(succ(tptp_fun_B_14(A!15)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[22])).
% 0.20/0.53 tff(160,plain,
% 0.20/0.53 (epsilon_transitive(succ(tptp_fun_B_14(A!15))) <=> epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))),
% 0.20/0.53 inference(symmetry,[status(thm)],[159])).
% 0.20/0.53 tff(161,plain,
% 0.20/0.53 ((empty(succ(tptp_fun_B_14(A!15))) | (~epsilon_transitive(succ(tptp_fun_B_14(A!15)))) | (~epsilon_connected(succ(tptp_fun_B_14(A!15)))) | (~ordinal(succ(tptp_fun_B_14(A!15))))) | epsilon_transitive(succ(tptp_fun_B_14(A!15)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(162,plain,
% 0.20/0.53 (epsilon_transitive(succ(tptp_fun_B_14(A!15)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[161, 84])).
% 0.20/0.53 tff(163,plain,
% 0.20/0.53 (epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[162, 160])).
% 0.20/0.53 tff(164,plain,
% 0.20/0.53 (^[A: $i] : refl(((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(165,plain,
% 0.20/0.53 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.53 tff(166,plain,
% 0.20/0.53 (^[A: $i] : rewrite(((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(167,plain,
% 0.20/0.53 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.53 tff(168,plain,
% 0.20/0.53 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[167, 165])).
% 0.20/0.53 tff(169,plain,
% 0.20/0.53 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(170,plain,
% 0.20/0.53 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((proper_subset(A, B) => in(A, B)) <=> ((~proper_subset(A, B)) | in(A, B))), ((ordinal(B) => (proper_subset(A, B) => in(A, B))) <=> (ordinal(B) => ((~proper_subset(A, B)) | in(A, B))))), rewrite((ordinal(B) => ((~proper_subset(A, B)) | in(A, B))) <=> (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))), ((ordinal(B) => (proper_subset(A, B) => in(A, B))) <=> (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))))), (![B: $i] : (ordinal(B) => (proper_subset(A, B) => in(A, B))) <=> ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))), ((epsilon_transitive(A) => ![B: $i] : (ordinal(B) => (proper_subset(A, B) => in(A, B)))) <=> (epsilon_transitive(A) => ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))))), rewrite((epsilon_transitive(A) => ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B)))) <=> ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))), ((epsilon_transitive(A) => ![B: $i] : (ordinal(B) => (proper_subset(A, B) => in(A, B)))) <=> ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(171,plain,
% 0.20/0.53 (![A: $i] : (epsilon_transitive(A) => ![B: $i] : (ordinal(B) => (proper_subset(A, B) => in(A, B)))) <=> ![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.53 tff(172,axiom,(![A: $i] : (epsilon_transitive(A) => ![B: $i] : (ordinal(B) => (proper_subset(A, B) => in(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_ordinal1')).
% 0.20/0.53 tff(173,plain,
% 0.20/0.53 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.20/0.53 tff(174,plain,
% 0.20/0.53 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.20/0.53 tff(175,plain,(
% 0.20/0.53 ![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[174])).
% 0.20/0.53 tff(176,plain,
% 0.20/0.53 (![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.20/0.53 tff(177,plain,
% 0.20/0.53 (((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | ((~epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B))))) <=> ((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | (~epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(178,plain,
% 0.20/0.53 (((~epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | ![B: $i] : (in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)) | (~ordinal(B)))) <=> ((~epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(179,plain,
% 0.20/0.53 (((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | ((~epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | ![B: $i] : (in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)) | (~ordinal(B))))) <=> ((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | ((~epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[178])).
% 0.20/0.54 tff(180,plain,
% 0.20/0.54 (((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | ((~epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | ![B: $i] : (in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)) | (~ordinal(B))))) <=> ((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | (~epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[179, 177])).
% 0.20/0.54 tff(181,plain,
% 0.20/0.54 ((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | ((~epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | ![B: $i] : (in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)) | (~ordinal(B))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(182,plain,
% 0.20/0.54 ((~![A: $i] : ((~epsilon_transitive(A)) | ![B: $i] : (in(A, B) | (~proper_subset(A, B)) | (~ordinal(B))))) | (~epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.54 tff(183,plain,
% 0.20/0.54 ((~epsilon_transitive(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))))) | ![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[182, 176])).
% 0.20/0.54 tff(184,plain,
% 0.20/0.54 (![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[183, 163])).
% 0.20/0.54 tff(185,plain,
% 0.20/0.54 (((~![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)))) | ((~ordinal(A!15)) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15))) <=> ((~![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)))) | (~ordinal(A!15)) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(186,plain,
% 0.20/0.54 (((~ordinal(A!15)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15))) <=> ((~ordinal(A!15)) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(187,plain,
% 0.20/0.54 (((~![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)))) | ((~ordinal(A!15)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)))) | ((~ordinal(A!15)) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[186])).
% 0.20/0.54 tff(188,plain,
% 0.20/0.54 (((~![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)))) | ((~ordinal(A!15)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)))) <=> ((~![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)))) | (~ordinal(A!15)) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15))),
% 0.20/0.54 inference(transitivity,[status(thm)],[187, 185])).
% 0.20/0.54 tff(189,plain,
% 0.20/0.54 ((~![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)))) | ((~ordinal(A!15)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(190,plain,
% 0.20/0.54 ((~![B: $i] : ((~ordinal(B)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), B)))) | (~ordinal(A!15)) | (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.20/0.54 tff(191,plain,
% 0.20/0.54 ((~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | in(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[190, 37, 184])).
% 0.20/0.54 tff(192,plain,
% 0.20/0.54 (~proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[191, 158])).
% 0.20/0.54 tff(193,plain,
% 0.20/0.54 ((((~subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | (set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = A!15)) <=> proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | ((~subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)) | (set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))) = A!15)) | proper_subset(set_union2(tptp_fun_B_14(A!15), singleton(tptp_fun_B_14(A!15))), A!15)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(194,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[193, 192, 152, 12])).
% 0.20/0.54 tff(195,plain,(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(196,plain,
% 0.20/0.54 (((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) | (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16)))))) <=> ((~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16))))) | (~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(197,plain,
% 0.20/0.54 ((~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))) <=> (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(198,plain,
% 0.20/0.54 ((being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B)))))) <=> (being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[197])).
% 0.20/0.54 tff(199,plain,
% 0.20/0.54 ((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) <=> (~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B)))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[198])).
% 0.20/0.54 tff(200,plain,
% 0.20/0.54 (((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) | (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16)))))) <=> ((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) | (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[199])).
% 0.20/0.54 tff(201,plain,
% 0.20/0.54 (((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) | (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16)))))) <=> ((~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16))))) | (~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[200, 196])).
% 0.20/0.54 tff(202,plain,
% 0.20/0.54 (((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) | (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16)))))) <=> ((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) | (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(203,plain,
% 0.20/0.54 (((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) | (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16)))))) <=> ((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) | (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(204,plain,
% 0.20/0.54 ((ordinal(B!16) & (A!15 = succ(B!16)) & being_limit_ordinal(A!15)) <=> (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(205,plain,
% 0.20/0.54 (((~being_limit_ordinal(A!15)) & ![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))) <=> (~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B)))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(206,plain,
% 0.20/0.54 ((((~being_limit_ordinal(A!15)) & ![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))) | (ordinal(B!16) & (A!15 = succ(B!16)) & being_limit_ordinal(A!15))) <=> ((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) | (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[205, 204])).
% 0.20/0.54 tff(207,plain,
% 0.20/0.54 ((((~being_limit_ordinal(A!15)) & ![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))) | (ordinal(B!16) & (A!15 = succ(B!16)) & being_limit_ordinal(A!15))) <=> ((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) | (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16))))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[206, 203])).
% 0.20/0.54 tff(208,plain,
% 0.20/0.54 (((~being_limit_ordinal(A!15)) & ![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))) | (ordinal(B!16) & (A!15 = succ(B!16)) & being_limit_ordinal(A!15))),
% 0.20/0.54 inference(and_elim,[status(thm)],[36])).
% 0.20/0.54 tff(209,plain,
% 0.20/0.54 ((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) | (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.20/0.54 tff(210,plain,
% 0.20/0.54 ((~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B))))))) | (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.20/0.54 tff(211,plain,
% 0.20/0.54 ((~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16))))) | (~(being_limit_ordinal(A!15) | (~![B: $i] : ((~ordinal(B)) | (~(A!15 = succ(B)))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[210, 201])).
% 0.20/0.54 tff(212,plain,
% 0.20/0.54 (~((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[211, 195])).
% 0.20/0.54 tff(213,plain,
% 0.20/0.54 (((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16)))) | (A!15 = succ(B!16))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(214,plain,
% 0.20/0.54 (A!15 = succ(B!16)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.20/0.54 tff(215,plain,
% 0.20/0.54 (succ(B!16) = A!15),
% 0.20/0.54 inference(symmetry,[status(thm)],[214])).
% 0.20/0.54 tff(216,plain,
% 0.20/0.54 (in(succ(B!16), A!15) <=> in(A!15, A!15)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[215])).
% 0.20/0.54 tff(217,plain,
% 0.20/0.54 (in(A!15, A!15) <=> in(succ(B!16), A!15)),
% 0.20/0.54 inference(symmetry,[status(thm)],[216])).
% 0.20/0.54 tff(218,plain,
% 0.20/0.54 ((~in(A!15, A!15)) <=> (~in(succ(B!16), A!15))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[217])).
% 0.20/0.54 tff(219,plain,
% 0.20/0.54 (^[A: $i, B: $i] : refl(((~in(B, A)) | (~in(A, B))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(220,plain,
% 0.20/0.54 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[219])).
% 0.20/0.54 tff(221,plain,
% 0.20/0.54 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(222,plain,
% 0.20/0.54 (^[A: $i, B: $i] : rewrite((in(A, B) => (~in(B, A))) <=> ((~in(B, A)) | (~in(A, B))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(223,plain,
% 0.20/0.54 (![A: $i, B: $i] : (in(A, B) => (~in(B, A))) <=> ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[222])).
% 0.20/0.54 tff(224,axiom,(![A: $i, B: $i] : (in(A, B) => (~in(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','antisymmetry_r2_hidden')).
% 0.20/0.54 tff(225,plain,
% 0.20/0.54 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.20/0.54 tff(226,plain,
% 0.20/0.54 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[225, 221])).
% 0.20/0.54 tff(227,plain,(
% 0.20/0.54 ![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.20/0.54 inference(skolemize,[status(sab)],[226])).
% 0.20/0.54 tff(228,plain,
% 0.20/0.54 (![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[227, 220])).
% 0.20/0.54 tff(229,plain,
% 0.20/0.54 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!15, A!15))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!15, A!15)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(230,plain,
% 0.20/0.54 (((~in(A!15, A!15)) | (~in(A!15, A!15))) <=> (~in(A!15, A!15))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(231,plain,
% 0.20/0.54 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!15, A!15)) | (~in(A!15, A!15)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!15, A!15)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[230])).
% 0.20/0.54 tff(232,plain,
% 0.20/0.54 (((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!15, A!15)) | (~in(A!15, A!15)))) <=> ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!15, A!15)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[231, 229])).
% 0.20/0.54 tff(233,plain,
% 0.20/0.54 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | ((~in(A!15, A!15)) | (~in(A!15, A!15)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(234,plain,
% 0.20/0.54 ((~![A: $i, B: $i] : ((~in(B, A)) | (~in(A, B)))) | (~in(A!15, A!15))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.20/0.54 tff(235,plain,
% 0.20/0.54 (~in(A!15, A!15)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[234, 228])).
% 0.20/0.54 tff(236,plain,
% 0.20/0.54 (~in(succ(B!16), A!15)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[235, 218])).
% 0.20/0.54 tff(237,plain,
% 0.20/0.54 (in(B!16, succ(B!16)) <=> in(B!16, A!15)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[215])).
% 0.20/0.54 tff(238,plain,
% 0.20/0.54 (^[A: $i] : refl(in(A, succ(A)) <=> in(A, succ(A)))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(239,plain,
% 0.20/0.54 (![A: $i] : in(A, succ(A)) <=> ![A: $i] : in(A, succ(A))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[238])).
% 0.20/0.54 tff(240,plain,
% 0.20/0.54 (![A: $i] : in(A, succ(A)) <=> ![A: $i] : in(A, succ(A))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(241,axiom,(![A: $i] : in(A, succ(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t10_ordinal1')).
% 0.20/0.54 tff(242,plain,
% 0.20/0.54 (![A: $i] : in(A, succ(A))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.20/0.54 tff(243,plain,(
% 0.20/0.54 ![A: $i] : in(A, succ(A))),
% 0.20/0.54 inference(skolemize,[status(sab)],[242])).
% 0.20/0.54 tff(244,plain,
% 0.20/0.54 (![A: $i] : in(A, succ(A))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[243, 239])).
% 0.20/0.54 tff(245,plain,
% 0.20/0.54 ((~![A: $i] : in(A, succ(A))) | in(B!16, succ(B!16))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(246,plain,
% 0.20/0.54 (in(B!16, succ(B!16))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.20/0.54 tff(247,plain,
% 0.20/0.54 (in(B!16, A!15)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[246, 237])).
% 0.20/0.54 tff(248,plain,
% 0.20/0.54 (((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16)))) | being_limit_ordinal(A!15)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(249,plain,
% 0.20/0.54 (being_limit_ordinal(A!15)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[248, 212])).
% 0.20/0.54 tff(250,plain,
% 0.20/0.54 (((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15)))) | (~(being_limit_ordinal(A!15) | (~((~ordinal(tptp_fun_B_14(A!15))) | in(succ(tptp_fun_B_14(A!15)), A!15) | (~in(tptp_fun_B_14(A!15), A!15))))))) | ((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(251,plain,
% 0.20/0.54 ((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[250, 60])).
% 0.20/0.54 tff(252,plain,
% 0.20/0.54 ((~((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15)))) | (~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(253,plain,
% 0.20/0.54 ((~being_limit_ordinal(A!15)) | ![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.20/0.54 tff(254,plain,
% 0.20/0.54 (![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[253, 249])).
% 0.20/0.54 tff(255,plain,
% 0.20/0.54 (((~being_limit_ordinal(A!15)) | (~ordinal(B!16)) | (~(A!15 = succ(B!16)))) | ordinal(B!16)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(256,plain,
% 0.20/0.54 (ordinal(B!16)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[255, 212])).
% 0.20/0.54 tff(257,plain,
% 0.20/0.54 (((~![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15))) | ((~ordinal(B!16)) | (~in(B!16, A!15)) | in(succ(B!16), A!15))) <=> ((~![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15))) | (~ordinal(B!16)) | (~in(B!16, A!15)) | in(succ(B!16), A!15))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(258,plain,
% 0.20/0.54 ((~![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15))) | ((~ordinal(B!16)) | (~in(B!16, A!15)) | in(succ(B!16), A!15))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(259,plain,
% 0.20/0.54 ((~![B: $i] : ((~ordinal(B)) | (~in(B, A!15)) | in(succ(B), A!15))) | (~ordinal(B!16)) | (~in(B!16, A!15)) | in(succ(B!16), A!15)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.20/0.54 tff(260,plain,
% 0.20/0.54 ((~in(B!16, A!15)) | in(succ(B!16), A!15)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[259, 256, 254])).
% 0.20/0.54 tff(261,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[260, 247, 236])).
% 0.37/0.54 % SZS output end Proof
% 0.37/0.55 % E exiting
%------------------------------------------------------------------------------