TSTP Solution File: SEU272+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU272+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 07:28:37 EDT 2022
% Result : Theorem 1.34s 1.15s
% Output : Proof 1.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU272+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.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 11:18:04 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.
% 1.34/1.15 % SZS status Theorem
% 1.34/1.15 % SZS output start Proof
% 1.34/1.15 tff(in_type, type, (
% 1.34/1.15 in: ( $i * $i ) > $o)).
% 1.34/1.15 tff(tptp_fun_A_1_type, type, (
% 1.34/1.15 tptp_fun_A_1: $i)).
% 1.34/1.15 tff(tptp_fun_D_2_type, type, (
% 1.34/1.15 tptp_fun_D_2: $i > $i)).
% 1.34/1.15 tff(tptp_fun_C_8_type, type, (
% 1.34/1.15 tptp_fun_C_8: ( $i * $i ) > $i)).
% 1.34/1.15 tff(tptp_fun_B_0_type, type, (
% 1.34/1.15 tptp_fun_B_0: $i)).
% 1.34/1.15 tff(tptp_fun_H_10_type, type, (
% 1.34/1.15 tptp_fun_H_10: ( $i * $i ) > $i)).
% 1.34/1.15 tff(ordinal_type, type, (
% 1.34/1.15 ordinal: $i > $o)).
% 1.34/1.15 tff(succ_type, type, (
% 1.34/1.15 succ: $i > $i)).
% 1.34/1.15 tff(tptp_fun_E_9_type, type, (
% 1.34/1.15 tptp_fun_E_9: ( $i * $i * $i ) > $i)).
% 1.34/1.15 tff(tptp_fun_G_15_type, type, (
% 1.34/1.15 tptp_fun_G_15: $i > $i)).
% 1.34/1.15 tff(tptp_fun_E_11_type, type, (
% 1.34/1.15 tptp_fun_E_11: $i > $i)).
% 1.34/1.15 tff(tptp_fun_F_14_type, type, (
% 1.34/1.15 tptp_fun_F_14: $i > $i)).
% 1.34/1.15 tff(tptp_fun_D_12_type, type, (
% 1.34/1.15 tptp_fun_D_12: $i > $i)).
% 1.34/1.15 tff(tptp_fun_C_13_type, type, (
% 1.34/1.15 tptp_fun_C_13: $i > $i)).
% 1.34/1.15 tff(tptp_fun_E_3_type, type, (
% 1.34/1.15 tptp_fun_E_3: $i > $i)).
% 1.34/1.15 tff(1,assumption,(~((~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1))))), introduced(assumption)).
% 1.34/1.15 tff(2,plain,
% 1.34/1.15 (((~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1)))) | (tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))),
% 1.34/1.15 inference(tautology,[status(thm)],[])).
% 1.34/1.15 tff(3,plain,
% 1.34/1.15 (tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[2, 1])).
% 1.34/1.15 tff(4,plain,
% 1.34/1.15 (((~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1)))) | (tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))),
% 1.34/1.15 inference(tautology,[status(thm)],[])).
% 1.34/1.15 tff(5,plain,
% 1.34/1.15 (tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1)),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[4, 1])).
% 1.34/1.15 tff(6,plain,
% 1.34/1.15 (tptp_fun_D_12(A!1) = tptp_fun_C_13(A!1)),
% 1.34/1.15 inference(symmetry,[status(thm)],[5])).
% 1.34/1.15 tff(7,plain,
% 1.34/1.15 (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)),
% 1.34/1.15 inference(transitivity,[status(thm)],[6, 3])).
% 1.34/1.15 tff(8,plain,
% 1.34/1.15 (((~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1)))) | (~(tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)))),
% 1.34/1.15 inference(tautology,[status(thm)],[])).
% 1.34/1.15 tff(9,plain,
% 1.34/1.15 (~(tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1))),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[8, 1])).
% 1.34/1.15 tff(10,plain,
% 1.34/1.15 ($false),
% 1.34/1.15 inference(unit_resolution,[status(thm)],[9, 7])).
% 1.34/1.15 tff(11,plain,((~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1)))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.15 tff(12,plain,
% 1.34/1.15 (^[A: $i, B: $i] : rewrite(((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A))))))))) <=> ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A))))))))))),
% 1.34/1.15 inference(bind,[status(th)],[])).
% 1.34/1.15 tff(13,plain,
% 1.34/1.15 (![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A))))))))) <=> ![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))),
% 1.34/1.15 inference(quant_intro,[status(thm)],[12])).
% 1.34/1.15 tff(14,plain,
% 1.34/1.15 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) <=> ((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))), rewrite((in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A))))) <=> (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))), ((((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) <=> (((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A))))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))), rewrite((((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A))))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))) <=> (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A))))))))), ((((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) <=> (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A))))))))))), (![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) <=> ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))), rewrite(((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A)))) <=> (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A))))), (((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | ((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A))))) <=> ((~ordinal(B)) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A))))))), rewrite(((~ordinal(B)) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A))))) <=> ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))), (((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | ((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A))))) <=> ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))))),
% 1.34/1.15 inference(bind,[status(th)],[])).
% 1.34/1.15 tff(15,plain,
% 1.34/1.15 (![A: $i, B: $i] : ((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | ((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A))))) <=> ![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))),
% 1.34/1.15 inference(quant_intro,[status(thm)],[14])).
% 1.34/1.15 tff(16,plain,
% 1.34/1.15 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : rewrite((((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & (ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A)))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) <=> (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))))), (![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & (ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A)))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) <=> ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))))), trans(monotonicity(rewrite(((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & (ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A)) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & (ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A))) <=> ((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A))), ((((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & (ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A)) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & (ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A))) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A)))) <=> (((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A)) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A)))))), rewrite((((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A)) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A)))) <=> ((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A))))), ((((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & (ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A)) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & (ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A))) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A)))) <=> ((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A)))))), (((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & (ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A)))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | (((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & (ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A)) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & (ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A))) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A))))) <=> ((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | ((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A))))))), rewrite(((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | ((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A))))) <=> ((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | ((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A)))))), (((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & (ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A)))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | (((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & (ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A)) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & (ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A))) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A))))) <=> ((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | ((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A)))))))),
% 1.34/1.15 inference(bind,[status(th)],[])).
% 1.34/1.15 tff(17,plain,
% 1.34/1.15 (![A: $i, B: $i] : ((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & (ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A)))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | (((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & (ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A)) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & (ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A))) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A))))) <=> ![A: $i, B: $i] : ((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | ((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A)))))),
% 1.34/1.15 inference(quant_intro,[status(thm)],[16])).
% 1.34/1.15 tff(18,plain,
% 1.34/1.15 (![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A)))) | (~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E)))) <=> ![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A)))) | (~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E))))),
% 1.34/1.15 inference(rewrite,[status(thm)],[])).
% 1.34/1.15 tff(19,plain,
% 1.34/1.15 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) <=> ((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)))), ((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) <=> (((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A))) & (C = E)))), rewrite((((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A))) & (C = E)) <=> ((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E))), ((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) <=> ((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E)))), quant_intro(proof_bind(^[G: $i] : rewrite(((ordinal(G) & (E = G)) & in(G, A)) <=> (ordinal(G) & (E = G) & in(G, A)))), (?[G: $i] : ((ordinal(G) & (E = G)) & in(G, A)) <=> ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))), (((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) & ?[G: $i] : ((ordinal(G) & (E = G)) & in(G, A))) <=> (((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E)) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A))))), rewrite((((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E)) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A))) <=> ((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))), (((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) & ?[G: $i] : ((ordinal(G) & (E = G)) & in(G, A))) <=> ((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A))))), ((((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) & ?[G: $i] : ((ordinal(G) & (E = G)) & in(G, A))) => (D = E)) <=> (((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A))) => (D = E)))), rewrite((((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A))) => (D = E)) <=> ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E))), ((((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) & ?[G: $i] : ((ordinal(G) & (E = G)) & in(G, A))) => (D = E)) <=> ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E))))), (![C: $i, D: $i, E: $i] : (((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) & ?[G: $i] : ((ordinal(G) & (E = G)) & in(G, A))) => (D = E)) <=> ![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E)))), quant_intro(proof_bind(^[C: $i] : quant_intro(proof_bind(^[D: $i] : rewrite((in(D, C) <=> ?[E: $i] : ((in(E, succ(B)) & (E = D)) & ?[H: $i] : ((ordinal(H) & (D = H)) & in(H, A)))) <=> (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A)))))), (![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, succ(B)) & (E = D)) & ?[H: $i] : ((ordinal(H) & (D = H)) & in(H, A)))) <=> ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A))))))), (?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, succ(B)) & (E = D)) & ?[H: $i] : ((ordinal(H) & (D = H)) & in(H, A)))) <=> ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A)))))), ((![C: $i, D: $i, E: $i] : (((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) & ?[G: $i] : ((ordinal(G) & (E = G)) & in(G, A))) => (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, succ(B)) & (E = D)) & ?[H: $i] : ((ordinal(H) & (D = H)) & in(H, A))))) <=> (![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A))))))), rewrite((![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A))))) <=> ((~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E))) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A)))))), ((![C: $i, D: $i, E: $i] : (((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) & ?[G: $i] : ((ordinal(G) & (E = G)) & in(G, A))) => (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, succ(B)) & (E = D)) & ?[H: $i] : ((ordinal(H) & (D = H)) & in(H, A))))) <=> ((~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E))) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A))))))), ((ordinal(B) => (![C: $i, D: $i, E: $i] : (((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) & ?[G: $i] : ((ordinal(G) & (E = G)) & in(G, A))) => (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, succ(B)) & (E = D)) & ?[H: $i] : ((ordinal(H) & (D = H)) & in(H, A)))))) <=> (ordinal(B) => ((~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E))) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A)))))))), rewrite((ordinal(B) => ((~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E))) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A)))))) <=> ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A)))) | (~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E))))), ((ordinal(B) => (![C: $i, D: $i, E: $i] : (((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) & ?[G: $i] : ((ordinal(G) & (E = G)) & in(G, A))) => (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, succ(B)) & (E = D)) & ?[H: $i] : ((ordinal(H) & (D = H)) & in(H, A)))))) <=> ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A)))) | (~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E))))))),
% 1.34/1.15 inference(bind,[status(th)],[])).
% 1.34/1.15 tff(20,plain,
% 1.34/1.15 (![A: $i, B: $i] : (ordinal(B) => (![C: $i, D: $i, E: $i] : (((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) & ?[G: $i] : ((ordinal(G) & (E = G)) & in(G, A))) => (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, succ(B)) & (E = D)) & ?[H: $i] : ((ordinal(H) & (D = H)) & in(H, A)))))) <=> ![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A)))) | (~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E))))),
% 1.34/1.15 inference(quant_intro,[status(thm)],[19])).
% 1.34/1.15 tff(21,axiom,(![A: $i, B: $i] : (ordinal(B) => (![C: $i, D: $i, E: $i] : (((((C = D) & ?[F: $i] : ((ordinal(F) & (D = F)) & in(F, A))) & (C = E)) & ?[G: $i] : ((ordinal(G) & (E = G)) & in(G, A))) => (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, succ(B)) & (E = D)) & ?[H: $i] : ((ordinal(H) & (D = H)) & in(H, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_tarski__e8_6__wellord2__1')).
% 1.34/1.15 tff(22,plain,
% 1.34/1.15 (![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A)))) | (~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E))))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[21, 20])).
% 1.34/1.15 tff(23,plain,
% 1.34/1.15 (![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, succ(B)) & (E = D) & ?[H: $i] : (ordinal(H) & (D = H) & in(H, A)))) | (~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i] : (ordinal(F) & (D = F) & in(F, A)) & (C = E) & ?[G: $i] : (ordinal(G) & (E = G) & in(G, A)))) | (D = E))))),
% 1.34/1.15 inference(modus_ponens,[status(thm)],[22, 18])).
% 1.34/1.15 tff(24,plain,(
% 1.34/1.15 ![A: $i, B: $i] : ((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & (ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A)))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | (((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & (ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A)) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & (ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A))) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A)))))),
% 1.34/1.15 inference(skolemize,[status(sab)],[23])).
% 1.34/1.15 tff(25,plain,
% 1.34/1.15 (![A: $i, B: $i] : ((~ordinal(B)) | ![D: $i] : (((~in(D, tptp_fun_C_8(B, A))) | (in(tptp_fun_E_9(D, B, A), succ(B)) & (tptp_fun_E_9(D, B, A) = D) & ordinal(tptp_fun_H_10(D, A)) & (D = tptp_fun_H_10(D, A)) & in(tptp_fun_H_10(D, A), A))) & (in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : (~(ordinal(H) & (D = H) & in(H, A)))))) | ((tptp_fun_C_13(A) = tptp_fun_D_12(A)) & ordinal(tptp_fun_F_14(A)) & (tptp_fun_D_12(A) = tptp_fun_F_14(A)) & in(tptp_fun_F_14(A), A) & (tptp_fun_C_13(A) = tptp_fun_E_11(A)) & ordinal(tptp_fun_G_15(A)) & (tptp_fun_E_11(A) = tptp_fun_G_15(A)) & in(tptp_fun_G_15(A), A) & (~(tptp_fun_D_12(A) = tptp_fun_E_11(A)))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[24, 17])).
% 1.34/1.16 tff(26,plain,
% 1.34/1.16 (![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[25, 15])).
% 1.34/1.16 tff(27,plain,
% 1.34/1.16 (![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[26, 13])).
% 1.34/1.16 tff(28,plain,
% 1.34/1.16 (((~(~ordinal(B!0))) & ![C: $i] : ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), succ(B!0)) & (ordinal(tptp_fun_E_3(C)) & (tptp_fun_D_2(C) = tptp_fun_E_3(C)) & in(tptp_fun_E_3(C), A!1)))) & ((~in(tptp_fun_D_2(C), C)) | ((~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : (~(ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1))))))) <=> (ordinal(B!0) & ![C: $i] : ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), succ(B!0)) & ordinal(tptp_fun_E_3(C)) & (tptp_fun_D_2(C) = tptp_fun_E_3(C)) & in(tptp_fun_E_3(C), A!1))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : (~(ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1))))))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(29,plain,
% 1.34/1.16 ((~![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, succ(B)) & ?[E: $i] : (ordinal(E) & (D = E) & in(E, A)))))) <=> (~![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, succ(B)) & ?[E: $i] : (ordinal(E) & (D = E) & in(E, A))))))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(30,plain,
% 1.34/1.16 ((~![A: $i, B: $i] : (ordinal(B) => ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, succ(B)) & ?[E: $i] : ((ordinal(E) & (D = E)) & in(E, A)))))) <=> (~![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, succ(B)) & ?[E: $i] : (ordinal(E) & (D = E) & in(E, A))))))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(31,axiom,(~![A: $i, B: $i] : (ordinal(B) => ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, succ(B)) & ?[E: $i] : ((ordinal(E) & (D = E)) & in(E, A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_xboole_0__e8_6__wellord2__1')).
% 1.34/1.16 tff(32,plain,
% 1.34/1.16 (~![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, succ(B)) & ?[E: $i] : (ordinal(E) & (D = E) & in(E, A)))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.34/1.16 tff(33,plain,
% 1.34/1.16 (~![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, succ(B)) & ?[E: $i] : (ordinal(E) & (D = E) & in(E, A)))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[32, 29])).
% 1.34/1.16 tff(34,plain,
% 1.34/1.16 (~![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, succ(B)) & ?[E: $i] : (ordinal(E) & (D = E) & in(E, A)))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[33, 29])).
% 1.34/1.16 tff(35,plain,
% 1.34/1.16 (~![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, succ(B)) & ?[E: $i] : (ordinal(E) & (D = E) & in(E, A)))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[34, 29])).
% 1.34/1.16 tff(36,plain,
% 1.34/1.16 (~![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, succ(B)) & ?[E: $i] : (ordinal(E) & (D = E) & in(E, A)))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[35, 29])).
% 1.34/1.16 tff(37,plain,
% 1.34/1.16 (~![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, succ(B)) & ?[E: $i] : (ordinal(E) & (D = E) & in(E, A)))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[36, 29])).
% 1.34/1.16 tff(38,plain,
% 1.34/1.16 (~![A: $i, B: $i] : ((~ordinal(B)) | ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, succ(B)) & ?[E: $i] : (ordinal(E) & (D = E) & in(E, A)))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[37, 29])).
% 1.34/1.16 tff(39,plain,
% 1.34/1.16 (ordinal(B!0) & ![C: $i] : ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), succ(B!0)) & ordinal(tptp_fun_E_3(C)) & (tptp_fun_D_2(C) = tptp_fun_E_3(C)) & in(tptp_fun_E_3(C), A!1))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : (~(ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1)))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[38, 28])).
% 1.34/1.16 tff(40,plain,
% 1.34/1.16 (ordinal(B!0)),
% 1.34/1.16 inference(and_elim,[status(thm)],[39])).
% 1.34/1.16 tff(41,plain,
% 1.34/1.16 (((~![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))) | ((~ordinal(B!0)) | (~((~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1)))))))))) <=> ((~![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))) | (~ordinal(B!0)) | (~((~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1)))))))))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(42,plain,
% 1.34/1.16 (((~ordinal(B!0)) | (~((tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~ordinal(tptp_fun_H_10(D, A!1))) | (~(D = tptp_fun_H_10(D, A!1))) | (~in(tptp_fun_H_10(D, A!1), A!1)))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))) <=> ((~ordinal(B!0)) | (~((~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1)))))))))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(43,plain,
% 1.34/1.16 (((~![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))) | ((~ordinal(B!0)) | (~((tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~ordinal(tptp_fun_H_10(D, A!1))) | (~(D = tptp_fun_H_10(D, A!1))) | (~in(tptp_fun_H_10(D, A!1), A!1)))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1)))))))))) <=> ((~![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))) | ((~ordinal(B!0)) | (~((~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[42])).
% 1.34/1.16 tff(44,plain,
% 1.34/1.16 (((~![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))) | ((~ordinal(B!0)) | (~((tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~ordinal(tptp_fun_H_10(D, A!1))) | (~(D = tptp_fun_H_10(D, A!1))) | (~in(tptp_fun_H_10(D, A!1), A!1)))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1)))))))))) <=> ((~![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))) | (~ordinal(B!0)) | (~((~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1)))))))))),
% 1.34/1.16 inference(transitivity,[status(thm)],[43, 41])).
% 1.34/1.16 tff(45,plain,
% 1.34/1.16 ((~![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))) | ((~ordinal(B!0)) | (~((tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~ordinal(tptp_fun_H_10(D, A!1))) | (~(D = tptp_fun_H_10(D, A!1))) | (~in(tptp_fun_H_10(D, A!1), A!1)))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1)))))))))),
% 1.34/1.16 inference(quant_inst,[status(thm)],[])).
% 1.34/1.16 tff(46,plain,
% 1.34/1.16 ((~![A: $i, B: $i] : ((~ordinal(B)) | (~((tptp_fun_D_12(A) = tptp_fun_E_11(A)) | (~(tptp_fun_C_13(A) = tptp_fun_D_12(A))) | (~ordinal(tptp_fun_F_14(A))) | (~(tptp_fun_D_12(A) = tptp_fun_F_14(A))) | (~in(tptp_fun_F_14(A), A)) | (~(tptp_fun_C_13(A) = tptp_fun_E_11(A))) | (~ordinal(tptp_fun_G_15(A))) | (~(tptp_fun_E_11(A) = tptp_fun_G_15(A))) | (~in(tptp_fun_G_15(A), A)))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B, A))) | (~((~in(tptp_fun_E_9(D, B, A), succ(B))) | (~(tptp_fun_E_9(D, B, A) = D)) | (~ordinal(tptp_fun_H_10(D, A))) | (~(D = tptp_fun_H_10(D, A))) | (~in(tptp_fun_H_10(D, A), A)))))) | (~(in(D, tptp_fun_C_8(B, A)) | ![E: $i] : ((~in(E, succ(B))) | (~(E = D)) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A)))))))))) | (~ordinal(B!0)) | (~((~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))),
% 1.34/1.16 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.34/1.16 tff(47,plain,
% 1.34/1.16 ((~((~ordinal(tptp_fun_F_14(A!1))) | (~(tptp_fun_C_13(A!1) = tptp_fun_E_11(A!1))) | (~ordinal(tptp_fun_G_15(A!1))) | (~in(tptp_fun_F_14(A!1), A!1)) | (tptp_fun_D_12(A!1) = tptp_fun_E_11(A!1)) | (~(tptp_fun_C_13(A!1) = tptp_fun_D_12(A!1))) | (~(tptp_fun_D_12(A!1) = tptp_fun_F_14(A!1))) | (~in(tptp_fun_G_15(A!1), A!1)) | (~(tptp_fun_E_11(A!1) = tptp_fun_G_15(A!1))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[46, 40, 27])).
% 1.34/1.16 tff(48,plain,
% 1.34/1.16 (![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))),
% 1.34/1.16 inference(unit_resolution,[status(thm)],[47, 11])).
% 1.34/1.16 tff(49,plain,
% 1.34/1.16 (((~![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))))))) <=> ((~![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))))))))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(50,plain,
% 1.34/1.16 ((~((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)) | (~in(H, A!1)))))))) <=> (~((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))))))),
% 1.34/1.16 inference(rewrite,[status(thm)],[])).
% 1.34/1.16 tff(51,plain,
% 1.34/1.16 (((~![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)) | (~in(H, A!1))))))))) <=> ((~![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))))))))),
% 1.34/1.16 inference(monotonicity,[status(thm)],[50])).
% 1.34/1.16 tff(52,plain,
% 1.34/1.16 (((~![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)) | (~in(H, A!1))))))))) <=> ((~![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))))))))),
% 1.34/1.17 inference(transitivity,[status(thm)],[51, 49])).
% 1.34/1.17 tff(53,plain,
% 1.34/1.17 ((~![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)) | (~in(H, A!1))))))))),
% 1.34/1.17 inference(quant_inst,[status(thm)],[])).
% 1.34/1.17 tff(54,plain,
% 1.34/1.17 ((~![D: $i] : (~((~((~in(D, tptp_fun_C_8(B!0, A!1))) | (~((~in(tptp_fun_E_9(D, B!0, A!1), succ(B!0))) | (~(tptp_fun_E_9(D, B!0, A!1) = D)) | (~in(tptp_fun_H_10(D, A!1), A!1)) | (~(D = tptp_fun_H_10(D, A!1))) | (~ordinal(tptp_fun_H_10(D, A!1))))))) | (~(in(D, tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~(D = H)) | (~in(H, A!1))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))))))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.34/1.17 tff(55,plain,
% 1.34/1.17 (~((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))))))),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[54, 48])).
% 1.34/1.17 tff(56,plain,
% 1.34/1.17 (((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))))) | ((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))),
% 1.34/1.17 inference(tautology,[status(thm)],[])).
% 1.34/1.17 tff(57,plain,
% 1.34/1.17 ((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)))))),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[56, 55])).
% 1.34/1.17 tff(58,assumption,(~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))), introduced(assumption)).
% 1.34/1.17 tff(59,plain,
% 1.34/1.17 (^[C: $i] : rewrite((~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1))))))) <=> (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1))))))))),
% 1.34/1.17 inference(bind,[status(th)],[])).
% 1.34/1.17 tff(60,plain,
% 1.34/1.17 (![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1))))))) <=> ![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))),
% 1.34/1.17 inference(quant_intro,[status(thm)],[59])).
% 1.34/1.17 tff(61,plain,
% 1.34/1.17 (^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_2(C), succ(B!0)) & ordinal(tptp_fun_E_3(C)) & (tptp_fun_D_2(C) = tptp_fun_E_3(C)) & in(tptp_fun_E_3(C), A!1)) <=> (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1))))), ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), succ(B!0)) & ordinal(tptp_fun_E_3(C)) & (tptp_fun_D_2(C) = tptp_fun_E_3(C)) & in(tptp_fun_E_3(C), A!1))) <=> (in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1))))))), rewrite((in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1))))) <=> (in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))), ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), succ(B!0)) & ordinal(tptp_fun_E_3(C)) & (tptp_fun_D_2(C) = tptp_fun_E_3(C)) & in(tptp_fun_E_3(C), A!1))) <=> (in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1))))))), trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite((ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1)) <=> (~((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1))))), ((~(ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1))) <=> (~(~((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1))))))), rewrite((~(~((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1))))) <=> ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))), ((~(ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1))) <=> ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))), (![E: $i] : (~(ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1))) <=> ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1))))), (((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : (~(ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1)))) <=> ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))), rewrite(((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))) <=> ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1))))), (((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : (~(ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1)))) <=> ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))), (((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), succ(B!0)) & ordinal(tptp_fun_E_3(C)) & (tptp_fun_D_2(C) = tptp_fun_E_3(C)) & in(tptp_fun_E_3(C), A!1))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : (~(ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1))))) <=> ((in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1))))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1))))))), rewrite(((in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1))))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1))))) <=> (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))), (((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), succ(B!0)) & ordinal(tptp_fun_E_3(C)) & (tptp_fun_D_2(C) = tptp_fun_E_3(C)) & in(tptp_fun_E_3(C), A!1))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : (~(ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1))))) <=> (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))))),
% 1.34/1.17 inference(bind,[status(th)],[])).
% 1.34/1.17 tff(62,plain,
% 1.34/1.17 (![C: $i] : ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), succ(B!0)) & ordinal(tptp_fun_E_3(C)) & (tptp_fun_D_2(C) = tptp_fun_E_3(C)) & in(tptp_fun_E_3(C), A!1))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : (~(ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1))))) <=> ![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))),
% 1.34/1.17 inference(quant_intro,[status(thm)],[61])).
% 1.34/1.17 tff(63,plain,
% 1.34/1.17 (![C: $i] : ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), succ(B!0)) & ordinal(tptp_fun_E_3(C)) & (tptp_fun_D_2(C) = tptp_fun_E_3(C)) & in(tptp_fun_E_3(C), A!1))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : (~(ordinal(E) & (tptp_fun_D_2(C) = E) & in(E, A!1)))))),
% 1.34/1.17 inference(and_elim,[status(thm)],[39])).
% 1.34/1.17 tff(64,plain,
% 1.34/1.17 (![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.34/1.17 tff(65,plain,
% 1.34/1.17 (![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.34/1.17 tff(66,plain,
% 1.34/1.17 (((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))))))) | (~(![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)))))))) <=> ((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))))))) | (~(![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))))))))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(67,plain,
% 1.34/1.17 ((~((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)) | (~in(E, A!1))))))) <=> (~((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))))))) | (~(![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)))))))),
% 1.34/1.17 inference(rewrite,[status(thm)],[])).
% 1.34/1.17 tff(68,plain,
% 1.34/1.17 (((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)) | (~in(E, A!1)))))))) <=> ((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))))))) | (~(![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))))))))),
% 1.34/1.17 inference(monotonicity,[status(thm)],[67])).
% 1.34/1.17 tff(69,plain,
% 1.34/1.17 (((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)) | (~in(E, A!1)))))))) <=> ((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))))))) | (~(![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))))))))),
% 1.34/1.17 inference(transitivity,[status(thm)],[68, 66])).
% 1.34/1.17 tff(70,plain,
% 1.34/1.17 ((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)) | (~in(E, A!1)))))))),
% 1.34/1.17 inference(quant_inst,[status(thm)],[])).
% 1.34/1.17 tff(71,plain,
% 1.34/1.17 ((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), succ(B!0))) | (~ordinal(tptp_fun_E_3(C))) | (~(tptp_fun_D_2(C) = tptp_fun_E_3(C))) | (~in(tptp_fun_E_3(C), A!1)))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), succ(B!0))) | ![E: $i] : ((~ordinal(E)) | (~(tptp_fun_D_2(C) = E)) | (~in(E, A!1)))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))))))) | (~(![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)))))))),
% 1.34/1.17 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.34/1.17 tff(72,plain,
% 1.34/1.17 (~((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))))))) | (~(![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))))))),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[71, 65])).
% 1.34/1.17 tff(73,plain,
% 1.34/1.17 (((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))))))) | (~(![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)))))) | (in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))))))),
% 1.34/1.17 inference(tautology,[status(thm)],[])).
% 1.34/1.17 tff(74,plain,
% 1.34/1.17 (in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0)))))),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[73, 72])).
% 1.34/1.17 tff(75,plain,
% 1.34/1.17 ((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))))))) | in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0)))))),
% 1.34/1.17 inference(tautology,[status(thm)],[])).
% 1.34/1.17 tff(76,plain,
% 1.34/1.17 (in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0)))))),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[75, 74])).
% 1.34/1.17 tff(77,plain,
% 1.34/1.17 (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))))),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[76, 58])).
% 1.34/1.17 tff(78,plain,
% 1.34/1.17 (((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0)))) | (tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))),
% 1.34/1.17 inference(tautology,[status(thm)],[])).
% 1.34/1.17 tff(79,plain,
% 1.34/1.17 (tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1))),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[78, 77])).
% 1.34/1.17 tff(80,plain,
% 1.34/1.17 (tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1))),
% 1.34/1.17 inference(symmetry,[status(thm)],[79])).
% 1.34/1.17 tff(81,plain,
% 1.34/1.17 (in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0)) <=> in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))),
% 1.34/1.17 inference(monotonicity,[status(thm)],[80])).
% 1.34/1.17 tff(82,plain,
% 1.34/1.17 (in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0)) <=> in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))),
% 1.34/1.17 inference(symmetry,[status(thm)],[81])).
% 1.34/1.17 tff(83,assumption,(~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))), introduced(assumption)).
% 1.34/1.17 tff(84,plain,
% 1.34/1.17 (((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0)))) | in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))),
% 1.34/1.17 inference(tautology,[status(thm)],[])).
% 1.34/1.17 tff(85,plain,
% 1.34/1.17 ((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0)))),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[84, 83])).
% 1.34/1.17 tff(86,plain,
% 1.34/1.17 (in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))),
% 1.34/1.17 inference(unit_resolution,[status(thm)],[76, 85])).
% 1.34/1.18 tff(87,plain,
% 1.34/1.18 ((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)))))),
% 1.34/1.18 inference(tautology,[status(thm)],[])).
% 1.34/1.18 tff(88,plain,
% 1.34/1.18 (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[87, 86, 57])).
% 1.34/1.18 tff(89,plain,
% 1.34/1.18 (((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)))) | (tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))),
% 1.34/1.18 inference(tautology,[status(thm)],[])).
% 1.34/1.18 tff(90,plain,
% 1.34/1.18 (tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1))),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[89, 88])).
% 1.34/1.18 tff(91,plain,
% 1.34/1.18 (in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0)) <=> in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))),
% 1.34/1.18 inference(monotonicity,[status(thm)],[90])).
% 1.34/1.18 tff(92,plain,
% 1.34/1.18 (in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0)) <=> in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))),
% 1.34/1.18 inference(symmetry,[status(thm)],[91])).
% 1.34/1.18 tff(93,plain,
% 1.34/1.18 ((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) <=> (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0)))),
% 1.34/1.18 inference(monotonicity,[status(thm)],[92])).
% 1.34/1.18 tff(94,plain,
% 1.34/1.18 (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))),
% 1.34/1.18 inference(modus_ponens,[status(thm)],[83, 93])).
% 1.34/1.18 tff(95,plain,
% 1.34/1.18 (((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)))) | in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))),
% 1.34/1.18 inference(tautology,[status(thm)],[])).
% 1.34/1.18 tff(96,plain,
% 1.34/1.18 (in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[95, 88])).
% 1.34/1.18 tff(97,plain,
% 1.34/1.18 ($false),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[96, 94])).
% 1.34/1.18 tff(98,plain,(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))), inference(lemma,lemma(discharge,[]))).
% 1.34/1.18 tff(99,plain,
% 1.34/1.18 (in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))),
% 1.34/1.18 inference(modus_ponens,[status(thm)],[98, 82])).
% 1.34/1.18 tff(100,plain,
% 1.34/1.18 (((~((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))))) | (in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))))),
% 1.34/1.18 inference(tautology,[status(thm)],[])).
% 1.34/1.18 tff(101,plain,
% 1.34/1.18 (in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[100, 55])).
% 1.34/1.18 tff(102,plain,
% 1.34/1.18 ((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))))) | in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | ![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))),
% 1.34/1.18 inference(tautology,[status(thm)],[])).
% 1.34/1.18 tff(103,plain,
% 1.34/1.18 (![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[102, 58, 101])).
% 1.34/1.18 tff(104,plain,
% 1.34/1.18 (((~![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))) | ((~(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))) <=> ((~![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))) | (~(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))),
% 1.34/1.18 inference(rewrite,[status(thm)],[])).
% 1.34/1.18 tff(105,plain,
% 1.34/1.18 (((~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))) <=> ((~(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))),
% 1.34/1.18 inference(rewrite,[status(thm)],[])).
% 1.34/1.18 tff(106,plain,
% 1.34/1.18 (((~![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))) | ((~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))) <=> ((~![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))) | ((~(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))))),
% 1.34/1.18 inference(monotonicity,[status(thm)],[105])).
% 1.34/1.18 tff(107,plain,
% 1.34/1.18 (((~![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))) | ((~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))) <=> ((~![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))) | (~(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))),
% 1.34/1.18 inference(transitivity,[status(thm)],[106, 104])).
% 1.34/1.18 tff(108,plain,
% 1.34/1.18 ((~![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))) | ((~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))),
% 1.34/1.18 inference(quant_inst,[status(thm)],[])).
% 1.34/1.18 tff(109,plain,
% 1.34/1.18 ((~![E: $i] : ((~in(E, succ(B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H))))) | (~(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))),
% 1.34/1.18 inference(modus_ponens,[status(thm)],[108, 107])).
% 1.34/1.18 tff(110,plain,
% 1.34/1.18 ((~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | ![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[109, 103, 80])).
% 1.34/1.18 tff(111,plain,
% 1.34/1.18 (![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[110, 99])).
% 1.34/1.18 tff(112,plain,
% 1.34/1.18 (((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0)))) | ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))),
% 1.34/1.18 inference(tautology,[status(thm)],[])).
% 1.34/1.18 tff(113,plain,
% 1.34/1.18 (ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[112, 77])).
% 1.34/1.18 tff(114,plain,
% 1.34/1.18 (((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0)))) | in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)),
% 1.34/1.18 inference(tautology,[status(thm)],[])).
% 1.34/1.18 tff(115,plain,
% 1.34/1.18 (in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)),
% 1.34/1.18 inference(unit_resolution,[status(thm)],[114, 77])).
% 1.34/1.18 tff(116,plain,
% 1.34/1.18 (((~![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))) | ((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))))) <=> ((~![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))))),
% 1.46/1.18 inference(rewrite,[status(thm)],[])).
% 1.46/1.18 tff(117,plain,
% 1.46/1.18 (((~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1))))) <=> ((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))))),
% 1.46/1.18 inference(rewrite,[status(thm)],[])).
% 1.46/1.18 tff(118,plain,
% 1.46/1.18 (((~![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))) | ((~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))))) <=> ((~![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))) | ((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1))))))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[117])).
% 1.46/1.18 tff(119,plain,
% 1.46/1.18 (((~![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))) | ((~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))))) <=> ((~![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))))),
% 1.46/1.18 inference(transitivity,[status(thm)],[118, 116])).
% 1.46/1.18 tff(120,plain,
% 1.46/1.18 ((~![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))) | ((~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))))),
% 1.46/1.18 inference(quant_inst,[status(thm)],[])).
% 1.46/1.18 tff(121,plain,
% 1.46/1.18 ((~![H: $i] : ((~ordinal(H)) | (~in(H, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = H)))) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1))))),
% 1.46/1.18 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.46/1.18 tff(122,plain,
% 1.46/1.18 ($false),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[121, 79, 115, 113, 111])).
% 1.46/1.18 tff(123,plain,(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 1.46/1.18 tff(124,plain,
% 1.46/1.18 (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))))),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[87, 123, 57])).
% 1.46/1.18 tff(125,plain,
% 1.46/1.18 (((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)))) | (tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))),
% 1.46/1.18 inference(tautology,[status(thm)],[])).
% 1.46/1.18 tff(126,plain,
% 1.46/1.18 (tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[125, 124])).
% 1.46/1.18 tff(127,plain,
% 1.46/1.18 (in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1) <=> in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)),
% 1.46/1.18 inference(monotonicity,[status(thm)],[126])).
% 1.46/1.18 tff(128,plain,
% 1.46/1.18 (in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1) <=> in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)),
% 1.46/1.18 inference(symmetry,[status(thm)],[127])).
% 1.46/1.18 tff(129,plain,
% 1.46/1.18 (((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)))) | in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)),
% 1.46/1.18 inference(tautology,[status(thm)],[])).
% 1.46/1.18 tff(130,plain,
% 1.46/1.18 (in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[129, 124])).
% 1.46/1.18 tff(131,plain,
% 1.46/1.18 (in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)),
% 1.46/1.18 inference(modus_ponens,[status(thm)],[130, 128])).
% 1.46/1.18 tff(132,plain,
% 1.46/1.18 (ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1))) <=> ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[126])).
% 1.46/1.18 tff(133,plain,
% 1.46/1.18 (ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) <=> ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))),
% 1.46/1.18 inference(symmetry,[status(thm)],[132])).
% 1.46/1.18 tff(134,plain,
% 1.46/1.18 (((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))) | (~in(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_9(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), B!0, A!1), succ(B!0))) | (~ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)))) | ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))),
% 1.46/1.18 inference(tautology,[status(thm)],[])).
% 1.46/1.18 tff(135,plain,
% 1.46/1.18 (ordinal(tptp_fun_H_10(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1))),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[134, 124])).
% 1.46/1.18 tff(136,plain,
% 1.46/1.18 (ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))),
% 1.46/1.18 inference(modus_ponens,[status(thm)],[135, 133])).
% 1.46/1.18 tff(137,plain,
% 1.46/1.18 (((~(in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)) | (~((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_E_3(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))))))) | (~(![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)))))) | (![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))))),
% 1.46/1.18 inference(tautology,[status(thm)],[])).
% 1.46/1.18 tff(138,plain,
% 1.46/1.18 (![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)))),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[137, 72])).
% 1.46/1.18 tff(139,plain,
% 1.46/1.18 ((~(![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1))))) | ![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)))),
% 1.46/1.18 inference(tautology,[status(thm)],[])).
% 1.46/1.18 tff(140,plain,
% 1.46/1.18 (![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), succ(B!0))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), tptp_fun_C_8(B!0, A!1)))),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[139, 138])).
% 1.46/1.18 tff(141,plain,
% 1.46/1.18 (![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)))),
% 1.46/1.18 inference(unit_resolution,[status(thm)],[140, 123, 98])).
% 1.46/1.18 tff(142,plain,
% 1.46/1.18 (((~![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)))) | ((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))))) <=> ((~![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))))),
% 1.46/1.18 inference(rewrite,[status(thm)],[])).
% 1.46/1.18 tff(143,plain,
% 1.46/1.18 (((~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | $false) <=> ((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))))),
% 1.46/1.18 inference(rewrite,[status(thm)],[])).
% 1.46/1.18 tff(144,plain,
% 1.46/1.18 ((~$true) <=> $false),
% 1.46/1.18 inference(rewrite,[status(thm)],[])).
% 1.46/1.18 tff(145,plain,
% 1.46/1.18 ((tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1))) <=> $true),
% 1.46/1.18 inference(rewrite,[status(thm)],[])).
% 1.46/1.18 tff(146,plain,
% 1.46/1.18 ((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) <=> (~$true)),
% 1.46/1.18 inference(monotonicity,[status(thm)],[145])).
% 1.46/1.18 tff(147,plain,
% 1.46/1.18 ((~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) <=> $false),
% 1.46/1.18 inference(transitivity,[status(thm)],[146, 144])).
% 1.46/1.18 tff(148,plain,
% 1.46/1.18 (((~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1))))) <=> ((~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | $false)),
% 1.46/1.18 inference(monotonicity,[status(thm)],[147])).
% 1.46/1.18 tff(149,plain,
% 1.46/1.18 (((~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1))))) <=> ((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))))),
% 1.46/1.18 inference(transitivity,[status(thm)],[148, 143])).
% 1.46/1.18 tff(150,plain,
% 1.46/1.18 (((~![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)))) | ((~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))))) <=> ((~![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)))) | ((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1))))))),
% 1.46/1.18 inference(monotonicity,[status(thm)],[149])).
% 1.46/1.18 tff(151,plain,
% 1.46/1.18 (((~![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)))) | ((~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))))) <=> ((~![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))))),
% 1.46/1.18 inference(transitivity,[status(thm)],[150, 142])).
% 1.46/1.18 tff(152,plain,
% 1.46/1.18 ((~![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)))) | ((~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)))))),
% 1.46/1.18 inference(quant_inst,[status(thm)],[])).
% 1.46/1.19 tff(153,plain,
% 1.46/1.19 ((~![E: $i] : ((~ordinal(E)) | (~in(E, A!1)) | (~(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)) = E)))) | (~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1))))),
% 1.46/1.19 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.46/1.19 tff(154,plain,
% 1.46/1.19 ((~in(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1)), A!1)) | (~ordinal(tptp_fun_D_2(tptp_fun_C_8(B!0, A!1))))),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[153, 141])).
% 1.46/1.19 tff(155,plain,
% 1.46/1.19 ($false),
% 1.46/1.19 inference(unit_resolution,[status(thm)],[154, 136, 131])).
% 1.46/1.19 % SZS output end Proof
%------------------------------------------------------------------------------