TSTP Solution File: SEU280+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU280+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:28:39 EDT 2022
% Result : Theorem 1.97s 1.47s
% Output : Proof 2.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SEU280+1 : TPTP v8.1.0. Released v3.3.0.
% 0.02/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.31 % Computer : n011.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Sat Sep 3 11:25:58 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.32 Usage: tptp [options] [-file:]file
% 0.12/0.32 -h, -? prints this message.
% 0.12/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.32 -m, -model generate model.
% 0.12/0.32 -p, -proof generate proof.
% 0.12/0.32 -c, -core generate unsat core of named formulas.
% 0.12/0.32 -st, -statistics display statistics.
% 0.12/0.32 -t:timeout set timeout (in second).
% 0.12/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.32 -<param>:<value> configuration parameter and value.
% 0.12/0.32 -o:<output-file> file to place output in.
% 1.97/1.47 % SZS status Theorem
% 1.97/1.47 % SZS output start Proof
% 1.97/1.47 tff(tptp_fun_C_1_type, type, (
% 1.97/1.47 tptp_fun_C_1: $i > $i)).
% 1.97/1.47 tff(tptp_fun_B_6_type, type, (
% 1.97/1.47 tptp_fun_B_6: $i > $i)).
% 1.97/1.47 tff(tptp_fun_A_0_type, type, (
% 1.97/1.47 tptp_fun_A_0: $i)).
% 1.97/1.47 tff(tptp_fun_D_7_type, type, (
% 1.97/1.47 tptp_fun_D_7: ( $i * $i ) > $i)).
% 1.97/1.47 tff(in_type, type, (
% 1.97/1.47 in: ( $i * $i ) > $o)).
% 1.97/1.47 tff(ordinal_type, type, (
% 1.97/1.47 ordinal: $i > $o)).
% 1.97/1.47 tff(tptp_fun_D_3_type, type, (
% 1.97/1.47 tptp_fun_D_3: $i)).
% 1.97/1.47 tff(tptp_fun_B_5_type, type, (
% 1.97/1.47 tptp_fun_B_5: $i)).
% 1.97/1.47 tff(tptp_fun_C_4_type, type, (
% 1.97/1.47 tptp_fun_C_4: $i)).
% 1.97/1.47 tff(tptp_fun_A_2_type, type, (
% 1.97/1.47 tptp_fun_A_2: $i)).
% 1.97/1.47 tff(1,assumption,((~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0)))))))), introduced(assumption)).
% 1.97/1.47 tff(2,assumption,(~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))), introduced(assumption)).
% 1.97/1.47 tff(3,plain,
% 1.97/1.47 (((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3))) | (B!5 = D!3)),
% 1.97/1.47 inference(tautology,[status(thm)],[])).
% 1.97/1.47 tff(4,plain,
% 1.97/1.47 (B!5 = D!3),
% 1.97/1.47 inference(unit_resolution,[status(thm)],[3, 2])).
% 1.97/1.47 tff(5,plain,
% 1.97/1.47 (((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3))) | (B!5 = C!4)),
% 1.97/1.47 inference(tautology,[status(thm)],[])).
% 1.97/1.47 tff(6,plain,
% 1.97/1.47 (B!5 = C!4),
% 1.97/1.47 inference(unit_resolution,[status(thm)],[5, 2])).
% 1.97/1.47 tff(7,plain,
% 1.97/1.47 (C!4 = B!5),
% 1.97/1.47 inference(symmetry,[status(thm)],[6])).
% 1.97/1.47 tff(8,plain,
% 1.97/1.47 (C!4 = D!3),
% 1.97/1.47 inference(transitivity,[status(thm)],[7, 4])).
% 1.97/1.47 tff(9,plain,
% 1.97/1.47 (((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3))) | (~(C!4 = D!3))),
% 1.97/1.47 inference(tautology,[status(thm)],[])).
% 1.97/1.47 tff(10,plain,
% 1.97/1.47 (~(C!4 = D!3)),
% 1.97/1.47 inference(unit_resolution,[status(thm)],[9, 2])).
% 1.97/1.47 tff(11,plain,
% 1.97/1.47 ($false),
% 1.97/1.47 inference(unit_resolution,[status(thm)],[10, 8])).
% 1.97/1.47 tff(12,plain,((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3))), inference(lemma,lemma(discharge,[]))).
% 1.97/1.47 tff(13,plain,
% 1.97/1.47 (^[A: $i, C: $i, D: $i] : rewrite(((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A))))))))),
% 1.97/1.47 inference(bind,[status(th)],[])).
% 1.97/1.47 tff(14,plain,
% 1.97/1.47 (![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))),
% 1.97/1.47 inference(quant_intro,[status(thm)],[13])).
% 1.97/1.47 tff(15,plain,
% 1.97/1.47 (^[A: $i, C: $i, D: $i] : refl(((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))))),
% 1.97/1.48 inference(bind,[status(th)],[])).
% 1.97/1.48 tff(16,plain,
% 1.97/1.48 (![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))),
% 1.97/1.48 inference(quant_intro,[status(thm)],[15])).
% 1.97/1.48 tff(17,plain,
% 1.97/1.48 (![A: $i] : ![C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))),
% 1.97/1.48 inference(pull_quant,[status(thm)],[])).
% 1.97/1.48 tff(18,plain,
% 1.97/1.48 (^[A: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant((in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))) <=> ![D: $i] : (in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))), ((~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))) <=> (~![D: $i] : (in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))), pull_quant((~![D: $i] : (in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))) <=> ?[D: $i] : (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))), ((~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))) <=> ?[D: $i] : (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))), (((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))) <=> ((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | ?[D: $i] : (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))), pull_quant(((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | ?[D: $i] : (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))) <=> ?[D: $i] : ((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))), (((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))) <=> ?[D: $i] : ((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))), ((~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))) <=> (~?[D: $i] : ((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))), pull_quant((~?[D: $i] : ((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))) <=> ![D: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))), ((~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))) <=> ![D: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))))), (![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))) <=> ![C: $i] : ![D: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))), pull_quant(![C: $i] : ![D: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))), (![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))), (((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i, D: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))))), pull_quant(((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i, D: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ![C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))), (((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ![C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))))),
% 1.97/1.48 inference(bind,[status(th)],[])).
% 1.97/1.48 tff(19,plain,
% 1.97/1.48 (![A: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ![A: $i] : ![C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))),
% 1.97/1.48 inference(quant_intro,[status(thm)],[18])).
% 1.97/1.48 tff(20,plain,
% 1.97/1.48 (![A: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))),
% 1.97/1.48 inference(transitivity,[status(thm)],[19, 17])).
% 1.97/1.48 tff(21,plain,
% 1.97/1.48 (![A: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))),
% 1.97/1.48 inference(transitivity,[status(thm)],[20, 16])).
% 1.97/1.48 tff(22,plain,
% 1.97/1.48 (^[A: $i] : rewrite(((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))))),
% 1.97/1.48 inference(bind,[status(th)],[])).
% 1.97/1.48 tff(23,plain,
% 1.97/1.48 (![A: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ![A: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))),
% 1.97/1.48 inference(quant_intro,[status(thm)],[22])).
% 1.97/1.48 tff(24,plain,
% 1.97/1.48 (![A: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))) <=> ![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))),
% 1.97/1.48 inference(transitivity,[status(thm)],[23, 21])).
% 1.97/1.48 tff(25,plain,
% 1.97/1.48 (^[A: $i] : rewrite(((~((~((B!5 = C!4) & ordinal(C!4) & (B!5 = D!3) & ordinal(D!3))) | (C!4 = D!3))) | ![C: $i] : (((~in(C, tptp_fun_B_6(A))) | (in(tptp_fun_D_7(C, A), A) & (tptp_fun_D_7(C, A) = C) & ordinal(C))) & (in(C, tptp_fun_B_6(A)) | ![D: $i] : (~(in(D, A) & (D = C) & ordinal(C)))))) <=> ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C)))))))))),
% 1.97/1.48 inference(bind,[status(th)],[])).
% 1.97/1.48 tff(26,plain,
% 1.97/1.48 (![A: $i] : ((~((~((B!5 = C!4) & ordinal(C!4) & (B!5 = D!3) & ordinal(D!3))) | (C!4 = D!3))) | ![C: $i] : (((~in(C, tptp_fun_B_6(A))) | (in(tptp_fun_D_7(C, A), A) & (tptp_fun_D_7(C, A) = C) & ordinal(C))) & (in(C, tptp_fun_B_6(A)) | ![D: $i] : (~(in(D, A) & (D = C) & ordinal(C)))))) <=> ![A: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))),
% 1.97/1.48 inference(quant_intro,[status(thm)],[25])).
% 1.97/1.48 tff(27,plain,
% 1.97/1.48 (![A: $i] : ((~![B: $i, C: $i, D: $i] : ((~((B = C) & ordinal(C) & (B = D) & ordinal(D))) | (C = D))) | ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, A) & (D = C) & ordinal(C)))) <=> ![A: $i] : ((~![B: $i, C: $i, D: $i] : ((~((B = C) & ordinal(C) & (B = D) & ordinal(D))) | (C = D))) | ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, A) & (D = C) & ordinal(C))))),
% 1.97/1.48 inference(rewrite,[status(thm)],[])).
% 1.97/1.48 tff(28,plain,
% 1.97/1.48 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((((B = C) & ordinal(C)) & (B = D)) <=> ((B = C) & ordinal(C) & (B = D))), (((((B = C) & ordinal(C)) & (B = D)) & ordinal(D)) <=> (((B = C) & ordinal(C) & (B = D)) & ordinal(D)))), rewrite((((B = C) & ordinal(C) & (B = D)) & ordinal(D)) <=> ((B = C) & ordinal(C) & (B = D) & ordinal(D))), (((((B = C) & ordinal(C)) & (B = D)) & ordinal(D)) <=> ((B = C) & ordinal(C) & (B = D) & ordinal(D)))), ((((((B = C) & ordinal(C)) & (B = D)) & ordinal(D)) => (C = D)) <=> (((B = C) & ordinal(C) & (B = D) & ordinal(D)) => (C = D)))), rewrite((((B = C) & ordinal(C) & (B = D) & ordinal(D)) => (C = D)) <=> ((~((B = C) & ordinal(C) & (B = D) & ordinal(D))) | (C = D))), ((((((B = C) & ordinal(C)) & (B = D)) & ordinal(D)) => (C = D)) <=> ((~((B = C) & ordinal(C) & (B = D) & ordinal(D))) | (C = D))))), (![B: $i, C: $i, D: $i] : (((((B = C) & ordinal(C)) & (B = D)) & ordinal(D)) => (C = D)) <=> ![B: $i, C: $i, D: $i] : ((~((B = C) & ordinal(C) & (B = D) & ordinal(D))) | (C = D)))), quant_intro(proof_bind(^[B: $i] : quant_intro(proof_bind(^[C: $i] : rewrite((in(C, B) <=> ?[D: $i] : ((in(D, A) & (D = C)) & ordinal(C))) <=> (in(C, B) <=> ?[D: $i] : (in(D, A) & (D = C) & ordinal(C))))), (![C: $i] : (in(C, B) <=> ?[D: $i] : ((in(D, A) & (D = C)) & ordinal(C))) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, A) & (D = C) & ordinal(C)))))), (?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : ((in(D, A) & (D = C)) & ordinal(C))) <=> ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, A) & (D = C) & ordinal(C))))), ((![B: $i, C: $i, D: $i] : (((((B = C) & ordinal(C)) & (B = D)) & ordinal(D)) => (C = D)) => ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : ((in(D, A) & (D = C)) & ordinal(C)))) <=> (![B: $i, C: $i, D: $i] : ((~((B = C) & ordinal(C) & (B = D) & ordinal(D))) | (C = D)) => ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, A) & (D = C) & ordinal(C)))))), rewrite((![B: $i, C: $i, D: $i] : ((~((B = C) & ordinal(C) & (B = D) & ordinal(D))) | (C = D)) => ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, A) & (D = C) & ordinal(C)))) <=> ((~![B: $i, C: $i, D: $i] : ((~((B = C) & ordinal(C) & (B = D) & ordinal(D))) | (C = D))) | ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, A) & (D = C) & ordinal(C))))), ((![B: $i, C: $i, D: $i] : (((((B = C) & ordinal(C)) & (B = D)) & ordinal(D)) => (C = D)) => ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : ((in(D, A) & (D = C)) & ordinal(C)))) <=> ((~![B: $i, C: $i, D: $i] : ((~((B = C) & ordinal(C) & (B = D) & ordinal(D))) | (C = D))) | ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, A) & (D = C) & ordinal(C))))))),
% 1.97/1.48 inference(bind,[status(th)],[])).
% 1.97/1.48 tff(29,plain,
% 1.97/1.48 (![A: $i] : (![B: $i, C: $i, D: $i] : (((((B = C) & ordinal(C)) & (B = D)) & ordinal(D)) => (C = D)) => ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : ((in(D, A) & (D = C)) & ordinal(C)))) <=> ![A: $i] : ((~![B: $i, C: $i, D: $i] : ((~((B = C) & ordinal(C) & (B = D) & ordinal(D))) | (C = D))) | ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, A) & (D = C) & ordinal(C))))),
% 1.97/1.48 inference(quant_intro,[status(thm)],[28])).
% 1.97/1.48 tff(30,axiom,(![A: $i] : (![B: $i, C: $i, D: $i] : (((((B = C) & ordinal(C)) & (B = D)) & ordinal(D)) => (C = D)) => ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : ((in(D, A) & (D = C)) & ordinal(C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_tarski__e6_22__wellord2__1')).
% 1.97/1.48 tff(31,plain,
% 1.97/1.48 (![A: $i] : ((~![B: $i, C: $i, D: $i] : ((~((B = C) & ordinal(C) & (B = D) & ordinal(D))) | (C = D))) | ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, A) & (D = C) & ordinal(C))))),
% 1.97/1.48 inference(modus_ponens,[status(thm)],[30, 29])).
% 1.97/1.48 tff(32,plain,
% 1.97/1.48 (![A: $i] : ((~![B: $i, C: $i, D: $i] : ((~((B = C) & ordinal(C) & (B = D) & ordinal(D))) | (C = D))) | ?[B: $i] : ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(D, A) & (D = C) & ordinal(C))))),
% 1.97/1.48 inference(modus_ponens,[status(thm)],[31, 27])).
% 1.97/1.48 tff(33,plain,(
% 1.97/1.48 ![A: $i] : ((~((~((B!5 = C!4) & ordinal(C!4) & (B!5 = D!3) & ordinal(D!3))) | (C!4 = D!3))) | ![C: $i] : (((~in(C, tptp_fun_B_6(A))) | (in(tptp_fun_D_7(C, A), A) & (tptp_fun_D_7(C, A) = C) & ordinal(C))) & (in(C, tptp_fun_B_6(A)) | ![D: $i] : (~(in(D, A) & (D = C) & ordinal(C))))))),
% 1.97/1.48 inference(skolemize,[status(sab)],[32])).
% 1.97/1.48 tff(34,plain,
% 1.97/1.48 (![A: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | ![C: $i] : (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ![D: $i] : ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))),
% 1.97/1.48 inference(modus_ponens,[status(thm)],[33, 26])).
% 1.97/1.48 tff(35,plain,
% 1.97/1.48 (![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~(in(C, tptp_fun_B_6(A)) | ((~in(D, A)) | (~(D = C)) | (~ordinal(C))))))))),
% 1.97/1.48 inference(modus_ponens,[status(thm)],[34, 24])).
% 1.97/1.48 tff(36,plain,
% 1.97/1.48 (![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))),
% 1.97/1.48 inference(modus_ponens,[status(thm)],[35, 14])).
% 1.97/1.48 tff(37,plain,
% 1.97/1.48 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))))))),
% 1.97/1.48 inference(rewrite,[status(thm)],[])).
% 1.97/1.48 tff(38,plain,
% 1.97/1.48 (((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))))) <=> ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))))))),
% 1.97/1.48 inference(rewrite,[status(thm)],[])).
% 1.97/1.48 tff(39,plain,
% 1.97/1.48 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0)))))))))))),
% 1.97/1.48 inference(monotonicity,[status(thm)],[38])).
% 1.97/1.48 tff(40,plain,
% 1.97/1.48 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))))))),
% 1.97/1.48 inference(transitivity,[status(thm)],[39, 37])).
% 1.97/1.48 tff(41,plain,
% 1.97/1.48 ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))))),
% 1.97/1.48 inference(quant_inst,[status(thm)],[])).
% 1.97/1.48 tff(42,plain,
% 1.97/1.48 ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0)))))))))),
% 1.97/1.48 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.97/1.48 tff(43,plain,
% 1.97/1.48 ($false),
% 1.97/1.48 inference(unit_resolution,[status(thm)],[42, 36, 12, 1])).
% 1.97/1.48 tff(44,plain,(~((~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/1.48 tff(45,plain,
% 1.97/1.48 (((~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0)))))))) | ((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))),
% 1.97/1.49 inference(tautology,[status(thm)],[])).
% 1.97/1.49 tff(46,plain,
% 1.97/1.49 ((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))),
% 1.97/1.49 inference(unit_resolution,[status(thm)],[45, 44])).
% 1.97/1.49 tff(47,assumption,(~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))), introduced(assumption)).
% 1.97/1.49 tff(48,plain,
% 1.97/1.49 (^[B: $i] : trans(monotonicity(rewrite((in(tptp_fun_C_1(B), A!0) & ordinal(tptp_fun_C_1(B))) <=> (~((~in(tptp_fun_C_1(B), A!0)) | (~ordinal(tptp_fun_C_1(B)))))), (((~in(tptp_fun_C_1(B), B)) <=> (in(tptp_fun_C_1(B), A!0) & ordinal(tptp_fun_C_1(B)))) <=> ((~in(tptp_fun_C_1(B), B)) <=> (~((~in(tptp_fun_C_1(B), A!0)) | (~ordinal(tptp_fun_C_1(B)))))))), rewrite(((~in(tptp_fun_C_1(B), B)) <=> (~((~in(tptp_fun_C_1(B), A!0)) | (~ordinal(tptp_fun_C_1(B)))))) <=> (in(tptp_fun_C_1(B), B) <=> ((~in(tptp_fun_C_1(B), A!0)) | (~ordinal(tptp_fun_C_1(B)))))), (((~in(tptp_fun_C_1(B), B)) <=> (in(tptp_fun_C_1(B), A!0) & ordinal(tptp_fun_C_1(B)))) <=> (in(tptp_fun_C_1(B), B) <=> ((~in(tptp_fun_C_1(B), A!0)) | (~ordinal(tptp_fun_C_1(B)))))))),
% 1.97/1.49 inference(bind,[status(th)],[])).
% 1.97/1.49 tff(49,plain,
% 1.97/1.49 (![B: $i] : ((~in(tptp_fun_C_1(B), B)) <=> (in(tptp_fun_C_1(B), A!0) & ordinal(tptp_fun_C_1(B)))) <=> ![B: $i] : (in(tptp_fun_C_1(B), B) <=> ((~in(tptp_fun_C_1(B), A!0)) | (~ordinal(tptp_fun_C_1(B)))))),
% 1.97/1.49 inference(quant_intro,[status(thm)],[48])).
% 1.97/1.49 tff(50,plain,
% 1.97/1.49 (^[B: $i] : rewrite((~(in(tptp_fun_C_1(B), B) <=> (in(tptp_fun_C_1(B), A!0) & ordinal(tptp_fun_C_1(B))))) <=> ((~in(tptp_fun_C_1(B), B)) <=> (in(tptp_fun_C_1(B), A!0) & ordinal(tptp_fun_C_1(B)))))),
% 1.97/1.49 inference(bind,[status(th)],[])).
% 1.97/1.49 tff(51,plain,
% 1.97/1.49 (![B: $i] : (~(in(tptp_fun_C_1(B), B) <=> (in(tptp_fun_C_1(B), A!0) & ordinal(tptp_fun_C_1(B))))) <=> ![B: $i] : ((~in(tptp_fun_C_1(B), B)) <=> (in(tptp_fun_C_1(B), A!0) & ordinal(tptp_fun_C_1(B))))),
% 1.97/1.49 inference(quant_intro,[status(thm)],[50])).
% 1.97/1.49 tff(52,plain,
% 1.97/1.49 ((~![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C)))) <=> (~![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C))))),
% 1.97/1.49 inference(rewrite,[status(thm)],[])).
% 1.97/1.49 tff(53,axiom,(~![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_xboole_0__e6_22__wellord2')).
% 1.97/1.49 tff(54,plain,
% 1.97/1.49 (~![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C)))),
% 1.97/1.49 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.97/1.49 tff(55,plain,
% 1.97/1.49 (~![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C)))),
% 1.97/1.49 inference(modus_ponens,[status(thm)],[54, 52])).
% 1.97/1.49 tff(56,plain,
% 1.97/1.49 (~![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C)))),
% 1.97/1.49 inference(modus_ponens,[status(thm)],[55, 52])).
% 1.97/1.49 tff(57,plain,
% 1.97/1.49 (~![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C)))),
% 1.97/1.49 inference(modus_ponens,[status(thm)],[56, 52])).
% 1.97/1.49 tff(58,plain,
% 1.97/1.49 (~![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C)))),
% 1.97/1.49 inference(modus_ponens,[status(thm)],[57, 52])).
% 1.97/1.49 tff(59,plain,
% 1.97/1.49 (~![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C)))),
% 1.97/1.49 inference(modus_ponens,[status(thm)],[58, 52])).
% 1.97/1.49 tff(60,plain,
% 1.97/1.49 (~![A: $i] : ?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A) & ordinal(C)))),
% 1.97/1.49 inference(modus_ponens,[status(thm)],[59, 52])).
% 1.97/1.49 tff(61,plain,(
% 1.97/1.49 $oeq((~?[B: $i] : ![C: $i] : (in(C, B) <=> (in(C, A!0) & ordinal(C)))), ![B: $i] : (~(in(tptp_fun_C_1(B), B) <=> (in(tptp_fun_C_1(B), A!0) & ordinal(tptp_fun_C_1(B))))))),
% 1.97/1.49 inference(transitivity,[status(sab)],[60])).
% 1.97/1.49 tff(62,plain,
% 1.97/1.49 (![B: $i] : ((~in(tptp_fun_C_1(B), B)) <=> (in(tptp_fun_C_1(B), A!0) & ordinal(tptp_fun_C_1(B))))),
% 1.97/1.49 inference(modus_ponens,[status(thm)],[61, 51])).
% 1.97/1.49 tff(63,plain,
% 1.97/1.49 (![B: $i] : (in(tptp_fun_C_1(B), B) <=> ((~in(tptp_fun_C_1(B), A!0)) | (~ordinal(tptp_fun_C_1(B)))))),
% 1.97/1.49 inference(modus_ponens,[status(thm)],[62, 49])).
% 1.97/1.49 tff(64,plain,
% 1.97/1.49 ((~![B: $i] : (in(tptp_fun_C_1(B), B) <=> ((~in(tptp_fun_C_1(B), A!0)) | (~ordinal(tptp_fun_C_1(B)))))) | (in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) <=> ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))),
% 1.97/1.49 inference(quant_inst,[status(thm)],[])).
% 1.97/1.49 tff(65,plain,
% 1.97/1.49 (in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) <=> ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))),
% 1.97/1.49 inference(unit_resolution,[status(thm)],[64, 63])).
% 1.97/1.49 tff(66,plain,
% 1.97/1.49 ((~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) <=> ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))),
% 1.97/1.49 inference(tautology,[status(thm)],[])).
% 1.97/1.49 tff(67,plain,
% 1.97/1.49 (in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))),
% 1.97/1.49 inference(unit_resolution,[status(thm)],[66, 65])).
% 1.97/1.49 tff(68,plain,
% 1.97/1.49 (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))),
% 1.97/1.49 inference(unit_resolution,[status(thm)],[67, 47])).
% 1.97/1.49 tff(69,plain,
% 1.97/1.49 (((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))) | ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))),
% 1.97/1.49 inference(tautology,[status(thm)],[])).
% 1.97/1.49 tff(70,plain,
% 1.97/1.49 (ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))),
% 1.97/1.49 inference(unit_resolution,[status(thm)],[69, 68])).
% 1.97/1.49 tff(71,assumption,((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))), introduced(assumption)).
% 1.97/1.49 tff(72,plain,
% 1.97/1.49 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))),
% 1.97/1.49 inference(rewrite,[status(thm)],[])).
% 1.97/1.49 tff(73,plain,
% 1.97/1.49 (((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))) <=> ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))),
% 1.97/1.49 inference(rewrite,[status(thm)],[])).
% 1.97/1.49 tff(74,plain,
% 1.97/1.49 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))))))),
% 1.97/1.49 inference(monotonicity,[status(thm)],[73])).
% 1.97/1.49 tff(75,plain,
% 1.97/1.49 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))),
% 1.97/1.49 inference(transitivity,[status(thm)],[74, 72])).
% 1.97/1.49 tff(76,plain,
% 1.97/1.49 ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))),
% 1.97/1.49 inference(quant_inst,[status(thm)],[])).
% 1.97/1.49 tff(77,plain,
% 1.97/1.49 ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))))),
% 1.97/1.49 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.97/1.49 tff(78,plain,
% 1.97/1.49 ($false),
% 1.97/1.49 inference(unit_resolution,[status(thm)],[77, 36, 12, 71])).
% 1.97/1.49 tff(79,plain,(~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))))), inference(lemma,lemma(discharge,[]))).
% 1.97/1.49 tff(80,plain,
% 1.97/1.49 (((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))) | (in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))),
% 1.97/1.49 inference(tautology,[status(thm)],[])).
% 1.97/1.49 tff(81,plain,
% 1.97/1.49 (in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))),
% 1.97/1.49 inference(unit_resolution,[status(thm)],[80, 79])).
% 1.97/1.49 tff(82,plain,
% 1.97/1.49 ((~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))),
% 1.97/1.49 inference(tautology,[status(thm)],[])).
% 1.97/1.49 tff(83,plain,
% 1.97/1.49 (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))),
% 1.97/1.49 inference(unit_resolution,[status(thm)],[82, 70, 47, 81])).
% 1.97/1.49 tff(84,assumption,((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))))), introduced(assumption)).
% 2.03/1.49 tff(85,plain,
% 2.03/1.49 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)))))))),
% 2.03/1.49 inference(rewrite,[status(thm)],[])).
% 2.03/1.49 tff(86,plain,
% 2.03/1.49 (((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))))))) <=> ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)))))))),
% 2.03/1.49 inference(rewrite,[status(thm)],[])).
% 2.03/1.49 tff(87,plain,
% 2.03/1.49 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))))))))),
% 2.03/1.49 inference(monotonicity,[status(thm)],[86])).
% 2.03/1.49 tff(88,plain,
% 2.03/1.49 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)))))))),
% 2.03/1.49 inference(transitivity,[status(thm)],[87, 85])).
% 2.03/1.49 tff(89,plain,
% 2.03/1.49 ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)))))))),
% 2.03/1.49 inference(quant_inst,[status(thm)],[])).
% 2.03/1.49 tff(90,plain,
% 2.03/1.49 ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))))))),
% 2.03/1.49 inference(modus_ponens,[status(thm)],[89, 88])).
% 2.03/1.49 tff(91,plain,
% 2.03/1.49 ($false),
% 2.03/1.49 inference(unit_resolution,[status(thm)],[90, 36, 12, 84])).
% 2.03/1.49 tff(92,plain,(~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)))))), inference(lemma,lemma(discharge,[]))).
% 2.03/1.49 tff(93,plain,
% 2.03/1.49 (((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))))) | ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)))),
% 2.03/1.50 inference(tautology,[status(thm)],[])).
% 2.03/1.50 tff(94,plain,
% 2.03/1.50 ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))),
% 2.03/1.50 inference(unit_resolution,[status(thm)],[93, 92])).
% 2.03/1.50 tff(95,plain,
% 2.03/1.50 (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)))))),
% 2.03/1.50 inference(unit_resolution,[status(thm)],[90, 36, 12])).
% 2.03/1.50 tff(96,plain,
% 2.03/1.50 (((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))) | (~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))))) | ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))),
% 2.03/1.50 inference(tautology,[status(thm)],[])).
% 2.03/1.50 tff(97,plain,
% 2.03/1.50 ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0))))),
% 2.03/1.50 inference(unit_resolution,[status(thm)],[96, 95])).
% 2.03/1.50 tff(98,plain,
% 2.03/1.50 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))) | (~((~in(A!2, tptp_fun_B_6(A!0))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) | (~(A!2 = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))) | (~((~in(A!2, tptp_fun_B_6(A!0))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) | (~(A!2 = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))))),
% 2.03/1.50 inference(rewrite,[status(thm)],[])).
% 2.03/1.50 tff(99,plain,
% 2.03/1.50 (((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(A!2, tptp_fun_B_6(A!0))) | (~(A!2 = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))))) <=> ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))) | (~((~in(A!2, tptp_fun_B_6(A!0))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) | (~(A!2 = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))))),
% 2.03/1.50 inference(rewrite,[status(thm)],[])).
% 2.03/1.50 tff(100,plain,
% 2.03/1.50 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(A!2, tptp_fun_B_6(A!0))) | (~(A!2 = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))) | (~((~in(A!2, tptp_fun_B_6(A!0))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) | (~(A!2 = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))))))),
% 2.03/1.50 inference(monotonicity,[status(thm)],[99])).
% 2.03/1.50 tff(101,plain,
% 2.03/1.50 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(A!2, tptp_fun_B_6(A!0))) | (~(A!2 = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))) | (~((~in(A!2, tptp_fun_B_6(A!0))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) | (~(A!2 = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))))),
% 2.03/1.50 inference(transitivity,[status(thm)],[100, 98])).
% 2.03/1.50 tff(102,plain,
% 2.03/1.50 ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(A!2, tptp_fun_B_6(A!0))) | (~(A!2 = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))))),
% 2.03/1.50 inference(quant_inst,[status(thm)],[])).
% 2.03/1.50 tff(103,plain,
% 2.03/1.50 ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))) | (~((~in(A!2, tptp_fun_B_6(A!0))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) | (~(A!2 = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))))),
% 2.03/1.50 inference(modus_ponens,[status(thm)],[102, 101])).
% 2.03/1.50 tff(104,plain,
% 2.03/1.50 (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))) | (~((~in(A!2, tptp_fun_B_6(A!0))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) | (~(A!2 = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))),
% 2.03/1.50 inference(unit_resolution,[status(thm)],[103, 36, 12])).
% 2.03/1.50 tff(105,plain,
% 2.03/1.50 (((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))) | (~((~in(A!2, tptp_fun_B_6(A!0))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) | (~(A!2 = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))) | ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))),
% 2.03/1.50 inference(tautology,[status(thm)],[])).
% 2.03/1.50 tff(106,plain,
% 2.03/1.50 ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0)))))),
% 2.03/1.50 inference(unit_resolution,[status(thm)],[105, 104])).
% 2.03/1.50 tff(107,assumption,(~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)), introduced(assumption)).
% 2.03/1.50 tff(108,plain,
% 2.03/1.50 (((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)),
% 2.03/1.50 inference(tautology,[status(thm)],[])).
% 2.03/1.50 tff(109,plain,
% 2.03/1.50 ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))),
% 2.03/1.50 inference(unit_resolution,[status(thm)],[108, 107])).
% 2.03/1.50 tff(110,plain,
% 2.03/1.50 (in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))),
% 2.03/1.50 inference(unit_resolution,[status(thm)],[67, 109])).
% 2.03/1.50 tff(111,plain,
% 2.03/1.50 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))),
% 2.03/1.50 inference(rewrite,[status(thm)],[])).
% 2.03/1.50 tff(112,plain,
% 2.03/1.50 (((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))) <=> ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))),
% 2.03/1.50 inference(rewrite,[status(thm)],[])).
% 2.03/1.50 tff(113,plain,
% 2.03/1.50 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))))))),
% 2.03/1.50 inference(monotonicity,[status(thm)],[112])).
% 2.03/1.50 tff(114,plain,
% 2.03/1.50 (((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) <=> ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))),
% 2.03/1.50 inference(transitivity,[status(thm)],[113, 111])).
% 2.03/1.50 tff(115,plain,
% 2.03/1.50 ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~((~in(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))),
% 2.03/1.50 inference(quant_inst,[status(thm)],[])).
% 2.03/1.50 tff(116,plain,
% 2.03/1.50 ((~![A: $i, C: $i, D: $i] : ((~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(C, tptp_fun_B_6(A))) | (~((~ordinal(C)) | (~in(tptp_fun_D_7(C, A), A)) | (~(tptp_fun_D_7(C, A) = C)))))) | (~((~in(D, A)) | (~(D = C)) | (~ordinal(C)) | in(C, tptp_fun_B_6(A)))))))) | (~((C!4 = D!3) | (~(B!5 = C!4)) | (~ordinal(C!4)) | (~(B!5 = D!3)) | (~ordinal(D!3)))) | (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))))),
% 2.03/1.50 inference(modus_ponens,[status(thm)],[115, 114])).
% 2.03/1.50 tff(117,plain,
% 2.03/1.50 (~((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))))))),
% 2.03/1.50 inference(unit_resolution,[status(thm)],[116, 36, 12])).
% 2.03/1.50 tff(118,plain,
% 2.03/1.50 (((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0))))))) | ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))),
% 2.03/1.50 inference(tautology,[status(thm)],[])).
% 2.03/1.50 tff(119,plain,
% 2.03/1.50 ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))),
% 2.03/1.50 inference(unit_resolution,[status(thm)],[118, 117])).
% 2.03/1.50 tff(120,plain,
% 2.03/1.50 ((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))),
% 2.03/1.50 inference(tautology,[status(thm)],[])).
% 2.03/1.50 tff(121,plain,
% 2.03/1.50 ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))),
% 2.03/1.50 inference(unit_resolution,[status(thm)],[120, 119])).
% 2.03/1.50 tff(122,plain,
% 2.03/1.50 (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))),
% 2.03/1.50 inference(unit_resolution,[status(thm)],[121, 110])).
% 2.03/1.50 tff(123,plain,
% 2.03/1.50 (((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))) | (tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(124,plain,
% 2.03/1.51 (tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[123, 122])).
% 2.03/1.51 tff(125,plain,
% 2.03/1.51 (tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) = tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))),
% 2.03/1.51 inference(symmetry,[status(thm)],[124])).
% 2.03/1.51 tff(126,plain,
% 2.03/1.51 (in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) <=> in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))),
% 2.03/1.51 inference(monotonicity,[status(thm)],[125])).
% 2.03/1.51 tff(127,plain,
% 2.03/1.51 (in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0))) <=> in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))),
% 2.03/1.51 inference(symmetry,[status(thm)],[126])).
% 2.03/1.51 tff(128,plain,
% 2.03/1.51 (((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))) | in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(129,plain,
% 2.03/1.51 (in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[128, 122])).
% 2.03/1.51 tff(130,plain,
% 2.03/1.51 (in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))),
% 2.03/1.51 inference(modus_ponens,[status(thm)],[129, 127])).
% 2.03/1.51 tff(131,plain,
% 2.03/1.51 ((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0)))))),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(132,plain,
% 2.03/1.51 ((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0)))))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[131, 130])).
% 2.03/1.51 tff(133,plain,
% 2.03/1.51 (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[132, 106])).
% 2.03/1.51 tff(134,plain,
% 2.03/1.51 (((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0)))) | (tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(135,plain,
% 2.03/1.51 (tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[134, 133])).
% 2.03/1.51 tff(136,plain,
% 2.03/1.51 (in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0)) <=> in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))),
% 2.03/1.51 inference(monotonicity,[status(thm)],[135])).
% 2.03/1.51 tff(137,plain,
% 2.03/1.51 (((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0)))) | in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(138,plain,
% 2.03/1.51 (in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)), tptp_fun_B_6(A!0))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[137, 133])).
% 2.03/1.51 tff(139,plain,
% 2.03/1.51 (in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))),
% 2.03/1.51 inference(modus_ponens,[status(thm)],[138, 136])).
% 2.03/1.51 tff(140,plain,
% 2.03/1.51 ((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0))))),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(141,plain,
% 2.03/1.51 (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[140, 139, 97])).
% 2.03/1.51 tff(142,plain,
% 2.03/1.51 (((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0))) | (tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(143,plain,
% 2.03/1.51 (tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[142, 141])).
% 2.03/1.51 tff(144,plain,
% 2.03/1.51 (in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0) <=> in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)),
% 2.03/1.51 inference(monotonicity,[status(thm)],[143])).
% 2.03/1.51 tff(145,plain,
% 2.03/1.51 (in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) <=> in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)),
% 2.03/1.51 inference(symmetry,[status(thm)],[144])).
% 2.03/1.51 tff(146,plain,
% 2.03/1.51 ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) <=> (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0))),
% 2.03/1.51 inference(monotonicity,[status(thm)],[145])).
% 2.03/1.51 tff(147,plain,
% 2.03/1.51 (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)),
% 2.03/1.51 inference(modus_ponens,[status(thm)],[107, 146])).
% 2.03/1.51 tff(148,plain,
% 2.03/1.51 (((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0))) | in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(149,plain,
% 2.03/1.51 (in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0), A!0)),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[148, 141])).
% 2.03/1.51 tff(150,plain,
% 2.03/1.51 ($false),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[149, 147])).
% 2.03/1.51 tff(151,plain,(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)), inference(lemma,lemma(discharge,[]))).
% 2.03/1.51 tff(152,plain,
% 2.03/1.51 ((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(153,plain,
% 2.03/1.51 ((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0)))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[152, 151])).
% 2.03/1.51 tff(154,plain,
% 2.03/1.51 (in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[153, 70, 94])).
% 2.03/1.51 tff(155,plain,
% 2.03/1.51 ((~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))))) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(A!0))) | in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0)))),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(156,plain,
% 2.03/1.51 ($false),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[155, 154, 83, 70, 46])).
% 2.03/1.51 tff(157,plain,(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))), inference(lemma,lemma(discharge,[]))).
% 2.03/1.51 tff(158,plain,
% 2.03/1.51 (~((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[121, 157])).
% 2.03/1.51 tff(159,plain,
% 2.03/1.51 ((~(in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))) <=> ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(160,plain,
% 2.03/1.51 ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))) | ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[159, 65])).
% 2.03/1.51 tff(161,plain,
% 2.03/1.51 ((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[160, 157])).
% 2.03/1.51 tff(162,plain,
% 2.03/1.51 ((~((~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))))) | (~in(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), A!0)) | (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(163,plain,
% 2.03/1.51 (~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[162, 161, 151])).
% 2.03/1.51 tff(164,plain,
% 2.03/1.51 (((~ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))) | (~in(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))), tptp_fun_B_6(tptp_fun_B_6(A!0)))) | (~(tptp_fun_D_7(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))), tptp_fun_B_6(tptp_fun_B_6(A!0))) = tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0))))))) | ordinal(tptp_fun_C_1(tptp_fun_B_6(tptp_fun_B_6(tptp_fun_B_6(A!0)))))),
% 2.03/1.51 inference(tautology,[status(thm)],[])).
% 2.03/1.51 tff(165,plain,
% 2.03/1.51 ($false),
% 2.03/1.51 inference(unit_resolution,[status(thm)],[164, 163, 158])).
% 2.03/1.51 % SZS output end Proof
%------------------------------------------------------------------------------