TSTP Solution File: LAT294+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT294+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:32:46 EDT 2022
% Result : Theorem 3.28s 2.37s
% Output : Proof 3.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT294+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 13:18:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 3.28/2.37 % SZS status Theorem
% 3.28/2.37 % SZS output start Proof
% 3.28/2.37 tff(r5_binop_1_type, type, (
% 3.28/2.37 r5_binop_1: ( $i * $i * $i ) > $o)).
% 3.28/2.37 tff(k1_realset1_type, type, (
% 3.28/2.37 k1_realset1: ( $i * $i ) > $i)).
% 3.28/2.37 tff(tptp_fun_B_1_type, type, (
% 3.28/2.37 tptp_fun_B_1: $i)).
% 3.28/2.37 tff(tptp_fun_D_3_type, type, (
% 3.28/2.37 tptp_fun_D_3: $i)).
% 3.28/2.37 tff(tptp_fun_C_2_type, type, (
% 3.28/2.37 tptp_fun_C_2: $i)).
% 3.28/2.37 tff(r4_binop_1_type, type, (
% 3.28/2.37 r4_binop_1: ( $i * $i * $i ) > $o)).
% 3.28/2.37 tff(r6_binop_1_type, type, (
% 3.28/2.37 r6_binop_1: ( $i * $i * $i ) > $o)).
% 3.28/2.37 tff(m2_relset_1_type, type, (
% 3.28/2.37 m2_relset_1: ( $i * $i * $i ) > $o)).
% 3.28/2.37 tff(k2_zfmisc_1_type, type, (
% 3.28/2.37 k2_zfmisc_1: ( $i * $i ) > $i)).
% 3.28/2.37 tff(tptp_fun_F_5_type, type, (
% 3.28/2.37 tptp_fun_F_5: $i)).
% 3.28/2.37 tff(tptp_fun_A_0_type, type, (
% 3.28/2.37 tptp_fun_A_0: $i)).
% 3.28/2.37 tff(tptp_fun_E_4_type, type, (
% 3.28/2.37 tptp_fun_E_4: $i)).
% 3.28/2.37 tff(v1_funct_2_type, type, (
% 3.28/2.37 v1_funct_2: ( $i * $i * $i ) > $o)).
% 3.28/2.37 tff(v1_funct_1_type, type, (
% 3.28/2.37 v1_funct_1: $i > $o)).
% 3.28/2.37 tff(m1_subset_1_type, type, (
% 3.28/2.37 m1_subset_1: ( $i * $i ) > $o)).
% 3.28/2.37 tff(k1_zfmisc_1_type, type, (
% 3.28/2.37 k1_zfmisc_1: $i > $i)).
% 3.28/2.37 tff(v1_xboole_0_type, type, (
% 3.28/2.37 v1_xboole_0: $i > $o)).
% 3.28/2.37 tff(1,plain,
% 3.28/2.37 (((~v1_xboole_0(A!0)) & ((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0)) & v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))) <=> ((~v1_xboole_0(A!0)) & (~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0)) & v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(2,plain,
% 3.28/2.37 ((((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0))) & (v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))) <=> ((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0)) & v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(3,plain,
% 3.28/2.37 (((v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) & (v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))) <=> (v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(4,plain,
% 3.28/2.37 (((v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) & (v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))) <=> (v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(5,plain,
% 3.28/2.37 (((v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))) <=> (v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(6,plain,
% 3.28/2.37 ((~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))) <=> (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(7,plain,
% 3.28/2.37 ((~(~(v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)))) <=> (v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(8,plain,
% 3.28/2.37 (((~(~(v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)))) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))) <=> ((v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))),
% 3.28/2.37 inference(monotonicity,[status(thm)],[7, 6])).
% 3.28/2.37 tff(9,plain,
% 3.28/2.37 (((~(~(v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)))) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))) <=> (v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))),
% 3.28/2.37 inference(transitivity,[status(thm)],[8, 5])).
% 3.28/2.37 tff(10,plain,
% 3.28/2.37 ((~(~(v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)))) <=> (v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(11,plain,
% 3.28/2.37 (((~(~(v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)))) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))) <=> ((v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) & (v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))))),
% 3.28/2.37 inference(monotonicity,[status(thm)],[10, 9])).
% 3.28/2.37 tff(12,plain,
% 3.28/2.37 (((~(~(v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)))) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))) <=> (v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))),
% 3.28/2.37 inference(transitivity,[status(thm)],[11, 4])).
% 3.28/2.37 tff(13,plain,
% 3.28/2.37 ((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)))) <=> (v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0))),
% 3.28/2.37 inference(rewrite,[status(thm)],[])).
% 3.28/2.37 tff(14,plain,
% 3.28/2.37 (((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)))) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))))) <=> ((v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) & (v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))))),
% 3.28/2.38 inference(monotonicity,[status(thm)],[13, 12])).
% 3.28/2.38 tff(15,plain,
% 3.28/2.38 (((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)))) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))))) <=> (v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))),
% 3.28/2.38 inference(transitivity,[status(thm)],[14, 3])).
% 3.28/2.38 tff(16,plain,
% 3.28/2.38 ((~(~((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0))))) <=> ((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0)))),
% 3.28/2.38 inference(rewrite,[status(thm)],[])).
% 3.28/2.38 tff(17,plain,
% 3.28/2.38 (((~(~((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0))))) & ((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)))) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))))) <=> (((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0))) & (v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))))),
% 3.28/2.38 inference(monotonicity,[status(thm)],[16, 15])).
% 3.28/2.38 tff(18,plain,
% 3.28/2.38 (((~(~((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0))))) & ((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)))) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))))) <=> ((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0)) & v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))),
% 3.28/2.38 inference(transitivity,[status(thm)],[17, 2])).
% 3.28/2.38 tff(19,plain,
% 3.28/2.38 (((~v1_xboole_0(A!0)) & ((~(~((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0))))) & ((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)))) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))))))) <=> ((~v1_xboole_0(A!0)) & ((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0)) & v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))))),
% 3.28/2.38 inference(monotonicity,[status(thm)],[18])).
% 3.28/2.38 tff(20,plain,
% 3.28/2.38 (((~v1_xboole_0(A!0)) & ((~(~((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0))))) & ((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)))) & ((~(~(v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)))) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))))))) <=> ((~v1_xboole_0(A!0)) & (~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0)) & v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))))),
% 3.28/2.38 inference(transitivity,[status(thm)],[19, 1])).
% 3.28/2.38 tff(21,plain,
% 3.28/2.38 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : (r6_binop_1(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r6_binop_1(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)))))))))) <=> (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : (r6_binop_1(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r6_binop_1(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))))))))))),
% 3.28/2.38 inference(rewrite,[status(thm)],[])).
% 3.28/2.38 tff(22,plain,
% 3.28/2.38 ((~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r6_binop_1(A, C, D)) => r6_binop_1(B, E, F))))))))) <=> (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : (r6_binop_1(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r6_binop_1(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))))))))))),
% 3.28/2.38 inference(rewrite,[status(thm)],[])).
% 3.28/2.38 tff(23,axiom,(~![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r6_binop_1(A, C, D)) => r6_binop_1(B, E, F))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t4_filter_2')).
% 3.28/2.38 tff(24,plain,
% 3.28/2.38 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : (r6_binop_1(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r6_binop_1(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)))))))))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 3.28/2.38 tff(25,plain,
% 3.28/2.38 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : (r6_binop_1(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r6_binop_1(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)))))))))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[24, 21])).
% 3.28/2.38 tff(26,plain,
% 3.28/2.38 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : (r6_binop_1(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r6_binop_1(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)))))))))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 3.28/2.38 tff(27,plain,
% 3.28/2.38 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : (r6_binop_1(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r6_binop_1(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)))))))))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[26, 21])).
% 3.28/2.38 tff(28,plain,
% 3.28/2.38 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : (r6_binop_1(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r6_binop_1(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)))))))))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[27, 21])).
% 3.28/2.38 tff(29,plain,
% 3.28/2.38 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : (r6_binop_1(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r6_binop_1(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)))))))))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[28, 21])).
% 3.28/2.38 tff(30,plain,
% 3.28/2.38 (~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : (r6_binop_1(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r6_binop_1(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)))))))))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[29, 21])).
% 3.28/2.38 tff(31,plain,
% 3.28/2.38 ((~v1_xboole_0(A!0)) & (~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(A!0)) & v1_funct_1(C!2) & v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(D!3) & v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0) & m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0) & v1_funct_1(E!4) & v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) & (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)))))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[30, 20])).
% 3.28/2.38 tff(32,plain,
% 3.28/2.38 (~(r6_binop_1(B!1, E!4, F!5) | (~((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3))) | (~(v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1))))),
% 3.28/2.38 inference(and_elim,[status(thm)],[31])).
% 3.28/2.38 tff(33,plain,
% 3.28/2.38 ((E!4 = k1_realset1(C!2, B!1)) & (F!5 = k1_realset1(D!3, B!1)) & r6_binop_1(A!0, C!2, D!3)),
% 3.28/2.38 inference(or_elim,[status(thm)],[32])).
% 3.28/2.38 tff(34,plain,
% 3.28/2.38 (F!5 = k1_realset1(D!3, B!1)),
% 3.28/2.38 inference(and_elim,[status(thm)],[33])).
% 3.28/2.38 tff(35,plain,
% 3.28/2.38 (k1_realset1(D!3, B!1) = F!5),
% 3.28/2.38 inference(symmetry,[status(thm)],[34])).
% 3.28/2.38 tff(36,plain,
% 3.28/2.38 (m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1) <=> m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(monotonicity,[status(thm)],[35])).
% 3.28/2.38 tff(37,plain,
% 3.28/2.38 (m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1) <=> m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(symmetry,[status(thm)],[36])).
% 3.28/2.38 tff(38,plain,
% 3.28/2.38 (v1_funct_1(F!5) & v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) & m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(or_elim,[status(thm)],[32])).
% 3.28/2.38 tff(39,plain,
% 3.28/2.38 (m2_relset_1(F!5, k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(and_elim,[status(thm)],[38])).
% 3.28/2.38 tff(40,plain,
% 3.28/2.38 (m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[39, 37])).
% 3.28/2.38 tff(41,plain,
% 3.28/2.38 (v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1) <=> v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(monotonicity,[status(thm)],[35])).
% 3.28/2.38 tff(42,plain,
% 3.28/2.38 (v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1) <=> v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(symmetry,[status(thm)],[41])).
% 3.28/2.38 tff(43,plain,
% 3.28/2.38 (v1_funct_2(F!5, k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(and_elim,[status(thm)],[38])).
% 3.28/2.38 tff(44,plain,
% 3.28/2.38 (v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 3.28/2.38 tff(45,plain,
% 3.28/2.38 (E!4 = k1_realset1(C!2, B!1)),
% 3.28/2.38 inference(and_elim,[status(thm)],[33])).
% 3.28/2.38 tff(46,plain,
% 3.28/2.38 (k1_realset1(C!2, B!1) = E!4),
% 3.28/2.38 inference(symmetry,[status(thm)],[45])).
% 3.28/2.38 tff(47,plain,
% 3.28/2.38 (v1_funct_1(k1_realset1(C!2, B!1)) <=> v1_funct_1(E!4)),
% 3.28/2.38 inference(monotonicity,[status(thm)],[46])).
% 3.28/2.38 tff(48,plain,
% 3.28/2.38 (v1_funct_1(E!4) <=> v1_funct_1(k1_realset1(C!2, B!1))),
% 3.28/2.38 inference(symmetry,[status(thm)],[47])).
% 3.28/2.38 tff(49,plain,
% 3.28/2.38 (v1_funct_1(E!4)),
% 3.28/2.38 inference(and_elim,[status(thm)],[31])).
% 3.28/2.38 tff(50,plain,
% 3.28/2.38 (v1_funct_1(k1_realset1(C!2, B!1))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 3.28/2.38 tff(51,plain,
% 3.28/2.38 (m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1) <=> m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(monotonicity,[status(thm)],[46])).
% 3.28/2.38 tff(52,plain,
% 3.28/2.38 (m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1) <=> m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(symmetry,[status(thm)],[51])).
% 3.28/2.38 tff(53,plain,
% 3.28/2.38 (m2_relset_1(E!4, k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(and_elim,[status(thm)],[31])).
% 3.28/2.38 tff(54,plain,
% 3.28/2.38 (m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 3.28/2.38 tff(55,plain,
% 3.28/2.38 (v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1) <=> v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(monotonicity,[status(thm)],[46])).
% 3.28/2.38 tff(56,plain,
% 3.28/2.38 (v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1) <=> v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(symmetry,[status(thm)],[55])).
% 3.28/2.38 tff(57,plain,
% 3.28/2.38 (v1_funct_2(E!4, k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(and_elim,[status(thm)],[31])).
% 3.28/2.38 tff(58,plain,
% 3.28/2.38 (v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 3.28/2.38 tff(59,plain,
% 3.28/2.38 (^[A: $i, B: $i] : refl(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C))))))))),
% 3.28/2.38 inference(bind,[status(th)],[])).
% 3.28/2.38 tff(60,plain,
% 3.28/2.38 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C))))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))),
% 3.28/2.38 inference(quant_intro,[status(thm)],[59])).
% 3.28/2.38 tff(61,plain,
% 3.28/2.38 (^[A: $i, B: $i] : rewrite(((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C))))))))),
% 3.28/2.38 inference(bind,[status(th)],[])).
% 3.28/2.38 tff(62,plain,
% 3.28/2.38 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C))))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))),
% 3.28/2.38 inference(quant_intro,[status(thm)],[61])).
% 3.28/2.38 tff(63,plain,
% 3.28/2.38 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C))))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))),
% 3.28/2.38 inference(transitivity,[status(thm)],[62, 60])).
% 3.28/2.38 tff(64,plain,
% 3.28/2.38 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))))), rewrite((r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C))) <=> (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))), (((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C))))))), (((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C))))))))), (![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))) <=> ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C))))) <=> (((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C))))))))), rewrite((((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C))))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C))))) <=> ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))))),
% 3.28/2.38 inference(bind,[status(th)],[])).
% 3.28/2.38 tff(65,plain,
% 3.28/2.38 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C))))) <=> ![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))),
% 3.28/2.38 inference(quant_intro,[status(thm)],[64])).
% 3.28/2.38 tff(66,plain,
% 3.28/2.38 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C))))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))))),
% 3.28/2.38 inference(rewrite,[status(thm)],[])).
% 3.28/2.38 tff(67,plain,
% 3.28/2.38 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m2_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))) <=> ((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C))))), ((((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C))))))), (![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))) <=> ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m2_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C))))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C))))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C))))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m2_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C))))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))))))),
% 3.28/2.38 inference(bind,[status(th)],[])).
% 3.28/2.38 tff(68,plain,
% 3.28/2.38 (![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m2_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C))))) <=> ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))))),
% 3.28/2.38 inference(quant_intro,[status(thm)],[67])).
% 3.28/2.38 tff(69,axiom,(![A: $i, B: $i] : (((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m2_relset_1(B, k2_zfmisc_1(A, A), A)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d11_binop_1')).
% 3.28/2.38 tff(70,plain,
% 3.28/2.38 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[69, 68])).
% 3.28/2.38 tff(71,plain,
% 3.28/2.38 (![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[70, 66])).
% 3.28/2.38 tff(72,plain,(
% 3.28/2.38 ![A: $i, B: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m2_relset_1(B, k2_zfmisc_1(A, A), A))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (r6_binop_1(A, B, C) <=> (r4_binop_1(A, B, C) & r5_binop_1(A, B, C)))))),
% 3.28/2.38 inference(skolemize,[status(sab)],[71])).
% 3.28/2.38 tff(73,plain,
% 3.28/2.38 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[72, 65])).
% 3.28/2.38 tff(74,plain,
% 3.28/2.38 (![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))),
% 3.28/2.38 inference(modus_ponens,[status(thm)],[73, 63])).
% 3.28/2.38 tff(75,plain,
% 3.28/2.38 (((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))) | ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C)))))))) <=> ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))) | (~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C)))))))),
% 3.28/2.38 inference(rewrite,[status(thm)],[])).
% 3.28/2.38 tff(76,plain,
% 3.28/2.38 (((~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C))))))) <=> ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C)))))))),
% 3.28/2.38 inference(rewrite,[status(thm)],[])).
% 3.28/2.38 tff(77,plain,
% 3.28/2.38 (^[C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C)))))) <=> ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C)))))))),
% 3.28/2.39 inference(bind,[status(th)],[])).
% 3.28/2.39 tff(78,plain,
% 3.28/2.39 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C)))))) <=> ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C))))))),
% 3.28/2.39 inference(quant_intro,[status(thm)],[77])).
% 3.28/2.39 tff(79,plain,
% 3.28/2.39 (((~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C))))))) <=> ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C)))))))),
% 3.28/2.39 inference(monotonicity,[status(thm)],[78])).
% 3.28/2.39 tff(80,plain,
% 3.28/2.39 (((~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C))))))) <=> ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C)))))))),
% 3.28/2.39 inference(transitivity,[status(thm)],[79, 76])).
% 3.28/2.39 tff(81,plain,
% 3.28/2.39 (((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))) | ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C)))))))) <=> ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))) | ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C))))))))),
% 3.28/2.39 inference(monotonicity,[status(thm)],[80])).
% 3.28/2.39 tff(82,plain,
% 3.28/2.39 (((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))) | ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C)))))))) <=> ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))) | (~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C)))))))),
% 3.28/2.39 inference(transitivity,[status(thm)],[81, 75])).
% 3.28/2.39 tff(83,plain,
% 3.28/2.39 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))) | ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C)))))))),
% 3.28/2.39 inference(quant_inst,[status(thm)],[])).
% 3.28/2.39 tff(84,plain,
% 3.28/2.39 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))) | (~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C))))))),
% 3.28/2.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 3.28/2.39 tff(85,plain,
% 3.28/2.39 ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C))))))),
% 3.28/2.39 inference(unit_resolution,[status(thm)],[84, 74])).
% 3.28/2.39 tff(86,plain,
% 3.28/2.39 (![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C))))))),
% 3.28/2.39 inference(unit_resolution,[status(thm)],[85, 58, 54, 50])).
% 3.28/2.39 tff(87,plain,
% 3.28/2.39 (v1_funct_1(k1_realset1(D!3, B!1)) <=> v1_funct_1(F!5)),
% 3.28/2.39 inference(monotonicity,[status(thm)],[35])).
% 3.28/2.39 tff(88,plain,
% 3.28/2.39 (v1_funct_1(F!5) <=> v1_funct_1(k1_realset1(D!3, B!1))),
% 3.28/2.39 inference(symmetry,[status(thm)],[87])).
% 3.28/2.39 tff(89,plain,
% 3.28/2.39 (v1_funct_1(F!5)),
% 3.28/2.39 inference(and_elim,[status(thm)],[38])).
% 3.28/2.39 tff(90,plain,
% 3.28/2.39 (v1_funct_1(k1_realset1(D!3, B!1))),
% 3.28/2.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 3.28/2.39 tff(91,plain,
% 3.28/2.39 (((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C))))))) | ((~v1_funct_1(k1_realset1(D!3, B!1))) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C))))))) | (~v1_funct_1(k1_realset1(D!3, B!1))) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))))),
% 3.28/2.39 inference(rewrite,[status(thm)],[])).
% 3.28/2.39 tff(92,plain,
% 3.28/2.39 ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C))))))) | ((~v1_funct_1(k1_realset1(D!3, B!1))) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))))),
% 3.28/2.39 inference(quant_inst,[status(thm)],[])).
% 3.28/2.39 tff(93,plain,
% 3.28/2.39 ((~![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(C, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(C, k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), C) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), C)) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), C))))))) | (~v1_funct_1(k1_realset1(D!3, B!1))) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (r6_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))))))),
% 3.28/2.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 3.28/2.39 tff(94,plain,
% 3.28/2.39 (r6_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))),
% 3.28/2.39 inference(unit_resolution,[status(thm)],[93, 90, 86, 44, 40])).
% 3.28/2.39 tff(95,plain,
% 3.28/2.39 (r6_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)) <=> r6_binop_1(B!1, E!4, F!5)),
% 3.28/2.39 inference(monotonicity,[status(thm)],[46, 35])).
% 3.28/2.39 tff(96,plain,
% 3.28/2.39 (r6_binop_1(B!1, E!4, F!5) <=> r6_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))),
% 3.28/2.39 inference(symmetry,[status(thm)],[95])).
% 3.28/2.39 tff(97,plain,
% 3.28/2.39 ((~r6_binop_1(B!1, E!4, F!5)) <=> (~r6_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))),
% 3.28/2.39 inference(monotonicity,[status(thm)],[96])).
% 3.28/2.39 tff(98,plain,
% 3.28/2.39 (~r6_binop_1(B!1, E!4, F!5)),
% 3.28/2.39 inference(or_elim,[status(thm)],[32])).
% 3.28/2.39 tff(99,plain,
% 3.28/2.39 (~r6_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))),
% 3.28/2.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 3.28/2.39 tff(100,plain,
% 3.28/2.39 ((~(r6_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)) <=> (~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))))))) | r6_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)) | ((~r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))))),
% 3.28/2.39 inference(tautology,[status(thm)],[])).
% 3.28/2.39 tff(101,plain,
% 3.28/2.39 ((~r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))),
% 3.28/2.39 inference(unit_resolution,[status(thm)],[100, 99, 94])).
% 3.28/2.39 tff(102,plain,
% 3.28/2.39 (^[A: $i] : refl((v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))))) <=> (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))))))),
% 3.28/2.39 inference(bind,[status(th)],[])).
% 3.28/2.39 tff(103,plain,
% 3.28/2.39 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))))),
% 3.28/2.39 inference(quant_intro,[status(thm)],[102])).
% 3.28/2.39 tff(104,plain,
% 3.28/2.39 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))))) <=> (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))))))),
% 3.28/2.39 inference(bind,[status(th)],[])).
% 3.28/2.39 tff(105,plain,
% 3.28/2.39 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))))),
% 3.28/2.39 inference(quant_intro,[status(thm)],[104])).
% 3.28/2.39 tff(106,plain,
% 3.28/2.39 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))))),
% 3.28/2.39 inference(transitivity,[status(thm)],[105, 103])).
% 3.28/2.39 tff(107,plain,
% 3.28/2.39 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))) <=> (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))))))),
% 3.28/2.39 inference(bind,[status(th)],[])).
% 3.28/2.39 tff(108,plain,
% 3.28/2.39 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))))),
% 3.28/2.39 inference(quant_intro,[status(thm)],[107])).
% 3.28/2.39 tff(109,plain,
% 3.28/2.39 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))),
% 3.28/2.39 inference(rewrite,[status(thm)],[])).
% 3.28/2.39 tff(110,plain,
% 3.28/2.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))), quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite(((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) <=> (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))), quant_intro(proof_bind(^[F: $i] : trans(monotonicity(rewrite(((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) <=> (v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))), trans(monotonicity(rewrite(((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F))) <=> (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))), ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F)))) <=> (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))), rewrite((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))) <=> ((~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))), ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F)))) <=> ((~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))), ((((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F))))) <=> ((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))), rewrite(((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))) <=> ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))), ((((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F))))) <=> ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))), (![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F))))) <=> ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))), ((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F)))))) <=> ((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))), rewrite(((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))) <=> ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))), ((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F)))))) <=> ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))), (![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F)))))) <=> ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))), ((((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F))))))) <=> ((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))), ((((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F))))))) <=> ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))), (![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F))))))) <=> ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))), ((((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F)))))))) <=> ((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))), ((((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F)))))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))), (![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F)))))))) <=> ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F))))))))) <=> (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))), rewrite((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F))))))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))))), (![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F))))))))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))), (((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F)))))))))) <=> ((~v1_xboole_0(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))))), rewrite(((~v1_xboole_0(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))), (((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F)))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))))),
% 3.40/2.40 inference(bind,[status(th)],[])).
% 3.40/2.40 tff(111,plain,
% 3.40/2.40 (![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F)))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))),
% 3.40/2.40 inference(quant_intro,[status(thm)],[110])).
% 3.40/2.40 tff(112,axiom,(![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) => ((r4_binop_1(A, C, D) => r4_binop_1(B, E, F)) & (r5_binop_1(A, C, D) => r5_binop_1(B, E, F))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_filter_2')).
% 3.40/2.40 tff(113,plain,
% 3.40/2.40 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))),
% 3.40/2.40 inference(modus_ponens,[status(thm)],[112, 111])).
% 3.40/2.40 tff(114,plain,
% 3.40/2.40 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))),
% 3.40/2.40 inference(modus_ponens,[status(thm)],[113, 109])).
% 3.40/2.40 tff(115,plain,(
% 3.40/2.40 ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | ![E: $i] : ((~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))) | ![F: $i] : ((~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)))) | (((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F)) & ((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))),
% 3.40/2.40 inference(skolemize,[status(sab)],[114])).
% 3.40/2.40 tff(116,plain,
% 3.40/2.40 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))))),
% 3.40/2.40 inference(modus_ponens,[status(thm)],[115, 108])).
% 3.40/2.40 tff(117,plain,
% 3.40/2.40 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))))),
% 3.40/2.40 inference(modus_ponens,[status(thm)],[116, 106])).
% 3.40/2.40 tff(118,plain,
% 3.40/2.40 (~v1_xboole_0(A!0)),
% 3.40/2.40 inference(and_elim,[status(thm)],[31])).
% 3.40/2.40 tff(119,plain,
% 3.40/2.40 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))))) | (v1_xboole_0(A!0) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F)))))))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))))) | v1_xboole_0(A!0) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F)))))))))))),
% 3.40/2.40 inference(rewrite,[status(thm)],[])).
% 3.40/2.40 tff(120,plain,
% 3.40/2.40 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))))) | (v1_xboole_0(A!0) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F)))))))))))),
% 3.40/2.40 inference(quant_inst,[status(thm)],[])).
% 3.40/2.40 tff(121,plain,
% 3.40/2.40 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A, C, D)) | r5_binop_1(B, E, F)))))))))))) | v1_xboole_0(A!0) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F))))))))))),
% 3.40/2.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 3.40/2.40 tff(122,plain,
% 3.40/2.40 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F))))))))))),
% 3.40/2.40 inference(unit_resolution,[status(thm)],[121, 118, 117])).
% 3.40/2.40 tff(123,plain,
% 3.40/2.40 (m1_subset_1(B!1, k1_zfmisc_1(A!0))),
% 3.40/2.40 inference(and_elim,[status(thm)],[31])).
% 3.40/2.40 tff(124,plain,
% 3.40/2.40 (~v1_xboole_0(B!1)),
% 3.40/2.40 inference(and_elim,[status(thm)],[31])).
% 3.40/2.40 tff(125,plain,
% 3.40/2.40 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F))))))))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F))))))))))) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F))))))))))),
% 3.40/2.40 inference(rewrite,[status(thm)],[])).
% 3.40/2.40 tff(126,plain,
% 3.40/2.40 ((v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F)))))))))) <=> (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F))))))))))),
% 3.40/2.40 inference(rewrite,[status(thm)],[])).
% 3.40/2.40 tff(127,plain,
% 3.40/2.40 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F))))))))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F))))))))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F)))))))))))),
% 3.40/2.40 inference(monotonicity,[status(thm)],[126])).
% 3.40/2.40 tff(128,plain,
% 3.40/2.40 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F))))))))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F))))))))))) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F))))))))))),
% 3.40/2.40 inference(transitivity,[status(thm)],[127, 125])).
% 3.40/2.40 tff(129,plain,
% 3.40/2.40 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F))))))))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F))))))))))),
% 3.40/2.40 inference(quant_inst,[status(thm)],[])).
% 3.40/2.40 tff(130,plain,
% 3.40/2.40 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | ![F: $i] : ((~v1_funct_1(F)) | (~v1_funct_2(F, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(F, k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(F = k1_realset1(D, B))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B, E, F))))))))))) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(A!0))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F)))))))))),
% 3.40/2.41 inference(modus_ponens,[status(thm)],[129, 128])).
% 3.40/2.41 tff(131,plain,
% 3.40/2.41 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F)))))))))),
% 3.40/2.41 inference(unit_resolution,[status(thm)],[130, 124, 123, 122])).
% 3.40/2.41 tff(132,plain,
% 3.40/2.41 (m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)),
% 3.40/2.41 inference(and_elim,[status(thm)],[31])).
% 3.40/2.41 tff(133,plain,
% 3.40/2.41 (v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)),
% 3.40/2.41 inference(and_elim,[status(thm)],[31])).
% 3.40/2.41 tff(134,plain,
% 3.40/2.41 (v1_funct_1(C!2)),
% 3.40/2.41 inference(and_elim,[status(thm)],[31])).
% 3.40/2.41 tff(135,plain,
% 3.40/2.41 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F)))))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F)))))))))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))))),
% 3.40/2.41 inference(rewrite,[status(thm)],[])).
% 3.40/2.41 tff(136,plain,
% 3.40/2.41 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))))),
% 3.40/2.41 inference(rewrite,[status(thm)],[])).
% 3.40/2.41 tff(137,plain,
% 3.40/2.41 (^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : rewrite(((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))) <=> ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))), (![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))) <=> ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))), (((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))))), rewrite(((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))), (((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))) <=> ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))))),
% 3.40/2.41 inference(bind,[status(th)],[])).
% 3.40/2.41 tff(138,plain,
% 3.40/2.41 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))) <=> ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))),
% 3.40/2.41 inference(quant_intro,[status(thm)],[137])).
% 3.40/2.41 tff(139,plain,
% 3.40/2.41 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))))),
% 3.40/2.41 inference(monotonicity,[status(thm)],[138])).
% 3.40/2.41 tff(140,plain,
% 3.40/2.41 (((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))) <=> ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))))),
% 3.40/2.41 inference(transitivity,[status(thm)],[139, 136])).
% 3.40/2.41 tff(141,plain,
% 3.40/2.41 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F)))))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F)))))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))))),
% 3.40/2.41 inference(monotonicity,[status(thm)],[140])).
% 3.40/2.41 tff(142,plain,
% 3.40/2.41 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F)))))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F)))))))))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))))),
% 3.40/2.42 inference(transitivity,[status(thm)],[141, 135])).
% 3.40/2.42 tff(143,plain,
% 3.40/2.42 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F)))))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F)))))))))),
% 3.40/2.42 inference(quant_inst,[status(thm)],[])).
% 3.40/2.42 tff(144,plain,
% 3.40/2.42 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C, B!1))) | (~(F = k1_realset1(D, B!1))) | (~((~((~r4_binop_1(A!0, C, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C, D)) | r5_binop_1(B!1, E, F)))))))))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))),
% 3.40/2.42 inference(modus_ponens,[status(thm)],[143, 142])).
% 3.40/2.42 tff(145,plain,
% 3.40/2.42 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))),
% 3.40/2.42 inference(unit_resolution,[status(thm)],[144, 134, 133, 132, 131])).
% 3.40/2.42 tff(146,plain,
% 3.40/2.42 (m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)),
% 3.40/2.42 inference(and_elim,[status(thm)],[31])).
% 3.40/2.42 tff(147,plain,
% 3.40/2.42 (v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)),
% 3.40/2.42 inference(and_elim,[status(thm)],[31])).
% 3.40/2.42 tff(148,plain,
% 3.40/2.42 (v1_funct_1(D!3)),
% 3.40/2.42 inference(and_elim,[status(thm)],[31])).
% 3.40/2.42 tff(149,plain,
% 3.40/2.42 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))) | ((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F))))))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))) | (~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F))))))))),
% 3.40/2.42 inference(rewrite,[status(thm)],[])).
% 3.40/2.42 tff(150,plain,
% 3.40/2.42 (((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))) <=> ((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F))))))))),
% 3.40/2.42 inference(rewrite,[status(thm)],[])).
% 3.40/2.42 tff(151,plain,
% 3.40/2.42 (^[E: $i] : rewrite(((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F))))))) <=> ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F))))))))),
% 3.40/2.42 inference(bind,[status(th)],[])).
% 3.40/2.42 tff(152,plain,
% 3.40/2.42 (![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F))))))) <=> ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))),
% 3.40/2.42 inference(quant_intro,[status(thm)],[151])).
% 3.40/2.42 tff(153,plain,
% 3.40/2.42 (((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))) <=> ((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F))))))))),
% 3.40/2.42 inference(monotonicity,[status(thm)],[152])).
% 3.40/2.42 tff(154,plain,
% 3.40/2.42 (((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))) <=> ((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F))))))))),
% 3.40/2.42 inference(transitivity,[status(thm)],[153, 150])).
% 3.40/2.42 tff(155,plain,
% 3.40/2.42 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))) | ((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F))))))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))) | ((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))))),
% 3.40/2.42 inference(monotonicity,[status(thm)],[154])).
% 3.40/2.42 tff(156,plain,
% 3.40/2.42 (((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))) | ((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F))))))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))) | (~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F))))))))),
% 3.40/2.42 inference(transitivity,[status(thm)],[155, 149])).
% 3.40/2.42 tff(157,plain,
% 3.40/2.42 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))) | ((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F))))))))),
% 3.40/2.42 inference(quant_inst,[status(thm)],[])).
% 3.40/2.42 tff(158,plain,
% 3.40/2.42 ((~![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D, B!1))) | (~(E = k1_realset1(C!2, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D)) | r5_binop_1(B!1, E, F))))))))) | (~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | ![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))),
% 3.40/2.42 inference(modus_ponens,[status(thm)],[157, 156])).
% 3.40/2.42 tff(159,plain,
% 3.40/2.42 (![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))),
% 3.40/2.42 inference(unit_resolution,[status(thm)],[158, 148, 147, 146, 145])).
% 3.40/2.42 tff(160,plain,
% 3.40/2.42 (((~![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))) | ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F)))))))) <=> ((~![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))) | (~v1_funct_1(k1_realset1(C!2, B!1))) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F)))))))),
% 3.40/2.43 inference(rewrite,[status(thm)],[])).
% 3.40/2.43 tff(161,plain,
% 3.40/2.43 (((~v1_funct_1(k1_realset1(C!2, B!1))) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(k1_realset1(C!2, B!1) = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F))))))) <=> ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F)))))))),
% 3.40/2.43 inference(rewrite,[status(thm)],[])).
% 3.40/2.43 tff(162,plain,
% 3.40/2.43 (((~![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))) | ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(k1_realset1(C!2, B!1) = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F)))))))) <=> ((~![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))) | ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F))))))))),
% 3.40/2.43 inference(monotonicity,[status(thm)],[161])).
% 3.40/2.43 tff(163,plain,
% 3.40/2.43 (((~![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))) | ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(k1_realset1(C!2, B!1) = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F)))))))) <=> ((~![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))) | (~v1_funct_1(k1_realset1(C!2, B!1))) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F)))))))),
% 3.40/2.43 inference(transitivity,[status(thm)],[162, 160])).
% 3.40/2.43 tff(164,plain,
% 3.40/2.43 ((~![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))) | ((~v1_funct_1(k1_realset1(C!2, B!1))) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(k1_realset1(C!2, B!1) = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F)))))))),
% 3.40/2.43 inference(quant_inst,[status(thm)],[])).
% 3.40/2.43 tff(165,plain,
% 3.40/2.43 ((~![E: $i] : ((~v1_funct_1(E)) | (~m2_relset_1(E, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(E, k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(E = k1_realset1(C!2, B!1))) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, E, F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, E, F)))))))) | (~v1_funct_1(k1_realset1(C!2, B!1))) | (~m2_relset_1(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C!2, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | ![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F))))))),
% 3.40/2.43 inference(modus_ponens,[status(thm)],[164, 163])).
% 3.40/2.43 tff(166,plain,
% 3.40/2.43 (![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F))))))),
% 3.40/2.43 inference(unit_resolution,[status(thm)],[165, 50, 58, 54, 159])).
% 3.40/2.43 tff(167,plain,
% 3.40/2.43 (((~![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F))))))) | ((~v1_funct_1(k1_realset1(D!3, B!1))) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))))) <=> ((~![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F))))))) | (~v1_funct_1(k1_realset1(D!3, B!1))) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))))),
% 3.40/2.43 inference(rewrite,[status(thm)],[])).
% 3.40/2.43 tff(168,plain,
% 3.40/2.43 (((~v1_funct_1(k1_realset1(D!3, B!1))) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | $false | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))))))) <=> ((~v1_funct_1(k1_realset1(D!3, B!1))) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))))),
% 3.40/2.43 inference(rewrite,[status(thm)],[])).
% 3.40/2.43 tff(169,plain,
% 3.40/2.43 ((~$true) <=> $false),
% 3.40/2.43 inference(rewrite,[status(thm)],[])).
% 3.40/2.43 tff(170,plain,
% 3.40/2.43 ((k1_realset1(D!3, B!1) = k1_realset1(D!3, B!1)) <=> $true),
% 3.40/2.43 inference(rewrite,[status(thm)],[])).
% 3.40/2.43 tff(171,plain,
% 3.40/2.43 ((~(k1_realset1(D!3, B!1) = k1_realset1(D!3, B!1))) <=> (~$true)),
% 3.40/2.43 inference(monotonicity,[status(thm)],[170])).
% 3.40/2.43 tff(172,plain,
% 3.40/2.43 ((~(k1_realset1(D!3, B!1) = k1_realset1(D!3, B!1))) <=> $false),
% 3.40/2.43 inference(transitivity,[status(thm)],[171, 169])).
% 3.40/2.43 tff(173,plain,
% 3.40/2.43 (((~v1_funct_1(k1_realset1(D!3, B!1))) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~(k1_realset1(D!3, B!1) = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))))))) <=> ((~v1_funct_1(k1_realset1(D!3, B!1))) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | $false | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))))),
% 3.40/2.43 inference(monotonicity,[status(thm)],[172])).
% 3.40/2.43 tff(174,plain,
% 3.40/2.43 (((~v1_funct_1(k1_realset1(D!3, B!1))) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~(k1_realset1(D!3, B!1) = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))))))) <=> ((~v1_funct_1(k1_realset1(D!3, B!1))) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))))),
% 3.40/2.43 inference(transitivity,[status(thm)],[173, 168])).
% 3.40/2.43 tff(175,plain,
% 3.40/2.43 (((~![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F))))))) | ((~v1_funct_1(k1_realset1(D!3, B!1))) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~(k1_realset1(D!3, B!1) = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))))) <=> ((~![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F))))))) | ((~v1_funct_1(k1_realset1(D!3, B!1))) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))))))))),
% 3.40/2.43 inference(monotonicity,[status(thm)],[174])).
% 3.40/2.43 tff(176,plain,
% 3.40/2.43 (((~![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F))))))) | ((~v1_funct_1(k1_realset1(D!3, B!1))) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~(k1_realset1(D!3, B!1) = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))))) <=> ((~![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F))))))) | (~v1_funct_1(k1_realset1(D!3, B!1))) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))))),
% 3.40/2.43 inference(transitivity,[status(thm)],[175, 167])).
% 3.40/2.43 tff(177,plain,
% 3.40/2.43 ((~![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F))))))) | ((~v1_funct_1(k1_realset1(D!3, B!1))) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~(k1_realset1(D!3, B!1) = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))))),
% 3.40/2.43 inference(quant_inst,[status(thm)],[])).
% 3.40/2.43 tff(178,plain,
% 3.40/2.43 ((~![F: $i] : ((~v1_funct_1(F)) | (~m2_relset_1(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(F, k2_zfmisc_1(B!1, B!1), B!1)) | (~(F = k1_realset1(D!3, B!1))) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), F))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), F))))))) | (~v1_funct_1(k1_realset1(D!3, B!1))) | (~v1_funct_2(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(D!3, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))))))),
% 3.40/2.43 inference(modus_ponens,[status(thm)],[177, 176])).
% 3.40/2.43 tff(179,plain,
% 3.40/2.43 (~((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))))),
% 3.40/2.43 inference(unit_resolution,[status(thm)],[178, 90, 44, 40, 166])).
% 3.40/2.43 tff(180,plain,
% 3.40/2.43 (((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))))) | ((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))),
% 3.40/2.43 inference(tautology,[status(thm)],[])).
% 3.40/2.43 tff(181,plain,
% 3.40/2.43 ((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))),
% 3.40/2.43 inference(unit_resolution,[status(thm)],[180, 179])).
% 3.40/2.43 tff(182,plain,
% 3.40/2.43 (((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, C) <=> (~((~r4_binop_1(A!0, C!2, C)) | (~r5_binop_1(A!0, C!2, C)))))))) <=> ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, C) <=> (~((~r4_binop_1(A!0, C!2, C)) | (~r5_binop_1(A!0, C!2, C)))))))),
% 3.40/2.43 inference(rewrite,[status(thm)],[])).
% 3.40/2.43 tff(183,plain,
% 3.40/2.43 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))) | ((~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, C) <=> (~((~r4_binop_1(A!0, C!2, C)) | (~r5_binop_1(A!0, C!2, C)))))))),
% 3.40/2.44 inference(quant_inst,[status(thm)],[])).
% 3.40/2.44 tff(184,plain,
% 3.40/2.44 ((~![A: $i, B: $i] : ((~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(B, k2_zfmisc_1(A, A), A)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | (r6_binop_1(A, B, C) <=> (~((~r4_binop_1(A, B, C)) | (~r5_binop_1(A, B, C)))))))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C!2, k2_zfmisc_1(A!0, A!0), A!0)) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, C) <=> (~((~r4_binop_1(A!0, C!2, C)) | (~r5_binop_1(A!0, C!2, C))))))),
% 3.40/2.44 inference(modus_ponens,[status(thm)],[183, 182])).
% 3.40/2.44 tff(185,plain,
% 3.40/2.44 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, C) <=> (~((~r4_binop_1(A!0, C!2, C)) | (~r5_binop_1(A!0, C!2, C))))))),
% 3.40/2.44 inference(unit_resolution,[status(thm)],[184, 134, 133, 132, 74])).
% 3.40/2.44 tff(186,plain,
% 3.40/2.44 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, C) <=> (~((~r4_binop_1(A!0, C!2, C)) | (~r5_binop_1(A!0, C!2, C))))))) | ((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, D!3) <=> (~((~r4_binop_1(A!0, C!2, D!3)) | (~r5_binop_1(A!0, C!2, D!3))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, C) <=> (~((~r4_binop_1(A!0, C!2, C)) | (~r5_binop_1(A!0, C!2, C))))))) | (~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, D!3) <=> (~((~r4_binop_1(A!0, C!2, D!3)) | (~r5_binop_1(A!0, C!2, D!3))))))),
% 3.40/2.44 inference(rewrite,[status(thm)],[])).
% 3.40/2.44 tff(187,plain,
% 3.40/2.44 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, C) <=> (~((~r4_binop_1(A!0, C!2, C)) | (~r5_binop_1(A!0, C!2, C))))))) | ((~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, D!3) <=> (~((~r4_binop_1(A!0, C!2, D!3)) | (~r5_binop_1(A!0, C!2, D!3))))))),
% 3.40/2.44 inference(quant_inst,[status(thm)],[])).
% 3.40/2.44 tff(188,plain,
% 3.40/2.44 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(C, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, C) <=> (~((~r4_binop_1(A!0, C!2, C)) | (~r5_binop_1(A!0, C!2, C))))))) | (~v1_funct_1(D!3)) | (~v1_funct_2(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (~m2_relset_1(D!3, k2_zfmisc_1(A!0, A!0), A!0)) | (r6_binop_1(A!0, C!2, D!3) <=> (~((~r4_binop_1(A!0, C!2, D!3)) | (~r5_binop_1(A!0, C!2, D!3)))))),
% 3.40/2.44 inference(modus_ponens,[status(thm)],[187, 186])).
% 3.40/2.44 tff(189,plain,
% 3.40/2.44 (r6_binop_1(A!0, C!2, D!3) <=> (~((~r4_binop_1(A!0, C!2, D!3)) | (~r5_binop_1(A!0, C!2, D!3))))),
% 3.40/2.44 inference(unit_resolution,[status(thm)],[188, 148, 147, 146, 185])).
% 3.40/2.44 tff(190,plain,
% 3.40/2.44 (r6_binop_1(A!0, C!2, D!3)),
% 3.40/2.44 inference(and_elim,[status(thm)],[33])).
% 3.40/2.44 tff(191,plain,
% 3.40/2.44 ((~(r6_binop_1(A!0, C!2, D!3) <=> (~((~r4_binop_1(A!0, C!2, D!3)) | (~r5_binop_1(A!0, C!2, D!3)))))) | (~r6_binop_1(A!0, C!2, D!3)) | (~((~r4_binop_1(A!0, C!2, D!3)) | (~r5_binop_1(A!0, C!2, D!3))))),
% 3.40/2.44 inference(tautology,[status(thm)],[])).
% 3.40/2.44 tff(192,plain,
% 3.40/2.44 ((~(r6_binop_1(A!0, C!2, D!3) <=> (~((~r4_binop_1(A!0, C!2, D!3)) | (~r5_binop_1(A!0, C!2, D!3)))))) | (~((~r4_binop_1(A!0, C!2, D!3)) | (~r5_binop_1(A!0, C!2, D!3))))),
% 3.40/2.44 inference(unit_resolution,[status(thm)],[191, 190])).
% 3.40/2.44 tff(193,plain,
% 3.40/2.44 (~((~r4_binop_1(A!0, C!2, D!3)) | (~r5_binop_1(A!0, C!2, D!3)))),
% 3.40/2.44 inference(unit_resolution,[status(thm)],[192, 189])).
% 3.40/2.44 tff(194,plain,
% 3.40/2.44 (((~r4_binop_1(A!0, C!2, D!3)) | (~r5_binop_1(A!0, C!2, D!3))) | r4_binop_1(A!0, C!2, D!3)),
% 3.40/2.44 inference(tautology,[status(thm)],[])).
% 3.40/2.44 tff(195,plain,
% 3.40/2.44 (r4_binop_1(A!0, C!2, D!3)),
% 3.40/2.44 inference(unit_resolution,[status(thm)],[194, 193])).
% 3.40/2.44 tff(196,plain,
% 3.40/2.44 ((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))),
% 3.40/2.44 inference(tautology,[status(thm)],[])).
% 3.40/2.44 tff(197,plain,
% 3.40/2.44 ((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))),
% 3.40/2.44 inference(unit_resolution,[status(thm)],[196, 195])).
% 3.40/2.44 tff(198,plain,
% 3.40/2.44 (r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))),
% 3.40/2.44 inference(unit_resolution,[status(thm)],[197, 181])).
% 3.40/2.44 tff(199,plain,
% 3.40/2.44 (((~((~r4_binop_1(A!0, C!2, D!3)) | r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))))) | ((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))),
% 3.40/2.44 inference(tautology,[status(thm)],[])).
% 3.40/2.44 tff(200,plain,
% 3.40/2.44 ((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))),
% 3.40/2.44 inference(unit_resolution,[status(thm)],[199, 179])).
% 3.40/2.44 tff(201,plain,
% 3.40/2.44 (((~r4_binop_1(A!0, C!2, D!3)) | (~r5_binop_1(A!0, C!2, D!3))) | r5_binop_1(A!0, C!2, D!3)),
% 3.40/2.44 inference(tautology,[status(thm)],[])).
% 3.40/2.44 tff(202,plain,
% 3.40/2.44 (r5_binop_1(A!0, C!2, D!3)),
% 3.40/2.44 inference(unit_resolution,[status(thm)],[201, 193])).
% 3.40/2.44 tff(203,plain,
% 3.40/2.44 ((~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | (~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))),
% 3.40/2.44 inference(tautology,[status(thm)],[])).
% 3.40/2.44 tff(204,plain,
% 3.40/2.44 ((~((~r5_binop_1(A!0, C!2, D!3)) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))) | r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))),
% 3.40/2.44 inference(unit_resolution,[status(thm)],[203, 202])).
% 3.40/2.44 tff(205,plain,
% 3.40/2.44 (r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))),
% 3.40/2.44 inference(unit_resolution,[status(thm)],[204, 200])).
% 3.40/2.44 tff(206,plain,
% 3.40/2.44 ((~((~r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))))) | (~r4_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1))) | (~r5_binop_1(B!1, k1_realset1(C!2, B!1), k1_realset1(D!3, B!1)))),
% 3.40/2.44 inference(tautology,[status(thm)],[])).
% 3.40/2.44 tff(207,plain,
% 3.40/2.44 ($false),
% 3.40/2.44 inference(unit_resolution,[status(thm)],[206, 205, 198, 101])).
% 3.40/2.44 % SZS output end Proof
%------------------------------------------------------------------------------