TSTP Solution File: GRP637+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP637+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 22:29:02 EDT 2022
% Result : Theorem 4.45s 3.03s
% Output : Proof 4.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP637+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Aug 31 18:44:54 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 4.45/3.03 % SZS status Theorem
% 4.45/3.03 % SZS output start Proof
% 4.45/3.03 tff(r1_tarski_type, type, (
% 4.45/3.03 r1_tarski: ( $i * $i ) > $o)).
% 4.45/3.03 tff(k9_relat_1_type, type, (
% 4.45/3.03 k9_relat_1: ( $i * $i ) > $i)).
% 4.45/3.03 tff(u1_struct_0_type, type, (
% 4.45/3.03 u1_struct_0: $i > $i)).
% 4.45/3.03 tff(tptp_fun_E_4_type, type, (
% 4.45/3.03 tptp_fun_E_4: $i)).
% 4.45/3.03 tff(tptp_fun_C_2_type, type, (
% 4.45/3.03 tptp_fun_C_2: $i)).
% 4.45/3.03 tff(tptp_fun_D_3_type, type, (
% 4.45/3.03 tptp_fun_D_3: $i)).
% 4.45/3.03 tff(tptp_fun_G_6_type, type, (
% 4.45/3.03 tptp_fun_G_6: $i)).
% 4.45/3.03 tff(tptp_fun_F_5_type, type, (
% 4.45/3.03 tptp_fun_F_5: $i)).
% 4.45/3.03 tff(k2_funct_2_type, type, (
% 4.45/3.03 k2_funct_2: ( $i * $i * $i * $i ) > $i)).
% 4.45/3.03 tff(tptp_fun_B_1_type, type, (
% 4.45/3.03 tptp_fun_B_1: $i)).
% 4.45/3.03 tff(tptp_fun_A_0_type, type, (
% 4.45/3.03 tptp_fun_A_0: $i)).
% 4.45/3.03 tff(m1_group_6_type, type, (
% 4.45/3.03 m1_group_6: ( $i * $i * $i ) > $o)).
% 4.45/3.03 tff(m1_group_2_type, type, (
% 4.45/3.03 m1_group_2: ( $i * $i ) > $o)).
% 4.45/3.03 tff(m2_relset_1_type, type, (
% 4.45/3.03 m2_relset_1: ( $i * $i * $i ) > $o)).
% 4.45/3.03 tff(v1_group_6_type, type, (
% 4.45/3.03 v1_group_6: ( $i * $i * $i ) > $o)).
% 4.45/3.03 tff(v1_funct_2_type, type, (
% 4.45/3.03 v1_funct_2: ( $i * $i * $i ) > $o)).
% 4.45/3.03 tff(v1_funct_1_type, type, (
% 4.45/3.03 v1_funct_1: $i > $o)).
% 4.45/3.03 tff(l1_group_1_type, type, (
% 4.45/3.03 l1_group_1: $i > $o)).
% 4.45/3.03 tff(v4_group_1_type, type, (
% 4.45/3.03 v4_group_1: $i > $o)).
% 4.45/3.03 tff(v3_group_1_type, type, (
% 4.45/3.03 v3_group_1: $i > $o)).
% 4.45/3.03 tff(v3_struct_0_type, type, (
% 4.45/3.03 v3_struct_0: $i > $o)).
% 4.45/3.03 tff(m1_relset_1_type, type, (
% 4.45/3.03 m1_relset_1: ( $i * $i * $i ) > $o)).
% 4.45/3.03 tff(k1_realset1_type, type, (
% 4.45/3.03 k1_realset1: ( $i * $i ) > $i)).
% 4.45/3.03 tff(u1_group_1_type, type, (
% 4.45/3.03 u1_group_1: $i > $i)).
% 4.45/3.03 tff(v1_relat_1_type, type, (
% 4.45/3.03 v1_relat_1: $i > $o)).
% 4.45/3.03 tff(m1_subset_1_type, type, (
% 4.45/3.03 m1_subset_1: ( $i * $i ) > $o)).
% 4.45/3.03 tff(k1_zfmisc_1_type, type, (
% 4.45/3.03 k1_zfmisc_1: $i > $i)).
% 4.45/3.03 tff(k2_zfmisc_1_type, type, (
% 4.45/3.03 k2_zfmisc_1: ( $i * $i ) > $i)).
% 4.45/3.03 tff(1,plain,
% 4.45/3.03 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 4.45/3.03 inference(rewrite,[status(thm)],[])).
% 4.45/3.03 tff(2,plain,
% 4.45/3.03 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 4.45/3.03 inference(rewrite,[status(thm)],[])).
% 4.45/3.03 tff(3,plain,
% 4.45/3.03 (((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 4.45/3.03 inference(rewrite,[status(thm)],[])).
% 4.45/3.03 tff(4,plain,
% 4.45/3.03 ((m1_group_2(D!3, A!0) & (m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> (m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 4.45/3.03 inference(rewrite,[status(thm)],[])).
% 4.45/3.03 tff(5,plain,
% 4.45/3.03 ((m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> (m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 4.45/3.03 inference(rewrite,[status(thm)],[])).
% 4.45/3.03 tff(6,plain,
% 4.45/3.03 (((~(~m1_group_2(F!5, B!1))) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))) <=> (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 4.45/3.03 inference(rewrite,[status(thm)],[])).
% 4.45/3.03 tff(7,plain,
% 4.45/3.03 ((~(~m1_group_2(E!4, A!0))) <=> m1_group_2(E!4, A!0)),
% 4.45/3.03 inference(rewrite,[status(thm)],[])).
% 4.45/3.03 tff(8,plain,
% 4.45/3.03 (((~(~m1_group_2(E!4, A!0))) & ((~(~m1_group_2(F!5, B!1))) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> (m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))),
% 4.45/3.04 inference(monotonicity,[status(thm)],[7, 6])).
% 4.45/3.04 tff(9,plain,
% 4.45/3.04 (((~(~m1_group_2(E!4, A!0))) & ((~(~m1_group_2(F!5, B!1))) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> (m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 4.45/3.04 inference(transitivity,[status(thm)],[8, 5])).
% 4.45/3.04 tff(10,plain,
% 4.45/3.04 ((~(~m1_group_2(D!3, A!0))) <=> m1_group_2(D!3, A!0)),
% 4.45/3.04 inference(rewrite,[status(thm)],[])).
% 4.45/3.04 tff(11,plain,
% 4.45/3.04 (((~(~m1_group_2(D!3, A!0))) & ((~(~m1_group_2(E!4, A!0))) & ((~(~m1_group_2(F!5, B!1))) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))) <=> (m1_group_2(D!3, A!0) & (m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))),
% 4.45/3.04 inference(monotonicity,[status(thm)],[10, 9])).
% 4.45/3.04 tff(12,plain,
% 4.45/3.04 (((~(~m1_group_2(D!3, A!0))) & ((~(~m1_group_2(E!4, A!0))) & ((~(~m1_group_2(F!5, B!1))) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))) <=> (m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 4.45/3.04 inference(transitivity,[status(thm)],[11, 4])).
% 4.45/3.04 tff(13,plain,
% 4.45/3.04 ((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.45/3.04 inference(rewrite,[status(thm)],[])).
% 4.45/3.04 tff(14,plain,
% 4.45/3.04 (((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) & ((~(~m1_group_2(D!3, A!0))) & ((~(~m1_group_2(E!4, A!0))) & ((~(~m1_group_2(F!5, B!1))) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))))) <=> ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))),
% 4.45/3.04 inference(monotonicity,[status(thm)],[13, 12])).
% 4.45/3.04 tff(15,plain,
% 4.45/3.04 (((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) & ((~(~m1_group_2(D!3, A!0))) & ((~(~m1_group_2(E!4, A!0))) & ((~(~m1_group_2(F!5, B!1))) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))))) <=> (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 4.45/3.04 inference(transitivity,[status(thm)],[14, 3])).
% 4.45/3.04 tff(16,plain,
% 4.45/3.04 ((~(~((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)))) <=> ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1))),
% 4.45/3.04 inference(rewrite,[status(thm)],[])).
% 4.45/3.04 tff(17,plain,
% 4.45/3.04 (((~(~((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)))) & ((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) & ((~(~m1_group_2(D!3, A!0))) & ((~(~m1_group_2(E!4, A!0))) & ((~(~m1_group_2(F!5, B!1))) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))))) <=> (((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))),
% 4.45/3.04 inference(monotonicity,[status(thm)],[16, 15])).
% 4.45/3.04 tff(18,plain,
% 4.45/3.04 (((~(~((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)))) & ((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) & ((~(~m1_group_2(D!3, A!0))) & ((~(~m1_group_2(E!4, A!0))) & ((~(~m1_group_2(F!5, B!1))) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))))) <=> ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 4.45/3.04 inference(transitivity,[status(thm)],[17, 2])).
% 4.45/3.04 tff(19,plain,
% 4.45/3.04 ((~(~((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0))),
% 4.45/3.05 inference(rewrite,[status(thm)],[])).
% 4.45/3.05 tff(20,plain,
% 4.45/3.05 (((~(~((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)))) & ((~(~((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)))) & ((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) & ((~(~m1_group_2(D!3, A!0))) & ((~(~m1_group_2(E!4, A!0))) & ((~(~m1_group_2(F!5, B!1))) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))))))) <=> (((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))),
% 4.45/3.05 inference(monotonicity,[status(thm)],[19, 18])).
% 4.45/3.05 tff(21,plain,
% 4.45/3.05 (((~(~((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)))) & ((~(~((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)))) & ((~(~(v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) & ((~(~m1_group_2(D!3, A!0))) & ((~(~m1_group_2(E!4, A!0))) & ((~(~m1_group_2(F!5, B!1))) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 4.45/3.05 inference(transitivity,[status(thm)],[20, 1])).
% 4.45/3.05 tff(22,plain,
% 4.45/3.05 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B))))))))))),
% 4.45/3.05 inference(rewrite,[status(thm)],[])).
% 4.45/3.05 tff(23,plain,
% 4.45/3.05 ((~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_group_2(D, A) => ![E: $i] : (m1_group_2(E, A) => ![F: $i] : (m1_group_2(F, B) => ![G: $i] : (m1_group_2(G, B) => ((((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E)))) & m1_group_6(D, A, E)) => m1_group_6(F, B, G)))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B))))))))))),
% 4.45/3.05 inference(rewrite,[status(thm)],[])).
% 4.45/3.05 tff(24,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_group_2(D, A) => ![E: $i] : (m1_group_2(E, A) => ![F: $i] : (m1_group_2(F, B) => ![G: $i] : (m1_group_2(G, B) => ((((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E)))) & m1_group_6(D, A, E)) => m1_group_6(F, B, G)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t10_latsubgr')).
% 4.45/3.05 tff(25,plain,
% 4.45/3.05 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[24, 23])).
% 4.45/3.05 tff(26,plain,
% 4.45/3.05 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[25, 22])).
% 4.45/3.05 tff(27,plain,
% 4.45/3.05 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[26, 22])).
% 4.45/3.05 tff(28,plain,
% 4.45/3.05 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[27, 22])).
% 4.45/3.05 tff(29,plain,
% 4.45/3.05 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[28, 22])).
% 4.45/3.05 tff(30,plain,
% 4.45/3.05 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[29, 22])).
% 4.45/3.05 tff(31,plain,
% 4.45/3.05 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[30, 22])).
% 4.45/3.05 tff(32,plain,
% 4.45/3.05 ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[31, 21])).
% 4.45/3.05 tff(33,plain,
% 4.45/3.05 (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))),
% 4.45/3.05 inference(and_elim,[status(thm)],[32])).
% 4.45/3.05 tff(34,plain,
% 4.45/3.05 ((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4)),
% 4.45/3.05 inference(or_elim,[status(thm)],[33])).
% 4.45/3.05 tff(35,plain,
% 4.45/3.05 (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))),
% 4.45/3.05 inference(and_elim,[status(thm)],[34])).
% 4.45/3.05 tff(36,plain,
% 4.45/3.05 (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = u1_struct_0(G!6)),
% 4.45/3.05 inference(symmetry,[status(thm)],[35])).
% 4.45/3.05 tff(37,plain,
% 4.45/3.05 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 4.45/3.05 inference(bind,[status(th)],[])).
% 4.45/3.05 tff(38,plain,
% 4.45/3.05 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.45/3.05 inference(quant_intro,[status(thm)],[37])).
% 4.45/3.05 tff(39,plain,
% 4.45/3.05 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.45/3.05 inference(rewrite,[status(thm)],[])).
% 4.45/3.05 tff(40,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 4.45/3.05 tff(41,plain,
% 4.45/3.05 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[40, 39])).
% 4.45/3.05 tff(42,plain,(
% 4.45/3.05 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.45/3.05 inference(skolemize,[status(sab)],[41])).
% 4.45/3.05 tff(43,plain,
% 4.45/3.05 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 4.45/3.05 inference(modus_ponens,[status(thm)],[42, 38])).
% 4.45/3.05 tff(44,plain,
% 4.45/3.05 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 4.45/3.05 inference(quant_inst,[status(thm)],[])).
% 4.45/3.05 tff(45,plain,
% 4.45/3.05 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.45/3.05 inference(unit_resolution,[status(thm)],[44, 43])).
% 4.45/3.05 tff(46,plain,
% 4.45/3.05 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.45/3.05 inference(and_elim,[status(thm)],[32])).
% 4.45/3.05 tff(47,plain,
% 4.45/3.05 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.45/3.05 inference(tautology,[status(thm)],[])).
% 4.45/3.05 tff(48,plain,
% 4.45/3.05 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.45/3.05 inference(unit_resolution,[status(thm)],[47, 46])).
% 4.45/3.05 tff(49,plain,
% 4.45/3.05 (m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.45/3.05 inference(unit_resolution,[status(thm)],[48, 45])).
% 4.45/3.05 tff(50,plain,
% 4.45/3.05 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))) <=> ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))),
% 4.45/3.05 inference(bind,[status(th)],[])).
% 4.45/3.05 tff(51,plain,
% 4.45/3.05 (![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))),
% 4.45/3.06 inference(quant_intro,[status(thm)],[50])).
% 4.45/3.06 tff(52,plain,
% 4.45/3.06 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))), (((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))), (((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))))),
% 4.45/3.06 inference(bind,[status(th)],[])).
% 4.45/3.06 tff(53,plain,
% 4.45/3.06 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))),
% 4.45/3.06 inference(quant_intro,[status(thm)],[52])).
% 4.45/3.06 tff(54,plain,
% 4.45/3.06 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 4.45/3.06 inference(rewrite,[status(thm)],[])).
% 4.45/3.06 tff(55,plain,
% 4.45/3.06 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> (v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))))),
% 4.45/3.06 inference(bind,[status(th)],[])).
% 4.45/3.06 tff(56,plain,
% 4.45/3.06 (![A: $i, B: $i, C: $i, D: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 4.45/3.06 inference(quant_intro,[status(thm)],[55])).
% 4.45/3.06 tff(57,axiom,(![A: $i, B: $i, C: $i, D: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k2_funct_2')).
% 4.45/3.06 tff(58,plain,
% 4.45/3.06 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 4.45/3.06 inference(modus_ponens,[status(thm)],[57, 56])).
% 4.45/3.06 tff(59,plain,
% 4.45/3.06 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 4.45/3.06 inference(modus_ponens,[status(thm)],[58, 54])).
% 4.45/3.06 tff(60,plain,(
% 4.45/3.06 ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 4.45/3.06 inference(skolemize,[status(sab)],[59])).
% 4.45/3.06 tff(61,plain,
% 4.45/3.06 (![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))),
% 4.45/3.06 inference(modus_ponens,[status(thm)],[60, 53])).
% 4.45/3.06 tff(62,plain,
% 4.45/3.06 (![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))),
% 4.45/3.06 inference(modus_ponens,[status(thm)],[61, 51])).
% 4.45/3.06 tff(63,plain,
% 4.45/3.06 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 4.45/3.06 inference(and_elim,[status(thm)],[32])).
% 4.45/3.06 tff(64,plain,
% 4.45/3.06 (v1_funct_1(C!2)),
% 4.45/3.06 inference(and_elim,[status(thm)],[32])).
% 4.45/3.06 tff(65,plain,
% 4.45/3.06 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))))),
% 4.45/3.06 inference(rewrite,[status(thm)],[])).
% 4.45/3.06 tff(66,plain,
% 4.45/3.06 (((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))))),
% 4.45/3.06 inference(rewrite,[status(thm)],[])).
% 4.45/3.06 tff(67,plain,
% 4.45/3.06 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4)))))),
% 4.45/3.06 inference(monotonicity,[status(thm)],[66])).
% 4.45/3.06 tff(68,plain,
% 4.45/3.06 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))))),
% 4.45/3.06 inference(transitivity,[status(thm)],[67, 65])).
% 4.45/3.06 tff(69,plain,
% 4.45/3.06 ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.45/3.06 inference(quant_inst,[status(thm)],[])).
% 4.45/3.06 tff(70,plain,
% 4.45/3.06 ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4)))),
% 4.45/3.06 inference(modus_ponens,[status(thm)],[69, 68])).
% 4.45/3.06 tff(71,plain,
% 4.45/3.06 ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4)))),
% 4.45/3.06 inference(unit_resolution,[status(thm)],[70, 64, 63, 62])).
% 4.45/3.06 tff(72,plain,
% 4.45/3.06 (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))),
% 4.45/3.06 inference(unit_resolution,[status(thm)],[71, 49])).
% 4.45/3.06 tff(73,plain,
% 4.45/3.06 (k9_relat_1(C!2, u1_struct_0(E!4)) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))),
% 4.45/3.06 inference(symmetry,[status(thm)],[72])).
% 4.45/3.06 tff(74,plain,
% 4.45/3.06 (k9_relat_1(C!2, u1_struct_0(E!4)) = u1_struct_0(G!6)),
% 4.45/3.06 inference(transitivity,[status(thm)],[73, 36])).
% 4.45/3.06 tff(75,plain,
% 4.45/3.06 (u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))),
% 4.45/3.06 inference(and_elim,[status(thm)],[34])).
% 4.45/3.06 tff(76,plain,
% 4.45/3.06 (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = u1_struct_0(F!5)),
% 4.45/3.06 inference(symmetry,[status(thm)],[75])).
% 4.45/3.06 tff(77,plain,
% 4.45/3.06 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))))),
% 4.45/3.06 inference(rewrite,[status(thm)],[])).
% 4.45/3.06 tff(78,plain,
% 4.45/3.06 (((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))))),
% 4.45/3.06 inference(rewrite,[status(thm)],[])).
% 4.45/3.06 tff(79,plain,
% 4.45/3.06 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3)))))),
% 4.45/3.07 inference(monotonicity,[status(thm)],[78])).
% 4.45/3.07 tff(80,plain,
% 4.45/3.07 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))))),
% 4.45/3.07 inference(transitivity,[status(thm)],[79, 77])).
% 4.45/3.07 tff(81,plain,
% 4.45/3.07 ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.45/3.07 inference(quant_inst,[status(thm)],[])).
% 4.45/3.07 tff(82,plain,
% 4.45/3.07 ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3)))),
% 4.45/3.07 inference(modus_ponens,[status(thm)],[81, 80])).
% 4.45/3.07 tff(83,plain,
% 4.45/3.07 ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3)))),
% 4.45/3.07 inference(unit_resolution,[status(thm)],[82, 64, 63, 62])).
% 4.45/3.07 tff(84,plain,
% 4.45/3.07 (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))),
% 4.45/3.07 inference(unit_resolution,[status(thm)],[83, 49])).
% 4.45/3.07 tff(85,plain,
% 4.45/3.07 (k9_relat_1(C!2, u1_struct_0(D!3)) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))),
% 4.45/3.07 inference(symmetry,[status(thm)],[84])).
% 4.45/3.07 tff(86,plain,
% 4.45/3.07 (k9_relat_1(C!2, u1_struct_0(D!3)) = u1_struct_0(F!5)),
% 4.45/3.07 inference(transitivity,[status(thm)],[85, 76])).
% 4.45/3.07 tff(87,plain,
% 4.45/3.07 (r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) <=> r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))),
% 4.45/3.07 inference(monotonicity,[status(thm)],[86, 74])).
% 4.45/3.07 tff(88,plain,
% 4.45/3.07 (r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6)) <=> r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4)))),
% 4.45/3.07 inference(symmetry,[status(thm)],[87])).
% 4.45/3.07 tff(89,plain,
% 4.45/3.07 ((~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))) <=> (~r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))))),
% 4.45/3.07 inference(monotonicity,[status(thm)],[88])).
% 4.45/3.07 tff(90,plain,
% 4.45/3.07 (^[A: $i, B: $i] : rewrite((v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))))),
% 4.45/3.07 inference(bind,[status(th)],[])).
% 4.45/3.07 tff(91,plain,
% 4.45/3.07 (![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 4.45/3.07 inference(quant_intro,[status(thm)],[90])).
% 4.45/3.07 tff(92,plain,
% 4.45/3.07 (^[A: $i, B: $i] : refl((v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))),
% 4.45/3.07 inference(bind,[status(th)],[])).
% 4.45/3.07 tff(93,plain,
% 4.45/3.07 (![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 4.45/3.07 inference(quant_intro,[status(thm)],[92])).
% 4.45/3.07 tff(94,plain,
% 4.45/3.07 (^[A: $i, B: $i] : rewrite((v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))),
% 4.45/3.07 inference(bind,[status(th)],[])).
% 4.45/3.07 tff(95,plain,
% 4.45/3.07 (![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 4.45/3.07 inference(quant_intro,[status(thm)],[94])).
% 4.45/3.07 tff(96,plain,
% 4.45/3.07 (![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 4.45/3.07 inference(transitivity,[status(thm)],[95, 93])).
% 4.45/3.07 tff(97,plain,
% 4.45/3.07 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) <=> (~(v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))) <=> (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) <=> (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> ((v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))))), rewrite(((v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))))),
% 4.45/3.07 inference(bind,[status(th)],[])).
% 4.45/3.07 tff(98,plain,
% 4.45/3.07 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 4.45/3.07 inference(quant_intro,[status(thm)],[97])).
% 4.45/3.07 tff(99,plain,
% 4.45/3.07 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 4.45/3.07 inference(rewrite,[status(thm)],[])).
% 4.45/3.07 tff(100,plain,
% 4.45/3.07 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) => ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) => ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) => ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) => ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))))),
% 4.45/3.07 inference(bind,[status(th)],[])).
% 4.45/3.07 tff(101,plain,
% 4.45/3.07 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) => ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 4.45/3.07 inference(quant_intro,[status(thm)],[100])).
% 4.45/3.07 tff(102,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) => ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m1_group_6')).
% 4.45/3.07 tff(103,plain,
% 4.45/3.07 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 4.45/3.07 inference(modus_ponens,[status(thm)],[102, 101])).
% 4.45/3.07 tff(104,plain,
% 4.45/3.07 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 4.45/3.07 inference(modus_ponens,[status(thm)],[103, 99])).
% 4.45/3.07 tff(105,plain,(
% 4.45/3.07 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 4.45/3.07 inference(skolemize,[status(sab)],[104])).
% 4.45/3.07 tff(106,plain,
% 4.45/3.07 (![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 4.45/3.07 inference(modus_ponens,[status(thm)],[105, 98])).
% 4.45/3.07 tff(107,plain,
% 4.45/3.07 (![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 4.45/3.07 inference(modus_ponens,[status(thm)],[106, 96])).
% 4.45/3.07 tff(108,plain,
% 4.45/3.07 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 4.45/3.07 inference(modus_ponens,[status(thm)],[107, 91])).
% 4.45/3.07 tff(109,plain,
% 4.45/3.07 (m1_group_2(G!6, B!1)),
% 4.45/3.07 inference(or_elim,[status(thm)],[33])).
% 4.45/3.07 tff(110,plain,
% 4.45/3.07 (l1_group_1(B!1)),
% 4.45/3.07 inference(and_elim,[status(thm)],[32])).
% 4.45/3.07 tff(111,plain,
% 4.45/3.07 (v4_group_1(B!1)),
% 4.45/3.07 inference(and_elim,[status(thm)],[32])).
% 4.45/3.07 tff(112,plain,
% 4.45/3.07 (v3_group_1(B!1)),
% 4.45/3.07 inference(and_elim,[status(thm)],[32])).
% 4.45/3.07 tff(113,plain,
% 4.45/3.07 (~v3_struct_0(B!1)),
% 4.45/3.07 inference(and_elim,[status(thm)],[32])).
% 4.45/3.07 tff(114,plain,
% 4.45/3.07 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))),
% 4.45/3.07 inference(rewrite,[status(thm)],[])).
% 4.45/3.07 tff(115,plain,
% 4.45/3.07 ((v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6))) <=> (v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))),
% 4.45/3.07 inference(rewrite,[status(thm)],[])).
% 4.45/3.07 tff(116,plain,
% 4.45/3.07 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6))))),
% 4.45/3.07 inference(monotonicity,[status(thm)],[115])).
% 4.45/3.07 tff(117,plain,
% 4.45/3.07 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))),
% 4.45/3.07 inference(transitivity,[status(thm)],[116, 114])).
% 4.45/3.07 tff(118,plain,
% 4.45/3.07 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))),
% 4.45/3.07 inference(quant_inst,[status(thm)],[])).
% 4.45/3.07 tff(119,plain,
% 4.45/3.07 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6))),
% 4.45/3.07 inference(modus_ponens,[status(thm)],[118, 117])).
% 4.45/3.07 tff(120,plain,
% 4.45/3.07 (![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6))),
% 4.45/3.07 inference(unit_resolution,[status(thm)],[119, 113, 112, 111, 110, 109, 108])).
% 4.45/3.07 tff(121,plain,
% 4.45/3.07 ((~![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6))) | (m1_group_6(F!5, B!1, G!6) <=> m1_group_2(F!5, G!6))),
% 4.45/3.07 inference(quant_inst,[status(thm)],[])).
% 4.45/3.07 tff(122,plain,
% 4.45/3.07 (m1_group_6(F!5, B!1, G!6) <=> m1_group_2(F!5, G!6)),
% 4.45/3.07 inference(unit_resolution,[status(thm)],[121, 120])).
% 4.45/3.07 tff(123,plain,
% 4.45/3.07 (~m1_group_6(F!5, B!1, G!6)),
% 4.45/3.07 inference(or_elim,[status(thm)],[33])).
% 4.45/3.07 tff(124,plain,
% 4.45/3.07 ((~(m1_group_6(F!5, B!1, G!6) <=> m1_group_2(F!5, G!6))) | m1_group_6(F!5, B!1, G!6) | (~m1_group_2(F!5, G!6))),
% 4.45/3.07 inference(tautology,[status(thm)],[])).
% 4.45/3.07 tff(125,plain,
% 4.45/3.07 ((~(m1_group_6(F!5, B!1, G!6) <=> m1_group_2(F!5, G!6))) | (~m1_group_2(F!5, G!6))),
% 4.45/3.07 inference(unit_resolution,[status(thm)],[124, 123])).
% 4.45/3.07 tff(126,plain,
% 4.45/3.07 (~m1_group_2(F!5, G!6)),
% 4.45/3.07 inference(unit_resolution,[status(thm)],[125, 122])).
% 4.45/3.07 tff(127,plain,
% 4.45/3.07 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))))),
% 4.45/3.07 inference(bind,[status(th)],[])).
% 4.45/3.07 tff(128,plain,
% 4.45/3.07 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 4.45/3.07 inference(quant_intro,[status(thm)],[127])).
% 4.45/3.07 tff(129,plain,
% 4.45/3.07 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 4.45/3.07 inference(bind,[status(th)],[])).
% 4.45/3.07 tff(130,plain,
% 4.45/3.07 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 4.45/3.07 inference(quant_intro,[status(thm)],[129])).
% 4.45/3.07 tff(131,plain,
% 4.45/3.07 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 4.45/3.07 inference(bind,[status(th)],[])).
% 4.45/3.07 tff(132,plain,
% 4.45/3.07 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 4.45/3.07 inference(quant_intro,[status(thm)],[131])).
% 4.45/3.07 tff(133,plain,
% 4.45/3.07 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 4.45/3.07 inference(transitivity,[status(thm)],[132, 130])).
% 4.45/3.07 tff(134,plain,
% 4.45/3.07 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 4.45/3.07 inference(bind,[status(th)],[])).
% 4.45/3.07 tff(135,plain,
% 4.45/3.07 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 4.45/3.07 inference(quant_intro,[status(thm)],[134])).
% 4.45/3.08 tff(136,plain,
% 4.45/3.08 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 4.45/3.08 inference(rewrite,[status(thm)],[])).
% 4.45/3.08 tff(137,plain,
% 4.45/3.08 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C)) <=> ((~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | m1_group_2(B, C))), ((m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C))) <=> (m1_group_2(C, A) => ((~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | m1_group_2(B, C))))), rewrite((m1_group_2(C, A) => ((~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | m1_group_2(B, C))) <=> (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))), ((m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C))) <=> (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))), (![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C))) <=> ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))), ((m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C)))) <=> (m1_group_2(B, A) => ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))), rewrite((m1_group_2(B, A) => ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) <=> ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))), ((m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C)))) <=> ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))))), (![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C)))) <=> ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))))),
% 4.45/3.08 inference(bind,[status(th)],[])).
% 4.45/3.08 tff(138,plain,
% 4.45/3.08 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 4.45/3.08 inference(quant_intro,[status(thm)],[137])).
% 4.45/3.08 tff(139,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t66_group_2')).
% 4.45/3.08 tff(140,plain,
% 4.45/3.08 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 4.45/3.08 inference(modus_ponens,[status(thm)],[139, 138])).
% 4.45/3.08 tff(141,plain,
% 4.45/3.08 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 4.45/3.08 inference(modus_ponens,[status(thm)],[140, 136])).
% 4.45/3.08 tff(142,plain,(
% 4.45/3.08 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 4.45/3.08 inference(skolemize,[status(sab)],[141])).
% 4.45/3.08 tff(143,plain,
% 4.45/3.08 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 4.45/3.08 inference(modus_ponens,[status(thm)],[142, 135])).
% 4.45/3.08 tff(144,plain,
% 4.45/3.08 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 4.45/3.08 inference(modus_ponens,[status(thm)],[143, 133])).
% 4.45/3.08 tff(145,plain,
% 4.45/3.08 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 4.45/3.08 inference(modus_ponens,[status(thm)],[144, 128])).
% 4.45/3.08 tff(146,plain,
% 4.45/3.08 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1)))))),
% 4.45/3.08 inference(rewrite,[status(thm)],[])).
% 4.45/3.08 tff(147,plain,
% 4.45/3.08 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1)))))),
% 4.45/3.08 inference(quant_inst,[status(thm)],[])).
% 4.45/3.08 tff(148,plain,
% 4.45/3.08 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))),
% 4.45/3.08 inference(modus_ponens,[status(thm)],[147, 146])).
% 4.45/3.08 tff(149,plain,
% 4.45/3.08 (![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))),
% 4.45/3.08 inference(unit_resolution,[status(thm)],[148, 113, 112, 111, 110, 145])).
% 4.45/3.08 tff(150,plain,
% 4.45/3.08 (m1_group_2(F!5, B!1)),
% 4.45/3.08 inference(and_elim,[status(thm)],[32])).
% 4.45/3.08 tff(151,plain,
% 4.45/3.08 (((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | ((~m1_group_2(F!5, B!1)) | ![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C)))))) <=> ((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | (~m1_group_2(F!5, B!1)) | ![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C)))))),
% 4.45/3.08 inference(rewrite,[status(thm)],[])).
% 4.45/3.08 tff(152,plain,
% 4.45/3.08 (((~m1_group_2(F!5, B!1)) | ![C: $i] : (m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))) | (~m1_group_2(C, B!1)))) <=> ((~m1_group_2(F!5, B!1)) | ![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C)))))),
% 4.45/3.08 inference(rewrite,[status(thm)],[])).
% 4.45/3.08 tff(153,plain,
% 4.45/3.08 (((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | ((~m1_group_2(F!5, B!1)) | ![C: $i] : (m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) <=> ((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | ((~m1_group_2(F!5, B!1)) | ![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))))),
% 4.45/3.08 inference(monotonicity,[status(thm)],[152])).
% 4.45/3.08 tff(154,plain,
% 4.45/3.08 (((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | ((~m1_group_2(F!5, B!1)) | ![C: $i] : (m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) <=> ((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | (~m1_group_2(F!5, B!1)) | ![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C)))))),
% 4.45/3.08 inference(transitivity,[status(thm)],[153, 151])).
% 4.45/3.08 tff(155,plain,
% 4.45/3.08 ((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | ((~m1_group_2(F!5, B!1)) | ![C: $i] : (m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))) | (~m1_group_2(C, B!1))))),
% 4.45/3.08 inference(quant_inst,[status(thm)],[])).
% 4.45/3.08 tff(156,plain,
% 4.45/3.08 ((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | (~m1_group_2(F!5, B!1)) | ![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))),
% 4.45/3.08 inference(modus_ponens,[status(thm)],[155, 154])).
% 4.45/3.08 tff(157,plain,
% 4.45/3.08 (![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))),
% 4.45/3.08 inference(unit_resolution,[status(thm)],[156, 150, 149])).
% 4.45/3.08 tff(158,plain,
% 4.45/3.08 (((~![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))) | ((~m1_group_2(G!6, B!1)) | m1_group_2(F!5, G!6) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))))) <=> ((~![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))) | (~m1_group_2(G!6, B!1)) | m1_group_2(F!5, G!6) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))))),
% 4.45/3.08 inference(rewrite,[status(thm)],[])).
% 4.45/3.08 tff(159,plain,
% 4.45/3.08 ((~![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))) | ((~m1_group_2(G!6, B!1)) | m1_group_2(F!5, G!6) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))))),
% 4.45/3.08 inference(quant_inst,[status(thm)],[])).
% 4.45/3.08 tff(160,plain,
% 4.45/3.08 ((~![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))) | (~m1_group_2(G!6, B!1)) | m1_group_2(F!5, G!6) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6)))),
% 4.45/3.08 inference(modus_ponens,[status(thm)],[159, 158])).
% 4.45/3.08 tff(161,plain,
% 4.45/3.08 (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))),
% 4.45/3.08 inference(unit_resolution,[status(thm)],[160, 109, 157, 126])).
% 4.45/3.08 tff(162,plain,
% 4.45/3.08 (~r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4)))),
% 4.45/3.08 inference(modus_ponens,[status(thm)],[161, 89])).
% 4.45/3.08 tff(163,plain,
% 4.45/3.08 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 4.45/3.08 inference(bind,[status(th)],[])).
% 4.45/3.08 tff(164,plain,
% 4.45/3.08 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 4.45/3.08 inference(quant_intro,[status(thm)],[163])).
% 4.45/3.08 tff(165,plain,
% 4.45/3.08 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 4.45/3.08 inference(bind,[status(th)],[])).
% 4.45/3.08 tff(166,plain,
% 4.45/3.08 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 4.45/3.08 inference(quant_intro,[status(thm)],[165])).
% 4.45/3.08 tff(167,plain,
% 4.45/3.08 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 4.45/3.08 inference(transitivity,[status(thm)],[166, 164])).
% 4.45/3.08 tff(168,plain,
% 4.45/3.08 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))))),
% 4.45/3.08 inference(bind,[status(th)],[])).
% 4.45/3.08 tff(169,plain,
% 4.45/3.08 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 4.45/3.08 inference(quant_intro,[status(thm)],[168])).
% 4.45/3.08 tff(170,plain,
% 4.45/3.08 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 4.45/3.08 inference(rewrite,[status(thm)],[])).
% 4.45/3.08 tff(171,plain,
% 4.45/3.08 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> (m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), rewrite((m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), (![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))))),
% 4.45/3.08 inference(bind,[status(th)],[])).
% 4.45/3.09 tff(172,plain,
% 4.45/3.09 (![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 4.45/3.09 inference(quant_intro,[status(thm)],[171])).
% 4.45/3.09 tff(173,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_group_2')).
% 4.45/3.09 tff(174,plain,
% 4.45/3.09 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 4.45/3.09 inference(modus_ponens,[status(thm)],[173, 172])).
% 4.45/3.09 tff(175,plain,
% 4.45/3.09 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 4.45/3.09 inference(modus_ponens,[status(thm)],[174, 170])).
% 4.45/3.09 tff(176,plain,(
% 4.45/3.09 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 4.45/3.09 inference(skolemize,[status(sab)],[175])).
% 4.45/3.09 tff(177,plain,
% 4.45/3.09 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 4.45/3.09 inference(modus_ponens,[status(thm)],[176, 169])).
% 4.45/3.09 tff(178,plain,
% 4.45/3.09 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 4.45/3.09 inference(modus_ponens,[status(thm)],[177, 167])).
% 4.45/3.09 tff(179,plain,
% 4.45/3.09 (l1_group_1(A!0)),
% 4.45/3.09 inference(and_elim,[status(thm)],[32])).
% 4.45/3.09 tff(180,plain,
% 4.45/3.09 (v3_group_1(A!0)),
% 4.45/3.09 inference(and_elim,[status(thm)],[32])).
% 4.45/3.09 tff(181,plain,
% 4.45/3.09 (~v3_struct_0(A!0)),
% 4.45/3.09 inference(and_elim,[status(thm)],[32])).
% 4.45/3.09 tff(182,plain,
% 4.45/3.09 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 4.45/3.09 inference(rewrite,[status(thm)],[])).
% 4.45/3.09 tff(183,plain,
% 4.45/3.09 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 4.45/3.09 inference(quant_inst,[status(thm)],[])).
% 4.45/3.09 tff(184,plain,
% 4.45/3.09 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 4.45/3.09 inference(modus_ponens,[status(thm)],[183, 182])).
% 4.45/3.09 tff(185,plain,
% 4.45/3.09 (![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 4.45/3.09 inference(unit_resolution,[status(thm)],[184, 181, 180, 179, 178])).
% 4.45/3.09 tff(186,plain,
% 4.45/3.09 (m1_group_2(E!4, A!0)),
% 4.45/3.09 inference(and_elim,[status(thm)],[32])).
% 4.45/3.09 tff(187,plain,
% 4.45/3.09 (((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(E!4, A!0)) | (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(E!4, A!0)) | (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)))))),
% 4.45/3.09 inference(rewrite,[status(thm)],[])).
% 4.45/3.09 tff(188,plain,
% 4.45/3.09 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(E!4, A!0)) | (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)))))),
% 4.45/3.09 inference(quant_inst,[status(thm)],[])).
% 4.45/3.09 tff(189,plain,
% 4.45/3.09 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(E!4, A!0)) | (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4))))),
% 4.45/3.09 inference(modus_ponens,[status(thm)],[188, 187])).
% 4.45/3.09 tff(190,plain,
% 4.45/3.09 (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)))),
% 4.45/3.09 inference(unit_resolution,[status(thm)],[189, 186, 185])).
% 4.45/3.09 tff(191,plain,
% 4.45/3.09 ((v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4))) | (~v3_struct_0(E!4))),
% 4.45/3.09 inference(tautology,[status(thm)],[])).
% 4.45/3.09 tff(192,plain,
% 4.45/3.09 (~v3_struct_0(E!4)),
% 4.45/3.09 inference(unit_resolution,[status(thm)],[191, 190])).
% 4.45/3.09 tff(193,plain,
% 4.45/3.09 ((v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4))) | v3_group_1(E!4)),
% 4.45/3.09 inference(tautology,[status(thm)],[])).
% 4.45/3.09 tff(194,plain,
% 4.45/3.09 (v3_group_1(E!4)),
% 4.45/3.09 inference(unit_resolution,[status(thm)],[193, 190])).
% 4.45/3.09 tff(195,plain,
% 4.45/3.09 ((v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4))) | l1_group_1(E!4)),
% 4.45/3.09 inference(tautology,[status(thm)],[])).
% 4.45/3.09 tff(196,plain,
% 4.45/3.09 (l1_group_1(E!4)),
% 4.45/3.09 inference(unit_resolution,[status(thm)],[195, 190])).
% 4.45/3.09 tff(197,plain,
% 4.45/3.09 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))))),
% 4.45/3.09 inference(bind,[status(th)],[])).
% 4.45/3.09 tff(198,plain,
% 4.45/3.09 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))),
% 4.45/3.09 inference(quant_intro,[status(thm)],[197])).
% 4.45/3.09 tff(199,plain,
% 4.45/3.09 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))))),
% 4.45/3.09 inference(bind,[status(th)],[])).
% 4.45/3.09 tff(200,plain,
% 4.45/3.09 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))),
% 4.45/3.09 inference(quant_intro,[status(thm)],[199])).
% 4.45/3.09 tff(201,plain,
% 4.45/3.09 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))),
% 4.45/3.09 inference(transitivity,[status(thm)],[200, 198])).
% 4.45/3.09 tff(202,plain,
% 4.45/3.09 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)) <=> (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))), ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> (~(~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), rewrite((~(~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))), ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))), rewrite((m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> ((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))), rewrite(((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))))),
% 4.45/3.09 inference(bind,[status(th)],[])).
% 4.45/3.09 tff(203,plain,
% 4.45/3.09 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))),
% 4.45/3.09 inference(quant_intro,[status(thm)],[202])).
% 4.45/3.09 tff(204,plain,
% 4.45/3.09 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))),
% 4.45/3.09 inference(rewrite,[status(thm)],[])).
% 4.45/3.09 tff(205,plain,
% 4.45/3.09 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))), (((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> (((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))), rewrite((((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))), (((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))), (![B: $i] : ((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))),
% 4.45/3.09 inference(bind,[status(th)],[])).
% 4.45/3.09 tff(206,plain,
% 4.45/3.09 (![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))),
% 4.45/3.09 inference(quant_intro,[status(thm)],[205])).
% 4.45/3.09 tff(207,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_group_2')).
% 4.45/3.09 tff(208,plain,
% 4.45/3.09 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))),
% 4.45/3.09 inference(modus_ponens,[status(thm)],[207, 206])).
% 4.45/3.09 tff(209,plain,
% 4.45/3.09 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))),
% 4.45/3.09 inference(modus_ponens,[status(thm)],[208, 204])).
% 4.45/3.09 tff(210,plain,(
% 4.45/3.09 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))),
% 4.45/3.09 inference(skolemize,[status(sab)],[209])).
% 4.45/3.09 tff(211,plain,
% 4.45/3.09 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))),
% 4.45/3.09 inference(modus_ponens,[status(thm)],[210, 203])).
% 4.45/3.09 tff(212,plain,
% 4.45/3.09 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))),
% 4.45/3.09 inference(modus_ponens,[status(thm)],[211, 201])).
% 4.45/3.09 tff(213,plain,
% 4.45/3.09 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))) | (v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, E!4) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B)))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))) | v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, E!4) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B)))))))))),
% 4.45/3.09 inference(rewrite,[status(thm)],[])).
% 4.45/3.09 tff(214,plain,
% 4.45/3.09 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))) | (v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, E!4) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B)))))))))),
% 4.45/3.09 inference(quant_inst,[status(thm)],[])).
% 4.45/3.09 tff(215,plain,
% 4.45/3.09 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))) | v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, E!4) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))))))),
% 4.45/3.09 inference(modus_ponens,[status(thm)],[214, 213])).
% 4.45/3.09 tff(216,plain,
% 4.45/3.09 (v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, E!4) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))))))),
% 4.45/3.09 inference(unit_resolution,[status(thm)],[215, 212])).
% 4.45/3.09 tff(217,plain,
% 4.45/3.09 (![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, E!4) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))))))),
% 4.45/3.09 inference(unit_resolution,[status(thm)],[216, 196, 194, 192])).
% 4.45/3.09 tff(218,plain,
% 4.45/3.09 (m1_group_2(D!3, A!0)),
% 4.45/3.09 inference(and_elim,[status(thm)],[32])).
% 4.45/3.09 tff(219,plain,
% 4.45/3.09 (((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(D!3, A!0)) | (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(D!3, A!0)) | (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)))))),
% 4.45/3.10 inference(rewrite,[status(thm)],[])).
% 4.45/3.10 tff(220,plain,
% 4.45/3.10 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(D!3, A!0)) | (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)))))),
% 4.45/3.10 inference(quant_inst,[status(thm)],[])).
% 4.45/3.10 tff(221,plain,
% 4.45/3.10 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(D!3, A!0)) | (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3))))),
% 4.45/3.10 inference(modus_ponens,[status(thm)],[220, 219])).
% 4.45/3.10 tff(222,plain,
% 4.45/3.10 (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)))),
% 4.45/3.10 inference(unit_resolution,[status(thm)],[221, 218, 185])).
% 4.45/3.10 tff(223,plain,
% 4.45/3.10 ((v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3))) | v3_group_1(D!3)),
% 4.45/3.10 inference(tautology,[status(thm)],[])).
% 4.45/3.10 tff(224,plain,
% 4.45/3.10 (v3_group_1(D!3)),
% 4.45/3.10 inference(unit_resolution,[status(thm)],[223, 222])).
% 4.45/3.10 tff(225,plain,
% 4.45/3.10 ((v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3))) | l1_group_1(D!3)),
% 4.45/3.10 inference(tautology,[status(thm)],[])).
% 4.45/3.10 tff(226,plain,
% 4.45/3.10 (l1_group_1(D!3)),
% 4.45/3.10 inference(unit_resolution,[status(thm)],[225, 222])).
% 4.45/3.10 tff(227,plain,
% 4.45/3.10 ((v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3))) | (~v3_struct_0(D!3))),
% 4.45/3.10 inference(tautology,[status(thm)],[])).
% 4.45/3.10 tff(228,plain,
% 4.45/3.10 (~v3_struct_0(D!3)),
% 4.45/3.10 inference(unit_resolution,[status(thm)],[227, 222])).
% 4.45/3.10 tff(229,plain,
% 4.45/3.10 (((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, E!4) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))))))) | (v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)) | (m1_group_2(D!3, E!4) <=> (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, E!4) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))))))) | v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)) | (m1_group_2(D!3, E!4) <=> (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))))))),
% 4.45/3.10 inference(rewrite,[status(thm)],[])).
% 4.45/3.10 tff(230,plain,
% 4.45/3.10 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, E!4) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))))))) | (v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)) | (m1_group_2(D!3, E!4) <=> (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))))))),
% 4.45/3.10 inference(quant_inst,[status(thm)],[])).
% 4.45/3.10 tff(231,plain,
% 4.45/3.10 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (m1_group_2(B, E!4) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))))))) | v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)) | (m1_group_2(D!3, E!4) <=> (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3)))))))),
% 4.45/3.10 inference(modus_ponens,[status(thm)],[230, 229])).
% 4.45/3.10 tff(232,plain,
% 4.45/3.10 (m1_group_2(D!3, E!4) <=> (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))))),
% 4.45/3.10 inference(unit_resolution,[status(thm)],[231, 228, 226, 224, 217])).
% 4.45/3.10 tff(233,plain,
% 4.45/3.10 (v4_group_1(A!0)),
% 4.45/3.10 inference(and_elim,[status(thm)],[32])).
% 4.45/3.10 tff(234,plain,
% 4.45/3.10 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))),
% 4.56/3.10 inference(rewrite,[status(thm)],[])).
% 4.56/3.10 tff(235,plain,
% 4.56/3.10 ((v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4))) <=> (v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))),
% 4.56/3.10 inference(rewrite,[status(thm)],[])).
% 4.56/3.10 tff(236,plain,
% 4.56/3.10 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4))))),
% 4.56/3.10 inference(monotonicity,[status(thm)],[235])).
% 4.56/3.10 tff(237,plain,
% 4.56/3.10 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))),
% 4.56/3.10 inference(transitivity,[status(thm)],[236, 234])).
% 4.56/3.10 tff(238,plain,
% 4.56/3.10 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))),
% 4.56/3.10 inference(quant_inst,[status(thm)],[])).
% 4.56/3.10 tff(239,plain,
% 4.56/3.10 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4))),
% 4.56/3.10 inference(modus_ponens,[status(thm)],[238, 237])).
% 4.56/3.10 tff(240,plain,
% 4.56/3.10 (![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4))),
% 4.56/3.10 inference(unit_resolution,[status(thm)],[239, 181, 180, 233, 179, 186, 108])).
% 4.56/3.10 tff(241,plain,
% 4.56/3.10 ((~![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4))) | (m1_group_6(D!3, A!0, E!4) <=> m1_group_2(D!3, E!4))),
% 4.56/3.10 inference(quant_inst,[status(thm)],[])).
% 4.56/3.10 tff(242,plain,
% 4.56/3.10 (m1_group_6(D!3, A!0, E!4) <=> m1_group_2(D!3, E!4)),
% 4.56/3.10 inference(unit_resolution,[status(thm)],[241, 240])).
% 4.56/3.10 tff(243,plain,
% 4.56/3.10 (m1_group_6(D!3, A!0, E!4)),
% 4.56/3.10 inference(and_elim,[status(thm)],[34])).
% 4.56/3.10 tff(244,plain,
% 4.56/3.10 ((~(m1_group_6(D!3, A!0, E!4) <=> m1_group_2(D!3, E!4))) | (~m1_group_6(D!3, A!0, E!4)) | m1_group_2(D!3, E!4)),
% 4.56/3.10 inference(tautology,[status(thm)],[])).
% 4.56/3.10 tff(245,plain,
% 4.56/3.10 ((~(m1_group_6(D!3, A!0, E!4) <=> m1_group_2(D!3, E!4))) | m1_group_2(D!3, E!4)),
% 4.56/3.10 inference(unit_resolution,[status(thm)],[244, 243])).
% 4.56/3.10 tff(246,plain,
% 4.56/3.10 (m1_group_2(D!3, E!4)),
% 4.56/3.10 inference(unit_resolution,[status(thm)],[245, 242])).
% 4.56/3.10 tff(247,plain,
% 4.56/3.10 ((~(m1_group_2(D!3, E!4) <=> (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3)))))))) | (~m1_group_2(D!3, E!4)) | (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))))),
% 4.56/3.10 inference(tautology,[status(thm)],[])).
% 4.56/3.10 tff(248,plain,
% 4.56/3.10 ((~(m1_group_2(D!3, E!4) <=> (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3)))))))) | (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))))),
% 4.56/3.10 inference(unit_resolution,[status(thm)],[247, 246])).
% 4.56/3.10 tff(249,plain,
% 4.56/3.10 (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3)))))),
% 4.56/3.10 inference(unit_resolution,[status(thm)],[248, 232])).
% 4.56/3.10 tff(250,plain,
% 4.56/3.10 (((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))) | r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))),
% 4.56/3.10 inference(tautology,[status(thm)],[])).
% 4.56/3.10 tff(251,plain,
% 4.56/3.10 (r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))),
% 4.56/3.10 inference(unit_resolution,[status(thm)],[250, 249])).
% 4.56/3.10 tff(252,plain,
% 4.56/3.10 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.56/3.10 inference(bind,[status(th)],[])).
% 4.56/3.10 tff(253,plain,
% 4.56/3.10 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 4.56/3.10 inference(quant_intro,[status(thm)],[252])).
% 4.56/3.10 tff(254,plain,
% 4.56/3.10 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 4.56/3.10 inference(rewrite,[status(thm)],[])).
% 4.56/3.10 tff(255,plain,
% 4.56/3.10 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.56/3.10 inference(bind,[status(th)],[])).
% 4.56/3.10 tff(256,plain,
% 4.56/3.10 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 4.56/3.10 inference(quant_intro,[status(thm)],[255])).
% 4.56/3.10 tff(257,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 4.56/3.10 tff(258,plain,
% 4.56/3.10 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 4.56/3.10 inference(modus_ponens,[status(thm)],[257, 256])).
% 4.56/3.10 tff(259,plain,
% 4.56/3.10 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 4.56/3.10 inference(modus_ponens,[status(thm)],[258, 254])).
% 4.56/3.10 tff(260,plain,(
% 4.56/3.10 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 4.56/3.10 inference(skolemize,[status(sab)],[259])).
% 4.56/3.10 tff(261,plain,
% 4.56/3.10 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 4.56/3.10 inference(modus_ponens,[status(thm)],[260, 253])).
% 4.56/3.10 tff(262,plain,
% 4.56/3.10 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 4.56/3.10 inference(rewrite,[status(thm)],[])).
% 4.56/3.10 tff(263,plain,
% 4.56/3.10 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 4.56/3.10 inference(quant_inst,[status(thm)],[])).
% 4.56/3.10 tff(264,plain,
% 4.56/3.10 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.56/3.10 inference(modus_ponens,[status(thm)],[263, 262])).
% 4.56/3.10 tff(265,plain,
% 4.56/3.10 (m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))),
% 4.56/3.10 inference(unit_resolution,[status(thm)],[264, 46, 261])).
% 4.56/3.10 tff(266,plain,
% 4.56/3.10 (^[A: $i, B: $i, C: $i] : refl((v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 4.56/3.10 inference(bind,[status(th)],[])).
% 4.56/3.10 tff(267,plain,
% 4.56/3.10 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.56/3.10 inference(quant_intro,[status(thm)],[266])).
% 4.56/3.10 tff(268,plain,
% 4.56/3.10 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.56/3.10 inference(rewrite,[status(thm)],[])).
% 4.56/3.10 tff(269,plain,
% 4.56/3.10 (^[A: $i, B: $i, C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 4.56/3.10 inference(bind,[status(th)],[])).
% 4.56/3.10 tff(270,plain,
% 4.56/3.10 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.56/3.10 inference(quant_intro,[status(thm)],[269])).
% 4.56/3.10 tff(271,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_relset_1')).
% 4.56/3.10 tff(272,plain,
% 4.56/3.10 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.56/3.10 inference(modus_ponens,[status(thm)],[271, 270])).
% 4.56/3.10 tff(273,plain,
% 4.56/3.10 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.56/3.10 inference(modus_ponens,[status(thm)],[272, 268])).
% 4.56/3.10 tff(274,plain,(
% 4.56/3.10 ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.56/3.10 inference(skolemize,[status(sab)],[273])).
% 4.56/3.10 tff(275,plain,
% 4.56/3.10 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 4.56/3.10 inference(modus_ponens,[status(thm)],[274, 267])).
% 4.56/3.10 tff(276,plain,
% 4.56/3.10 (((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.56/3.10 inference(rewrite,[status(thm)],[])).
% 4.56/3.10 tff(277,plain,
% 4.56/3.10 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 4.56/3.10 inference(quant_inst,[status(thm)],[])).
% 4.56/3.10 tff(278,plain,
% 4.56/3.10 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 4.56/3.10 inference(modus_ponens,[status(thm)],[277, 276])).
% 4.56/3.10 tff(279,plain,
% 4.56/3.10 (v1_relat_1(C!2)),
% 4.56/3.10 inference(unit_resolution,[status(thm)],[278, 275, 265])).
% 4.56/3.10 tff(280,plain,
% 4.56/3.10 (^[A: $i, B: $i, C: $i] : refl((r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))) <=> (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))))),
% 4.56/3.11 inference(bind,[status(th)],[])).
% 4.56/3.11 tff(281,plain,
% 4.56/3.11 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 4.56/3.11 inference(quant_intro,[status(thm)],[280])).
% 4.56/3.11 tff(282,plain,
% 4.56/3.11 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 4.56/3.11 inference(rewrite,[status(thm)],[])).
% 4.56/3.11 tff(283,plain,
% 4.56/3.11 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B))) <=> ((~r1_tarski(A, B)) | r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))), ((v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> (v1_relat_1(C) => ((~r1_tarski(A, B)) | r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))))), rewrite((v1_relat_1(C) => ((~r1_tarski(A, B)) | r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))), ((v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))))),
% 4.56/3.11 inference(bind,[status(th)],[])).
% 4.56/3.11 tff(284,plain,
% 4.56/3.11 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 4.56/3.11 inference(quant_intro,[status(thm)],[283])).
% 4.56/3.11 tff(285,axiom,(![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t156_relat_1')).
% 4.56/3.11 tff(286,plain,
% 4.56/3.11 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 4.56/3.11 inference(modus_ponens,[status(thm)],[285, 284])).
% 4.56/3.11 tff(287,plain,
% 4.56/3.11 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 4.56/3.11 inference(modus_ponens,[status(thm)],[286, 282])).
% 4.56/3.11 tff(288,plain,(
% 4.56/3.11 ![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 4.56/3.11 inference(skolemize,[status(sab)],[287])).
% 4.56/3.11 tff(289,plain,
% 4.56/3.11 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 4.56/3.11 inference(modus_ponens,[status(thm)],[288, 281])).
% 4.56/3.11 tff(290,plain,
% 4.56/3.11 (((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | ((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_relat_1(C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_relat_1(C!2)))),
% 4.56/3.11 inference(rewrite,[status(thm)],[])).
% 4.56/3.11 tff(291,plain,
% 4.56/3.11 ((r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~v1_relat_1(C!2))) <=> ((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_relat_1(C!2)))),
% 4.56/3.11 inference(rewrite,[status(thm)],[])).
% 4.56/3.11 tff(292,plain,
% 4.56/3.11 (((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~v1_relat_1(C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | ((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_relat_1(C!2))))),
% 4.56/3.12 inference(monotonicity,[status(thm)],[291])).
% 4.56/3.12 tff(293,plain,
% 4.56/3.12 (((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~v1_relat_1(C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_relat_1(C!2)))),
% 4.56/3.12 inference(transitivity,[status(thm)],[292, 290])).
% 4.56/3.12 tff(294,plain,
% 4.56/3.12 ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~v1_relat_1(C!2)))),
% 4.56/3.12 inference(quant_inst,[status(thm)],[])).
% 4.56/3.12 tff(295,plain,
% 4.56/3.12 ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_relat_1(C!2))),
% 4.56/3.12 inference(modus_ponens,[status(thm)],[294, 293])).
% 4.56/3.12 tff(296,plain,
% 4.56/3.12 (r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4)))),
% 4.56/3.12 inference(unit_resolution,[status(thm)],[295, 289, 279, 251])).
% 4.56/3.12 tff(297,plain,
% 4.56/3.12 ($false),
% 4.56/3.12 inference(unit_resolution,[status(thm)],[296, 162])).
% 4.56/3.12 % SZS output end Proof
%------------------------------------------------------------------------------