%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP638+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:15 AM UTC 2025
% Result : Theorem 0.41s 0.56s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP638+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 16:34:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.41/0.56 % SZS status Theorem
% 0.41/0.56 % SZS output start Proof
% 0.41/0.56 tff(r1_tarski_type, type, (
% 0.41/0.56 r1_tarski: ( $i * $i ) > $o)).
% 0.41/0.56 tff(u1_struct_0_type, type, (
% 0.41/0.56 u1_struct_0: $i > $i)).
% 0.41/0.56 tff(tptp_fun_G_6_type, type, (
% 0.41/0.56 tptp_fun_G_6: $i)).
% 0.41/0.56 tff(tptp_fun_F_5_type, type, (
% 0.41/0.56 tptp_fun_F_5: $i)).
% 0.41/0.56 tff(k10_relat_1_type, type, (
% 0.41/0.56 k10_relat_1: ( $i * $i ) > $i)).
% 0.41/0.56 tff(tptp_fun_E_4_type, type, (
% 0.41/0.56 tptp_fun_E_4: $i)).
% 0.41/0.56 tff(tptp_fun_C_2_type, type, (
% 0.41/0.56 tptp_fun_C_2: $i)).
% 0.41/0.56 tff(tptp_fun_D_3_type, type, (
% 0.41/0.56 tptp_fun_D_3: $i)).
% 0.41/0.56 tff(k3_funct_2_type, type, (
% 0.41/0.56 k3_funct_2: ( $i * $i * $i * $i ) > $i)).
% 0.41/0.56 tff(tptp_fun_B_1_type, type, (
% 0.41/0.56 tptp_fun_B_1: $i)).
% 0.41/0.56 tff(tptp_fun_A_0_type, type, (
% 0.41/0.56 tptp_fun_A_0: $i)).
% 0.41/0.56 tff(m1_relset_1_type, type, (
% 0.41/0.56 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.41/0.56 tff(m2_relset_1_type, type, (
% 0.41/0.56 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.41/0.56 tff(m1_group_2_type, type, (
% 0.41/0.56 m1_group_2: ( $i * $i ) > $o)).
% 0.41/0.56 tff(m1_group_6_type, type, (
% 0.41/0.56 m1_group_6: ( $i * $i * $i ) > $o)).
% 0.41/0.56 tff(v1_group_6_type, type, (
% 0.41/0.56 v1_group_6: ( $i * $i * $i ) > $o)).
% 0.41/0.56 tff(v1_funct_2_type, type, (
% 0.41/0.56 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.41/0.56 tff(v1_funct_1_type, type, (
% 0.41/0.56 v1_funct_1: $i > $o)).
% 0.41/0.56 tff(l1_group_1_type, type, (
% 0.41/0.56 l1_group_1: $i > $o)).
% 0.41/0.56 tff(v4_group_1_type, type, (
% 0.41/0.56 v4_group_1: $i > $o)).
% 0.41/0.56 tff(v3_group_1_type, type, (
% 0.41/0.56 v3_group_1: $i > $o)).
% 0.41/0.56 tff(v3_struct_0_type, type, (
% 0.41/0.56 v3_struct_0: $i > $o)).
% 0.41/0.56 tff(k1_realset1_type, type, (
% 0.41/0.56 k1_realset1: ( $i * $i ) > $i)).
% 0.41/0.56 tff(u1_group_1_type, type, (
% 0.41/0.56 u1_group_1: $i > $i)).
% 0.41/0.56 tff(v1_relat_1_type, type, (
% 0.41/0.56 v1_relat_1: $i > $o)).
% 0.41/0.56 tff(m1_subset_1_type, type, (
% 0.41/0.56 m1_subset_1: ( $i * $i ) > $o)).
% 0.41/0.56 tff(k1_zfmisc_1_type, type, (
% 0.41/0.56 k1_zfmisc_1: $i > $i)).
% 0.41/0.56 tff(k2_zfmisc_1_type, type, (
% 0.41/0.56 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.41/0.56 tff(1,plain,
% 0.41/0.56 (^[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)))),
% 0.41/0.56 inference(bind,[status(th)],[])).
% 0.41/0.56 tff(2,plain,
% 0.41/0.56 (![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))),
% 0.41/0.56 inference(quant_intro,[status(thm)],[1])).
% 0.41/0.56 tff(3,plain,
% 0.41/0.56 (![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))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(4,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.41/0.56 tff(5,plain,
% 0.41/0.56 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.41/0.56 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.41/0.56 tff(6,plain,(
% 0.41/0.56 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.41/0.56 inference(skolemize,[status(sab)],[5])).
% 0.41/0.56 tff(7,plain,
% 0.41/0.56 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.41/0.56 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.41/0.56 tff(8,plain,
% 0.41/0.56 ((~![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)))),
% 0.41/0.56 inference(quant_inst,[status(thm)],[])).
% 0.41/0.56 tff(9,plain,
% 0.41/0.56 (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))),
% 0.41/0.56 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.41/0.56 tff(10,plain,
% 0.41/0.56 ((((~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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))) <=> ((~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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(11,plain,
% 0.41/0.56 ((((~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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, 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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(12,plain,
% 0.41/0.56 (((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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))) <=> (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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(13,plain,
% 0.41/0.56 ((m1_group_2(D!3, B!1) & (m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))) <=> (m1_group_2(D!3, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(14,plain,
% 0.41/0.56 ((m1_group_2(E!4, B!1) & (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))) <=> (m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(15,plain,
% 0.41/0.56 ((~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))) <=> (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(16,plain,
% 0.41/0.56 ((m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0))))) <=> (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[15])).
% 0.41/0.56 tff(17,plain,
% 0.41/0.56 ((m1_group_2(E!4, B!1) & (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))) <=> (m1_group_2(E!4, B!1) & (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0))))))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[16])).
% 0.41/0.56 tff(18,plain,
% 0.41/0.56 ((m1_group_2(E!4, B!1) & (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))) <=> (m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))),
% 0.41/0.56 inference(transitivity,[status(thm)],[17, 14])).
% 0.41/0.56 tff(19,plain,
% 0.41/0.56 ((m1_group_2(D!3, B!1) & (m1_group_2(E!4, B!1) & (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0))))))) <=> (m1_group_2(D!3, B!1) & (m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0))))))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[18])).
% 0.41/0.56 tff(20,plain,
% 0.41/0.56 ((m1_group_2(D!3, B!1) & (m1_group_2(E!4, B!1) & (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0))))))) <=> (m1_group_2(D!3, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[19, 13])).
% 0.41/0.57 tff(21,plain,
% 0.41/0.57 (((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, B!1) & (m1_group_2(E!4, B!1) & (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))))) <=> ((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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0))))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[20])).
% 0.41/0.57 tff(22,plain,
% 0.41/0.57 (((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, B!1) & (m1_group_2(E!4, B!1) & (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))))) <=> (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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[21, 12])).
% 0.41/0.57 tff(23,plain,
% 0.41/0.57 ((((~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, B!1) & (m1_group_2(E!4, B!1) & (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, 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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0))))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[22])).
% 0.41/0.57 tff(24,plain,
% 0.41/0.57 ((((~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, B!1) & (m1_group_2(E!4, B!1) & (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, 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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[23, 11])).
% 0.41/0.57 tff(25,plain,
% 0.41/0.57 ((((~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, B!1) & (m1_group_2(E!4, B!1) & (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))))))) <=> (((~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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0))))))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[24])).
% 0.41/0.57 tff(26,plain,
% 0.41/0.57 ((((~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, B!1) & (m1_group_2(E!4, B!1) & (m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))))))) <=> ((~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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[25, 10])).
% 0.41/0.57 tff(27,plain,
% 0.41/0.57 ((~![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, B)) | ![E: $i] : ((~m1_group_2(E, B)) | ![F: $i] : ((~m1_group_2(F, A)) | ![G: $i] : (m1_group_6(F, A, G) | (~((u1_struct_0(F) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, B, E))) | (~m1_group_2(G, A)))))))))) <=> (~![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, B)) | ![E: $i] : ((~m1_group_2(E, B)) | ![F: $i] : ((~m1_group_2(F, A)) | ![G: $i] : (m1_group_6(F, A, G) | (~((u1_struct_0(F) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, B, E))) | (~m1_group_2(G, A))))))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(28,plain,
% 0.41/0.57 ((~![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, B) => ![E: $i] : (m1_group_2(E, B) => ![F: $i] : (m1_group_2(F, A) => ![G: $i] : (m1_group_2(G, A) => ((((u1_struct_0(F) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E)))) & m1_group_6(D, B, E)) => m1_group_6(F, A, 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, B)) | ![E: $i] : ((~m1_group_2(E, B)) | ![F: $i] : ((~m1_group_2(F, A)) | ![G: $i] : (m1_group_6(F, A, G) | (~((u1_struct_0(F) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, B, E))) | (~m1_group_2(G, A))))))))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(29,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, B) => ![E: $i] : (m1_group_2(E, B) => ![F: $i] : (m1_group_2(F, A) => ![G: $i] : (m1_group_2(G, A) => ((((u1_struct_0(F) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E)))) & m1_group_6(D, B, E)) => m1_group_6(F, A, G)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t11_latsubgr')).
% 0.41/0.57 tff(30,plain,
% 0.41/0.57 (~![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, B)) | ![E: $i] : ((~m1_group_2(E, B)) | ![F: $i] : ((~m1_group_2(F, A)) | ![G: $i] : (m1_group_6(F, A, G) | (~((u1_struct_0(F) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, B, E))) | (~m1_group_2(G, A)))))))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.41/0.57 tff(31,plain,
% 0.41/0.57 (~![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, B)) | ![E: $i] : ((~m1_group_2(E, B)) | ![F: $i] : ((~m1_group_2(F, A)) | ![G: $i] : (m1_group_6(F, A, G) | (~((u1_struct_0(F) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, B, E))) | (~m1_group_2(G, A)))))))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.41/0.57 tff(32,plain,
% 0.41/0.57 (~![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, B)) | ![E: $i] : ((~m1_group_2(E, B)) | ![F: $i] : ((~m1_group_2(F, A)) | ![G: $i] : (m1_group_6(F, A, G) | (~((u1_struct_0(F) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, B, E))) | (~m1_group_2(G, A)))))))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.41/0.57 tff(33,plain,
% 0.41/0.57 (~![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, B)) | ![E: $i] : ((~m1_group_2(E, B)) | ![F: $i] : ((~m1_group_2(F, A)) | ![G: $i] : (m1_group_6(F, A, G) | (~((u1_struct_0(F) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k3_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, B, E))) | (~m1_group_2(G, A)))))))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.41/0.57 tff(34,plain,
% 0.41/0.57 ((~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, B!1) & m1_group_2(E!4, B!1) & m1_group_2(F!5, A!0) & (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.41/0.57 tff(35,plain,
% 0.41/0.57 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.41/0.57 inference(and_elim,[status(thm)],[34])).
% 0.41/0.57 tff(36,plain,
% 0.41/0.57 ((~(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))),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(37,plain,
% 0.41/0.57 ((~(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))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.41/0.57 tff(38,plain,
% 0.41/0.57 (m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[37, 9])).
% 0.41/0.57 tff(39,plain,
% 0.41/0.57 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B))) <=> ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B))))),
% 0.43/0.57 inference(bind,[status(th)],[])).
% 0.43/0.57 tff(40,plain,
% 0.43/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))),
% 0.43/0.57 inference(quant_intro,[status(thm)],[39])).
% 0.43/0.57 tff(41,plain,
% 0.43/0.57 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & m1_relset_1(C, A, B)) <=> (~((~v1_funct_1(C)) | (~m1_relset_1(C, A, B))))), ((~(v1_funct_1(C) & m1_relset_1(C, A, B))) <=> (~(~((~v1_funct_1(C)) | (~m1_relset_1(C, A, B))))))), rewrite((~(~((~v1_funct_1(C)) | (~m1_relset_1(C, A, B))))) <=> ((~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))), ((~(v1_funct_1(C) & m1_relset_1(C, A, B))) <=> ((~v1_funct_1(C)) | (~m1_relset_1(C, A, B))))), (((~(v1_funct_1(C) & m1_relset_1(C, A, B))) | (k3_funct_2(A, B, C, D) = k10_relat_1(C, D))) <=> (((~v1_funct_1(C)) | (~m1_relset_1(C, A, B))) | (k3_funct_2(A, B, C, D) = k10_relat_1(C, D))))), rewrite((((~v1_funct_1(C)) | (~m1_relset_1(C, A, B))) | (k3_funct_2(A, B, C, D) = k10_relat_1(C, D))) <=> ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))), (((~(v1_funct_1(C) & m1_relset_1(C, A, B))) | (k3_funct_2(A, B, C, D) = k10_relat_1(C, D))) <=> ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))))),
% 0.43/0.57 inference(bind,[status(th)],[])).
% 0.43/0.57 tff(42,plain,
% 0.43/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & m1_relset_1(C, A, B))) | (k3_funct_2(A, B, C, D) = k10_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))),
% 0.43/0.57 inference(quant_intro,[status(thm)],[41])).
% 0.43/0.57 tff(43,plain,
% 0.43/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & m1_relset_1(C, A, B))) | (k3_funct_2(A, B, C, D) = k10_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & m1_relset_1(C, A, B))) | (k3_funct_2(A, B, C, D) = k10_relat_1(C, D)))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(44,plain,
% 0.43/0.57 (^[A: $i, B: $i, C: $i, D: $i] : rewrite(((v1_funct_1(C) & m1_relset_1(C, A, B)) => (k3_funct_2(A, B, C, D) = k10_relat_1(C, D))) <=> ((~(v1_funct_1(C) & m1_relset_1(C, A, B))) | (k3_funct_2(A, B, C, D) = k10_relat_1(C, D))))),
% 0.43/0.57 inference(bind,[status(th)],[])).
% 0.43/0.57 tff(45,plain,
% 0.43/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((v1_funct_1(C) & m1_relset_1(C, A, B)) => (k3_funct_2(A, B, C, D) = k10_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & m1_relset_1(C, A, B))) | (k3_funct_2(A, B, C, D) = k10_relat_1(C, D)))),
% 0.43/0.57 inference(quant_intro,[status(thm)],[44])).
% 0.43/0.57 tff(46,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((v1_funct_1(C) & m1_relset_1(C, A, B)) => (k3_funct_2(A, B, C, D) = k10_relat_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k3_funct_2')).
% 0.43/0.57 tff(47,plain,
% 0.43/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & m1_relset_1(C, A, B))) | (k3_funct_2(A, B, C, D) = k10_relat_1(C, D)))),
% 0.43/0.57 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.43/0.57 tff(48,plain,
% 0.43/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & m1_relset_1(C, A, B))) | (k3_funct_2(A, B, C, D) = k10_relat_1(C, D)))),
% 0.43/0.57 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.43/0.57 tff(49,plain,(
% 0.43/0.57 ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & m1_relset_1(C, A, B))) | (k3_funct_2(A, B, C, D) = k10_relat_1(C, D)))),
% 0.43/0.57 inference(skolemize,[status(sab)],[48])).
% 0.43/0.57 tff(50,plain,
% 0.43/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))),
% 0.43/0.57 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.43/0.57 tff(51,plain,
% 0.43/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))),
% 0.43/0.57 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.43/0.57 tff(52,plain,
% 0.43/0.57 (v1_funct_1(C!2)),
% 0.43/0.57 inference(and_elim,[status(thm)],[34])).
% 0.43/0.57 tff(53,plain,
% 0.43/0.57 (((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~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)) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k10_relat_1(C!2, u1_struct_0(E!4))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~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)) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k10_relat_1(C!2, u1_struct_0(E!4))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(54,plain,
% 0.43/0.57 (((k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k10_relat_1(C!2, u1_struct_0(E!4))) | (~v1_funct_1(C!2)) | (~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)) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k10_relat_1(C!2, u1_struct_0(E!4))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(55,plain,
% 0.43/0.57 (((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))) | ((k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k10_relat_1(C!2, u1_struct_0(E!4))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~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)) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k10_relat_1(C!2, u1_struct_0(E!4)))))),
% 0.43/0.57 inference(monotonicity,[status(thm)],[54])).
% 0.43/0.57 tff(56,plain,
% 0.43/0.57 (((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))) | ((k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k10_relat_1(C!2, u1_struct_0(E!4))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~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)) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k10_relat_1(C!2, u1_struct_0(E!4))))),
% 0.43/0.57 inference(transitivity,[status(thm)],[55, 53])).
% 0.43/0.57 tff(57,plain,
% 0.43/0.57 ((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))) | ((k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k10_relat_1(C!2, u1_struct_0(E!4))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 0.43/0.57 inference(quant_inst,[status(thm)],[])).
% 0.43/0.57 tff(58,plain,
% 0.43/0.57 ((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~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)) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k10_relat_1(C!2, u1_struct_0(E!4)))),
% 0.43/0.57 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.43/0.57 tff(59,plain,
% 0.43/0.57 ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k10_relat_1(C!2, u1_struct_0(E!4)))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[58, 52, 51])).
% 0.43/0.57 tff(60,plain,
% 0.43/0.57 (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k10_relat_1(C!2, u1_struct_0(E!4))),
% 0.43/0.57 inference(unit_resolution,[status(thm)],[59, 38])).
% 0.43/0.57 tff(61,plain,
% 0.43/0.57 (~(m1_group_6(F!5, A!0, G!6) | (~((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4))) | (~m1_group_2(G!6, A!0)))),
% 0.43/0.57 inference(and_elim,[status(thm)],[34])).
% 0.43/0.58 tff(62,plain,
% 0.43/0.58 ((u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, B!1, E!4)),
% 0.43/0.58 inference(or_elim,[status(thm)],[61])).
% 0.43/0.58 tff(63,plain,
% 0.43/0.58 (u1_struct_0(G!6) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))),
% 0.43/0.58 inference(and_elim,[status(thm)],[62])).
% 0.43/0.58 tff(64,plain,
% 0.43/0.58 (u1_struct_0(G!6) = k10_relat_1(C!2, u1_struct_0(E!4))),
% 0.43/0.58 inference(transitivity,[status(thm)],[63, 60])).
% 0.43/0.58 tff(65,plain,
% 0.43/0.58 (((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~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)) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k10_relat_1(C!2, u1_struct_0(D!3))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~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)) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k10_relat_1(C!2, u1_struct_0(D!3))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(66,plain,
% 0.43/0.58 (((k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k10_relat_1(C!2, u1_struct_0(D!3))) | (~v1_funct_1(C!2)) | (~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)) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k10_relat_1(C!2, u1_struct_0(D!3))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(67,plain,
% 0.43/0.58 (((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))) | ((k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k10_relat_1(C!2, u1_struct_0(D!3))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~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)) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k10_relat_1(C!2, u1_struct_0(D!3)))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[66])).
% 0.43/0.58 tff(68,plain,
% 0.43/0.58 (((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))) | ((k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k10_relat_1(C!2, u1_struct_0(D!3))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~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)) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k10_relat_1(C!2, u1_struct_0(D!3))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[67, 65])).
% 0.43/0.58 tff(69,plain,
% 0.43/0.58 ((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~m1_relset_1(C, A, B)))) | ((k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k10_relat_1(C!2, u1_struct_0(D!3))) | (~v1_funct_1(C!2)) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(70,plain,
% 0.43/0.58 ((~![A: $i, B: $i, C: $i, D: $i] : ((k3_funct_2(A, B, C, D) = k10_relat_1(C, D)) | (~v1_funct_1(C)) | (~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)) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k10_relat_1(C!2, u1_struct_0(D!3)))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.43/0.58 tff(71,plain,
% 0.43/0.58 ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k10_relat_1(C!2, u1_struct_0(D!3)))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[70, 52, 51])).
% 0.43/0.58 tff(72,plain,
% 0.43/0.58 (k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k10_relat_1(C!2, u1_struct_0(D!3))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[71, 38])).
% 0.43/0.58 tff(73,plain,
% 0.43/0.58 (u1_struct_0(F!5) = k3_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))),
% 0.43/0.58 inference(and_elim,[status(thm)],[62])).
% 0.43/0.58 tff(74,plain,
% 0.43/0.58 (u1_struct_0(F!5) = k10_relat_1(C!2, u1_struct_0(D!3))),
% 0.43/0.58 inference(transitivity,[status(thm)],[73, 72])).
% 0.43/0.58 tff(75,plain,
% 0.43/0.58 (r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6)) <=> r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_relat_1(C!2, u1_struct_0(E!4)))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[74, 64])).
% 0.43/0.58 tff(76,plain,
% 0.43/0.58 (r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_relat_1(C!2, u1_struct_0(E!4))) <=> r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))),
% 0.43/0.58 inference(symmetry,[status(thm)],[75])).
% 0.43/0.58 tff(77,plain,
% 0.43/0.58 (^[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)))))))),
% 0.43/0.58 inference(bind,[status(th)],[])).
% 0.43/0.58 tff(78,plain,
% 0.43/0.58 (![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))))))),
% 0.43/0.58 inference(quant_intro,[status(thm)],[77])).
% 0.43/0.58 tff(79,plain,
% 0.43/0.58 (^[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)))))))),
% 0.43/0.58 inference(bind,[status(th)],[])).
% 0.43/0.58 tff(80,plain,
% 0.43/0.58 (![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))))))),
% 0.43/0.58 inference(quant_intro,[status(thm)],[79])).
% 0.43/0.58 tff(81,plain,
% 0.43/0.58 (![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))))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[80, 78])).
% 0.43/0.58 tff(82,plain,
% 0.43/0.58 (^[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))))))))),
% 0.43/0.58 inference(bind,[status(th)],[])).
% 0.43/0.58 tff(83,plain,
% 0.43/0.58 (![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))))))),
% 0.43/0.58 inference(quant_intro,[status(thm)],[82])).
% 0.43/0.58 tff(84,plain,
% 0.43/0.58 (![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))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(85,plain,
% 0.43/0.58 (^[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))))))),
% 0.43/0.58 inference(bind,[status(th)],[])).
% 0.43/0.58 tff(86,plain,
% 0.43/0.58 (![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))))),
% 0.43/0.58 inference(quant_intro,[status(thm)],[85])).
% 0.43/0.58 tff(87,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/sandbox2/benchmark/theBenchmark.p','dt_m1_group_2')).
% 0.43/0.58 tff(88,plain,
% 0.43/0.58 (![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))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.43/0.58 tff(89,plain,
% 0.43/0.58 (![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))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.43/0.58 tff(90,plain,(
% 0.43/0.58 ![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))))),
% 0.43/0.58 inference(skolemize,[status(sab)],[89])).
% 0.43/0.58 tff(91,plain,
% 0.43/0.58 (![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))))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.43/0.58 tff(92,plain,
% 0.43/0.58 (![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))))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[91, 81])).
% 0.43/0.58 tff(93,plain,
% 0.43/0.58 (l1_group_1(B!1)),
% 0.43/0.58 inference(and_elim,[status(thm)],[34])).
% 0.43/0.58 tff(94,plain,
% 0.43/0.58 (v3_group_1(B!1)),
% 0.43/0.58 inference(and_elim,[status(thm)],[34])).
% 0.43/0.58 tff(95,plain,
% 0.43/0.58 (~v3_struct_0(B!1)),
% 0.43/0.58 inference(and_elim,[status(thm)],[34])).
% 0.43/0.58 tff(96,plain,
% 0.43/0.58 (((~![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(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | ![B: $i] : ((~m1_group_2(B, B!1)) | (~(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(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | ![B: $i] : ((~m1_group_2(B, B!1)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(97,plain,
% 0.43/0.58 ((~![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(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | ![B: $i] : ((~m1_group_2(B, B!1)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(98,plain,
% 0.43/0.58 ((~![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(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | ![B: $i] : ((~m1_group_2(B, B!1)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.43/0.58 tff(99,plain,
% 0.43/0.58 (![B: $i] : ((~m1_group_2(B, B!1)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[98, 95, 94, 93, 92])).
% 0.43/0.58 tff(100,plain,
% 0.43/0.58 (m1_group_2(E!4, B!1)),
% 0.43/0.58 inference(and_elim,[status(thm)],[34])).
% 0.43/0.58 tff(101,plain,
% 0.43/0.58 (((~![B: $i] : ((~m1_group_2(B, B!1)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(E!4, B!1)) | (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)))))) <=> ((~![B: $i] : ((~m1_group_2(B, B!1)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(E!4, B!1)) | (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(102,plain,
% 0.43/0.58 ((~![B: $i] : ((~m1_group_2(B, B!1)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(E!4, B!1)) | (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)))))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(103,plain,
% 0.43/0.58 ((~![B: $i] : ((~m1_group_2(B, B!1)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(E!4, B!1)) | (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.43/0.58 tff(104,plain,
% 0.43/0.58 (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[103, 100, 99])).
% 0.43/0.58 tff(105,plain,
% 0.43/0.58 ((v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4))) | (~v3_struct_0(E!4))),
% 0.43/0.58 inference(tautology,[status(thm)],[])).
% 0.43/0.58 tff(106,plain,
% 0.43/0.58 (~v3_struct_0(E!4)),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.43/0.58 tff(107,plain,
% 0.43/0.58 ((v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4))) | v3_group_1(E!4)),
% 0.43/0.58 inference(tautology,[status(thm)],[])).
% 0.43/0.58 tff(108,plain,
% 0.43/0.58 (v3_group_1(E!4)),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[107, 104])).
% 0.43/0.58 tff(109,plain,
% 0.43/0.58 ((v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4))) | l1_group_1(E!4)),
% 0.43/0.58 inference(tautology,[status(thm)],[])).
% 0.43/0.58 tff(110,plain,
% 0.43/0.58 (l1_group_1(E!4)),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[109, 104])).
% 0.43/0.58 tff(111,plain,
% 0.43/0.58 (^[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)) | (~(((~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))))) <=> (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)) | (~(((~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))))))),
% 0.43/0.58 inference(bind,[status(th)],[])).
% 0.43/0.58 tff(112,plain,
% 0.43/0.58 (![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)) | (~(((~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))))) <=> ![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)) | (~(((~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)))))),
% 0.43/0.58 inference(quant_intro,[status(thm)],[111])).
% 0.43/0.58 tff(113,plain,
% 0.43/0.58 (^[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)) | (~(((~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))))) <=> (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)) | (~(((~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))))))),
% 0.43/0.58 inference(bind,[status(th)],[])).
% 0.43/0.58 tff(114,plain,
% 0.43/0.58 (![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)) | (~(((~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))))) <=> ![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)) | (~(((~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)))))),
% 0.43/0.58 inference(quant_intro,[status(thm)],[113])).
% 0.43/0.58 tff(115,plain,
% 0.43/0.58 (![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)) | (~(((~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))))) <=> ![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)) | (~(((~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)))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[114, 112])).
% 0.43/0.58 tff(116,plain,
% 0.43/0.58 (^[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))))), trans(trans(monotonicity(rewrite((r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))) <=> (~((~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))))) <=> (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((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))))))) <=> (~(((~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)))), ((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))))) <=> (~(((~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))))), rewrite((~(((~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))))) <=> m1_group_2(B, A)))), ((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))))) <=> (~(((~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))))), (((~((~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))) | (~(((~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)))))), rewrite(((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))) | (~(((~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)))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~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))))), (((~((~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)) | (~(((~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))))))), (![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)) | (~(((~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)))))), (((~((~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)) | (~(((~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))))))), 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)) | (~(((~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))))) <=> (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)) | (~(((~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)))))), (((~((~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)) | (~(((~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)))))))),
% 0.43/0.58 inference(bind,[status(th)],[])).
% 0.43/0.58 tff(117,plain,
% 0.43/0.58 (![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)) | (~(((~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)))))),
% 0.43/0.58 inference(quant_intro,[status(thm)],[116])).
% 0.43/0.58 tff(118,plain,
% 0.43/0.58 (![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)))))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(119,plain,
% 0.43/0.58 (^[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)))))))))),
% 0.43/0.58 inference(bind,[status(th)],[])).
% 0.43/0.58 tff(120,plain,
% 0.43/0.58 (![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)))))))),
% 0.43/0.58 inference(quant_intro,[status(thm)],[119])).
% 0.43/0.58 tff(121,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/sandbox2/benchmark/theBenchmark.p','d5_group_2')).
% 0.43/0.58 tff(122,plain,
% 0.43/0.58 (![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)))))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.43/0.58 tff(123,plain,
% 0.43/0.58 (![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)))))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.43/0.58 tff(124,plain,(
% 0.43/0.58 ![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)))))))),
% 0.43/0.58 inference(skolemize,[status(sab)],[123])).
% 0.43/0.58 tff(125,plain,
% 0.43/0.58 (![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)) | (~(((~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)))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.43/0.58 tff(126,plain,
% 0.43/0.58 (![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)) | (~(((~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)))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[125, 115])).
% 0.43/0.58 tff(127,plain,
% 0.43/0.58 (((~![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)) | (~(((~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)))))) | (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)) | (~(((~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))))) <=> m1_group_2(B, E!4)))))) <=> ((~![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)) | (~(((~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)))))) | 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)) | (~(((~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))))) <=> m1_group_2(B, E!4)))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(128,plain,
% 0.43/0.58 ((~![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)) | (~(((~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)))))) | (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)) | (~(((~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))))) <=> m1_group_2(B, E!4)))))),
% 0.43/0.58 inference(quant_inst,[status(thm)],[])).
% 0.43/0.58 tff(129,plain,
% 0.43/0.58 ((~![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)) | (~(((~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)))))) | 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)) | (~(((~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))))) <=> m1_group_2(B, E!4))))),
% 0.43/0.58 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.43/0.58 tff(130,plain,
% 0.43/0.58 (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)) | (~(((~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))))) <=> m1_group_2(B, E!4))))),
% 0.43/0.58 inference(unit_resolution,[status(thm)],[129, 126])).
% 0.43/0.58 tff(131,plain,
% 0.43/0.58 (![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~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))))) <=> m1_group_2(B, E!4))))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[130, 110, 108, 106])).
% 0.43/0.59 tff(132,plain,
% 0.43/0.59 (m1_group_2(D!3, B!1)),
% 0.43/0.59 inference(and_elim,[status(thm)],[34])).
% 0.43/0.59 tff(133,plain,
% 0.43/0.59 (((~![B: $i] : ((~m1_group_2(B, B!1)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(D!3, B!1)) | (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)))))) <=> ((~![B: $i] : ((~m1_group_2(B, B!1)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(D!3, B!1)) | (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(134,plain,
% 0.43/0.59 ((~![B: $i] : ((~m1_group_2(B, B!1)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(D!3, B!1)) | (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)))))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(135,plain,
% 0.43/0.59 ((~![B: $i] : ((~m1_group_2(B, B!1)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(D!3, B!1)) | (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3))))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.43/0.59 tff(136,plain,
% 0.43/0.59 (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[135, 132, 99])).
% 0.43/0.59 tff(137,plain,
% 0.43/0.59 ((v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3))) | v3_group_1(D!3)),
% 0.43/0.59 inference(tautology,[status(thm)],[])).
% 0.43/0.59 tff(138,plain,
% 0.43/0.59 (v3_group_1(D!3)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.43/0.59 tff(139,plain,
% 0.43/0.59 ((v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3))) | l1_group_1(D!3)),
% 0.43/0.59 inference(tautology,[status(thm)],[])).
% 0.43/0.59 tff(140,plain,
% 0.43/0.59 (l1_group_1(D!3)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[139, 136])).
% 0.43/0.59 tff(141,plain,
% 0.43/0.59 ((v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3))) | (~v3_struct_0(D!3))),
% 0.43/0.59 inference(tautology,[status(thm)],[])).
% 0.43/0.59 tff(142,plain,
% 0.43/0.59 (~v3_struct_0(D!3)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[141, 136])).
% 0.43/0.59 tff(143,plain,
% 0.43/0.59 (((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~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))))) <=> m1_group_2(B, E!4))))) | (v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(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))))) <=> m1_group_2(D!3, E!4))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~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))))) <=> m1_group_2(B, E!4))))) | v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(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))))) <=> m1_group_2(D!3, E!4))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(144,plain,
% 0.43/0.59 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~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))))) <=> m1_group_2(B, E!4))))) | (v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(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))))) <=> m1_group_2(D!3, E!4))))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(145,plain,
% 0.43/0.59 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~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))))) <=> m1_group_2(B, E!4))))) | v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(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))))) <=> m1_group_2(D!3, E!4)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.43/0.59 tff(146,plain,
% 0.43/0.59 (~(((~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))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[145, 142, 140, 138, 131])).
% 0.43/0.59 tff(147,plain,
% 0.43/0.59 (^[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))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(148,plain,
% 0.43/0.59 (![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)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[147])).
% 0.43/0.59 tff(149,plain,
% 0.43/0.59 (^[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))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(150,plain,
% 0.43/0.59 (![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)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[149])).
% 0.43/0.59 tff(151,plain,
% 0.43/0.59 (^[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))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(152,plain,
% 0.43/0.59 (![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)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[151])).
% 0.43/0.59 tff(153,plain,
% 0.43/0.59 (![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)))),
% 0.43/0.59 inference(transitivity,[status(thm)],[152, 150])).
% 0.43/0.59 tff(154,plain,
% 0.43/0.59 (^[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)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(155,plain,
% 0.43/0.59 (![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)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[154])).
% 0.43/0.59 tff(156,plain,
% 0.43/0.59 (![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)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(157,plain,
% 0.43/0.59 (^[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)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(158,plain,
% 0.43/0.59 (![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)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[157])).
% 0.43/0.59 tff(159,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/sandbox2/benchmark/theBenchmark.p','redefinition_m1_group_6')).
% 0.43/0.59 tff(160,plain,
% 0.43/0.59 (![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)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.43/0.59 tff(161,plain,
% 0.43/0.59 (![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)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.43/0.59 tff(162,plain,(
% 0.43/0.59 ![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)))),
% 0.43/0.59 inference(skolemize,[status(sab)],[161])).
% 0.43/0.59 tff(163,plain,
% 0.43/0.59 (![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)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.43/0.59 tff(164,plain,
% 0.43/0.59 (![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)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[163, 153])).
% 0.43/0.59 tff(165,plain,
% 0.43/0.59 (![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)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[164, 148])).
% 0.43/0.59 tff(166,plain,
% 0.43/0.59 (v4_group_1(B!1)),
% 0.43/0.59 inference(and_elim,[status(thm)],[34])).
% 0.43/0.59 tff(167,plain,
% 0.43/0.59 (((~![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(E!4, B!1)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, 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(B!1) | (~m1_group_2(E!4, B!1)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, E!4) <=> m1_group_2(C, E!4)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(168,plain,
% 0.43/0.59 ((v3_struct_0(B!1) | (~m1_group_2(E!4, 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, E!4) <=> m1_group_2(C, E!4))) <=> (v3_struct_0(B!1) | (~m1_group_2(E!4, B!1)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, E!4) <=> m1_group_2(C, E!4)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(169,plain,
% 0.43/0.59 (((~![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(E!4, 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, 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(B!1) | (~m1_group_2(E!4, B!1)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, E!4) <=> m1_group_2(C, E!4))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[168])).
% 0.43/0.59 tff(170,plain,
% 0.43/0.59 (((~![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(E!4, 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, 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(B!1) | (~m1_group_2(E!4, B!1)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, E!4) <=> m1_group_2(C, E!4)))),
% 0.43/0.59 inference(transitivity,[status(thm)],[169, 167])).
% 0.43/0.59 tff(171,plain,
% 0.43/0.59 ((~![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(E!4, 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, E!4) <=> m1_group_2(C, E!4)))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(172,plain,
% 0.43/0.59 ((~![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(E!4, B!1)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, E!4) <=> m1_group_2(C, E!4))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.43/0.59 tff(173,plain,
% 0.43/0.59 (![C: $i] : (m1_group_6(C, B!1, E!4) <=> m1_group_2(C, E!4))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[172, 95, 94, 166, 93, 100, 165])).
% 0.43/0.59 tff(174,plain,
% 0.43/0.59 ((~![C: $i] : (m1_group_6(C, B!1, E!4) <=> m1_group_2(C, E!4))) | (m1_group_6(D!3, B!1, E!4) <=> m1_group_2(D!3, E!4))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(175,plain,
% 0.43/0.59 (m1_group_6(D!3, B!1, E!4) <=> m1_group_2(D!3, E!4)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.43/0.59 tff(176,plain,
% 0.43/0.59 (m1_group_6(D!3, B!1, E!4)),
% 0.43/0.59 inference(and_elim,[status(thm)],[62])).
% 0.43/0.59 tff(177,plain,
% 0.43/0.59 ((~(m1_group_6(D!3, B!1, E!4) <=> m1_group_2(D!3, E!4))) | (~m1_group_6(D!3, B!1, E!4)) | m1_group_2(D!3, E!4)),
% 0.43/0.59 inference(tautology,[status(thm)],[])).
% 0.43/0.59 tff(178,plain,
% 0.43/0.59 ((~(m1_group_6(D!3, B!1, E!4) <=> m1_group_2(D!3, E!4))) | m1_group_2(D!3, E!4)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.43/0.59 tff(179,plain,
% 0.43/0.59 (m1_group_2(D!3, E!4)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[178, 175])).
% 0.43/0.59 tff(180,plain,
% 0.43/0.59 ((((~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)))))) | (~m1_group_2(D!3, E!4))),
% 0.43/0.59 inference(tautology,[status(thm)],[])).
% 0.43/0.59 tff(181,plain,
% 0.43/0.59 ((((~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))))))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.43/0.59 tff(182,plain,
% 0.43/0.59 (~((~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)))))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[181, 146])).
% 0.43/0.59 tff(183,plain,
% 0.43/0.59 (((~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))),
% 0.43/0.59 inference(tautology,[status(thm)],[])).
% 0.43/0.59 tff(184,plain,
% 0.43/0.59 (r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.43/0.59 tff(185,plain,
% 0.43/0.59 (^[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)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(186,plain,
% 0.43/0.59 (![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))))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[185])).
% 0.43/0.59 tff(187,plain,
% 0.43/0.59 (![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))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(188,plain,
% 0.43/0.59 (^[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)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(189,plain,
% 0.43/0.59 (![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))))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[188])).
% 0.43/0.59 tff(190,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/sandbox2/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 0.43/0.59 tff(191,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.43/0.59 tff(192,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.43/0.59 tff(193,plain,(
% 0.43/0.59 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.43/0.59 inference(skolemize,[status(sab)],[192])).
% 0.43/0.59 tff(194,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[193, 186])).
% 0.43/0.59 tff(195,plain,
% 0.43/0.59 (((~![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)))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(196,plain,
% 0.43/0.59 ((~![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)))))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(197,plain,
% 0.43/0.59 ((~![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))))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.43/0.59 tff(198,plain,
% 0.43/0.59 (m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[197, 35, 194])).
% 0.43/0.59 tff(199,plain,
% 0.43/0.59 (^[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))))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(200,plain,
% 0.43/0.59 (![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)))))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[199])).
% 0.43/0.59 tff(201,plain,
% 0.43/0.59 (![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)))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(202,plain,
% 0.43/0.59 (^[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))))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(203,plain,
% 0.43/0.59 (![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)))))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[202])).
% 0.43/0.59 tff(204,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/sandbox2/benchmark/theBenchmark.p','cc1_relset_1')).
% 0.43/0.59 tff(205,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.43/0.59 tff(206,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[205, 201])).
% 0.43/0.59 tff(207,plain,(
% 0.43/0.59 ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.43/0.59 inference(skolemize,[status(sab)],[206])).
% 0.43/0.59 tff(208,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[207, 200])).
% 0.43/0.59 tff(209,plain,
% 0.43/0.59 (((~![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))))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(210,plain,
% 0.43/0.59 ((~![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))))))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(211,plain,
% 0.43/0.59 ((~![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)))))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.43/0.59 tff(212,plain,
% 0.43/0.59 (v1_relat_1(C!2)),
% 0.43/0.59 inference(unit_resolution,[status(thm)],[211, 208, 198])).
% 0.43/0.59 tff(213,plain,
% 0.43/0.59 (^[A: $i, B: $i, C: $i] : refl((r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))) <=> (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(214,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[213])).
% 0.43/0.59 tff(215,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(216,plain,
% 0.43/0.59 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((r1_tarski(A, B) => r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B))) <=> ((~r1_tarski(A, B)) | r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)))), ((v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)))) <=> (v1_relat_1(C) => ((~r1_tarski(A, B)) | r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)))))), rewrite((v1_relat_1(C) => ((~r1_tarski(A, B)) | r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)))) <=> (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))), ((v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)))) <=> (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(217,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[216])).
% 0.43/0.59 tff(218,axiom,(![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t178_relat_1')).
% 0.43/0.59 tff(219,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.43/0.59 tff(220,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.43/0.59 tff(221,plain,(
% 0.43/0.59 ![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.43/0.59 inference(skolemize,[status(sab)],[220])).
% 0.43/0.59 tff(222,plain,
% 0.43/0.59 (![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.43/0.59 tff(223,plain,
% 0.43/0.59 (((~![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | ((~v1_relat_1(C!2)) | r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (~v1_relat_1(C!2)) | r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(224,plain,
% 0.43/0.59 ((r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_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))) <=> ((~v1_relat_1(C!2)) | r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(225,plain,
% 0.43/0.59 (((~![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_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(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | ((~v1_relat_1(C!2)) | r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4)))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[224])).
% 0.43/0.59 tff(226,plain,
% 0.43/0.59 (((~![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_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(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (~v1_relat_1(C!2)) | r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[225, 223])).
% 0.43/0.59 tff(227,plain,
% 0.43/0.59 ((~![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_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)))),
% 0.43/0.59 inference(quant_inst,[status(thm)],[])).
% 0.43/0.59 tff(228,plain,
% 0.43/0.59 ((~![A: $i, B: $i, C: $i] : (r1_tarski(k10_relat_1(C, A), k10_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (~v1_relat_1(C!2)) | r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4)))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.43/0.60 tff(229,plain,
% 0.43/0.60 (r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4)))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[228, 222, 212])).
% 0.43/0.60 tff(230,plain,
% 0.43/0.60 (r1_tarski(k10_relat_1(C!2, u1_struct_0(D!3)), k10_relat_1(C!2, u1_struct_0(E!4)))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[229, 184])).
% 0.43/0.60 tff(231,plain,
% 0.43/0.60 (r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[230, 76])).
% 0.43/0.60 tff(232,plain,
% 0.43/0.60 (m1_group_2(G!6, A!0)),
% 0.43/0.60 inference(or_elim,[status(thm)],[61])).
% 0.43/0.60 tff(233,plain,
% 0.43/0.60 (l1_group_1(A!0)),
% 0.43/0.60 inference(and_elim,[status(thm)],[34])).
% 0.43/0.60 tff(234,plain,
% 0.43/0.60 (v4_group_1(A!0)),
% 0.43/0.60 inference(and_elim,[status(thm)],[34])).
% 0.43/0.60 tff(235,plain,
% 0.43/0.60 (v3_group_1(A!0)),
% 0.43/0.60 inference(and_elim,[status(thm)],[34])).
% 0.43/0.60 tff(236,plain,
% 0.43/0.60 (~v3_struct_0(A!0)),
% 0.43/0.60 inference(and_elim,[status(thm)],[34])).
% 0.43/0.60 tff(237,plain,
% 0.43/0.60 (((~![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(G!6, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, 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(A!0) | (~m1_group_2(G!6, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, G!6) <=> m1_group_2(C, G!6)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(238,plain,
% 0.43/0.60 ((v3_struct_0(A!0) | (~m1_group_2(G!6, 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, G!6) <=> m1_group_2(C, G!6))) <=> (v3_struct_0(A!0) | (~m1_group_2(G!6, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, G!6) <=> m1_group_2(C, G!6)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(239,plain,
% 0.43/0.60 (((~![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(G!6, 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, 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(A!0) | (~m1_group_2(G!6, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, G!6) <=> m1_group_2(C, G!6))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[238])).
% 0.43/0.60 tff(240,plain,
% 0.43/0.60 (((~![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(G!6, 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, 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(A!0) | (~m1_group_2(G!6, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, G!6) <=> m1_group_2(C, G!6)))),
% 0.43/0.60 inference(transitivity,[status(thm)],[239, 237])).
% 0.43/0.60 tff(241,plain,
% 0.43/0.60 ((~![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(G!6, 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, G!6) <=> m1_group_2(C, G!6)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(242,plain,
% 0.43/0.60 ((~![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(G!6, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, G!6) <=> m1_group_2(C, G!6))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.43/0.60 tff(243,plain,
% 0.43/0.60 (![C: $i] : (m1_group_6(C, A!0, G!6) <=> m1_group_2(C, G!6))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[242, 236, 235, 234, 233, 232, 165])).
% 0.43/0.60 tff(244,plain,
% 0.43/0.60 ((~![C: $i] : (m1_group_6(C, A!0, G!6) <=> m1_group_2(C, G!6))) | (m1_group_6(F!5, A!0, G!6) <=> m1_group_2(F!5, G!6))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(245,plain,
% 0.43/0.60 (m1_group_6(F!5, A!0, G!6) <=> m1_group_2(F!5, G!6)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.43/0.60 tff(246,plain,
% 0.43/0.60 (~m1_group_6(F!5, A!0, G!6)),
% 0.43/0.60 inference(or_elim,[status(thm)],[61])).
% 0.43/0.60 tff(247,plain,
% 0.43/0.60 ((~(m1_group_6(F!5, A!0, G!6) <=> m1_group_2(F!5, G!6))) | m1_group_6(F!5, A!0, G!6) | (~m1_group_2(F!5, G!6))),
% 0.43/0.60 inference(tautology,[status(thm)],[])).
% 0.43/0.60 tff(248,plain,
% 0.43/0.60 ((~(m1_group_6(F!5, A!0, G!6) <=> m1_group_2(F!5, G!6))) | (~m1_group_2(F!5, G!6))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[247, 246])).
% 0.43/0.60 tff(249,plain,
% 0.43/0.60 (~m1_group_2(F!5, G!6)),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[248, 245])).
% 0.43/0.60 tff(250,plain,
% 0.43/0.60 (^[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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C)))))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(251,plain,
% 0.43/0.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[250])).
% 0.43/0.60 tff(252,plain,
% 0.43/0.60 (^[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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(253,plain,
% 0.43/0.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[252])).
% 0.43/0.60 tff(254,plain,
% 0.43/0.60 (^[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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(255,plain,
% 0.43/0.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[254])).
% 0.43/0.60 tff(256,plain,
% 0.43/0.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.43/0.60 inference(transitivity,[status(thm)],[255, 253])).
% 0.43/0.60 tff(257,plain,
% 0.43/0.60 (^[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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C)))))) <=> ((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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C)))))))), 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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(258,plain,
% 0.43/0.60 (![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[257])).
% 0.43/0.60 tff(259,plain,
% 0.43/0.60 (![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(260,plain,
% 0.43/0.60 (^[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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))), ((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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))), (![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C)))))), ((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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))), rewrite((m1_group_2(B, A) => ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) <=> ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C)))))), ((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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C)))))))), (![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(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(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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C)))))))), 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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(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(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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(261,plain,
% 0.43/0.60 (![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[260])).
% 0.43/0.60 tff(262,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/sandbox2/benchmark/theBenchmark.p','t66_group_2')).
% 0.43/0.60 tff(263,plain,
% 0.43/0.60 (![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.43/0.60 tff(264,plain,
% 0.43/0.60 (![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.43/0.60 tff(265,plain,(
% 0.43/0.60 ![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))),
% 0.43/0.60 inference(skolemize,[status(sab)],[264])).
% 0.43/0.60 tff(266,plain,
% 0.43/0.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.43/0.60 tff(267,plain,
% 0.43/0.60 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[266, 256])).
% 0.43/0.60 tff(268,plain,
% 0.43/0.60 (![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[267, 251])).
% 0.43/0.60 tff(269,plain,
% 0.43/0.60 (((~![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0)))))) <=> ((~![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0)))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(270,plain,
% 0.43/0.60 ((v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A!0)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C)))))) <=> (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0)))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(271,plain,
% 0.43/0.60 (((~![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A!0)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))) <=> ((~![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0))))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[270])).
% 0.43/0.60 tff(272,plain,
% 0.43/0.60 (((~![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A!0)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))) <=> ((~![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0)))))),
% 0.43/0.60 inference(transitivity,[status(thm)],[271, 269])).
% 0.43/0.60 tff(273,plain,
% 0.43/0.60 ((~![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~m1_group_2(C, A!0)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(274,plain,
% 0.43/0.60 ((~![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) | (~m1_group_2(C, A)) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.43/0.60 tff(275,plain,
% 0.43/0.60 (![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0))))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[274, 236, 235, 234, 233, 268])).
% 0.43/0.60 tff(276,plain,
% 0.43/0.60 (m1_group_2(F!5, A!0)),
% 0.43/0.60 inference(and_elim,[status(thm)],[34])).
% 0.43/0.60 tff(277,plain,
% 0.43/0.60 (((~![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0))))) | ((~m1_group_2(F!5, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C)))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0))))) | (~m1_group_2(F!5, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C)))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(278,plain,
% 0.43/0.60 (((~m1_group_2(F!5, A!0)) | ![C: $i] : (m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))) | (~m1_group_2(C, A!0)))) <=> ((~m1_group_2(F!5, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C)))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(279,plain,
% 0.43/0.60 (((~![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0))))) | ((~m1_group_2(F!5, A!0)) | ![C: $i] : (m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))) | (~m1_group_2(C, A!0))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0))))) | ((~m1_group_2(F!5, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[278])).
% 0.43/0.61 tff(280,plain,
% 0.43/0.61 (((~![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0))))) | ((~m1_group_2(F!5, A!0)) | ![C: $i] : (m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))) | (~m1_group_2(C, A!0))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0))))) | (~m1_group_2(F!5, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C)))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[279, 277])).
% 0.43/0.61 tff(281,plain,
% 0.43/0.61 ((~![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0))))) | ((~m1_group_2(F!5, A!0)) | ![C: $i] : (m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))) | (~m1_group_2(C, A!0))))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(282,plain,
% 0.43/0.61 ((~![B: $i] : ((~m1_group_2(B, A!0)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A!0))))) | (~m1_group_2(F!5, A!0)) | ![C: $i] : ((~m1_group_2(C, A!0)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.43/0.61 tff(283,plain,
% 0.43/0.61 (![C: $i] : ((~m1_group_2(C, A!0)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[282, 276, 275])).
% 0.43/0.61 tff(284,plain,
% 0.43/0.61 (((~![C: $i] : ((~m1_group_2(C, A!0)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))) | ((~m1_group_2(G!6, A!0)) | 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, A!0)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))) | (~m1_group_2(G!6, A!0)) | m1_group_2(F!5, G!6) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(285,plain,
% 0.43/0.61 ((~![C: $i] : ((~m1_group_2(C, A!0)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))) | ((~m1_group_2(G!6, A!0)) | m1_group_2(F!5, G!6) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(286,plain,
% 0.43/0.61 ((~![C: $i] : ((~m1_group_2(C, A!0)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))) | (~m1_group_2(G!6, A!0)) | m1_group_2(F!5, G!6) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6)))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.43/0.61 tff(287,plain,
% 0.43/0.61 (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[286, 232, 283, 249])).
% 0.43/0.61 tff(288,plain,
% 0.43/0.61 ($false),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[287, 231])).
% 0.43/0.61 % SZS output end Proof
% 0.43/0.61 % E exiting
%------------------------------------------------------------------------------