TSTP Solution File: LAT331+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT331+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:33:10 EDT 2022
% Result : Theorem 0.53s 0.60s
% Output : Proof 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : LAT331+1 : TPTP v8.1.0. Released v3.4.0.
% 0.05/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.32 % Computer : n009.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu Sep 1 14:44:20 EDT 2022
% 0.10/0.32 % CPUTime :
% 0.10/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.32 Usage: tptp [options] [-file:]file
% 0.10/0.32 -h, -? prints this message.
% 0.10/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.32 -m, -model generate model.
% 0.10/0.32 -p, -proof generate proof.
% 0.10/0.32 -c, -core generate unsat core of named formulas.
% 0.10/0.32 -st, -statistics display statistics.
% 0.10/0.32 -t:timeout set timeout (in second).
% 0.10/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.32 -<param>:<value> configuration parameter and value.
% 0.10/0.32 -o:<output-file> file to place output in.
% 0.53/0.60 % SZS status Theorem
% 0.53/0.60 % SZS output start Proof
% 0.53/0.60 tff(k8_filter_0_type, type, (
% 0.53/0.60 k8_filter_0: ( $i * $i ) > $i)).
% 0.53/0.60 tff(tptp_fun_D_3_type, type, (
% 0.53/0.60 tptp_fun_D_3: $i)).
% 0.53/0.60 tff(tptp_fun_B_1_type, type, (
% 0.53/0.60 tptp_fun_B_1: $i)).
% 0.53/0.60 tff(tptp_fun_C_2_type, type, (
% 0.53/0.60 tptp_fun_C_2: $i)).
% 0.53/0.60 tff(tptp_fun_A_0_type, type, (
% 0.53/0.60 tptp_fun_A_0: $i)).
% 0.53/0.60 tff(g3_lattices_type, type, (
% 0.53/0.60 g3_lattices: ( $i * $i * $i ) > $i)).
% 0.53/0.60 tff(tptp_fun_E_5_type, type, (
% 0.53/0.60 tptp_fun_E_5: ( $i * $i * $i ) > $i)).
% 0.53/0.60 tff(tptp_fun_D_4_type, type, (
% 0.53/0.60 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 0.53/0.60 tff(k1_realset1_type, type, (
% 0.53/0.60 k1_realset1: ( $i * $i ) > $i)).
% 0.53/0.60 tff(u1_lattices_type, type, (
% 0.53/0.60 u1_lattices: $i > $i)).
% 0.53/0.60 tff(u2_lattices_type, type, (
% 0.53/0.60 u2_lattices: $i > $i)).
% 0.53/0.60 tff(m2_relset_1_type, type, (
% 0.53/0.60 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.53/0.60 tff(k2_zfmisc_1_type, type, (
% 0.53/0.60 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.53/0.60 tff(v1_funct_2_type, type, (
% 0.53/0.60 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.53/0.60 tff(v1_funct_1_type, type, (
% 0.53/0.60 v1_funct_1: $i > $o)).
% 0.53/0.60 tff(v10_lattices_type, type, (
% 0.53/0.60 v10_lattices: $i > $o)).
% 0.53/0.60 tff(l3_lattices_type, type, (
% 0.53/0.60 l3_lattices: $i > $o)).
% 0.53/0.60 tff(v3_struct_0_type, type, (
% 0.53/0.60 v3_struct_0: $i > $o)).
% 0.53/0.60 tff(m1_filter_0_type, type, (
% 0.53/0.60 m1_filter_0: ( $i * $i ) > $o)).
% 0.53/0.60 tff(m1_filter_2_type, type, (
% 0.53/0.60 m1_filter_2: ( $i * $i ) > $o)).
% 0.53/0.60 tff(u1_struct_0_type, type, (
% 0.53/0.60 u1_struct_0: $i > $i)).
% 0.53/0.60 tff(m1_relset_1_type, type, (
% 0.53/0.60 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.53/0.60 tff(l1_lattices_type, type, (
% 0.53/0.60 l1_lattices: $i > $o)).
% 0.53/0.60 tff(l2_lattices_type, type, (
% 0.53/0.60 l2_lattices: $i > $o)).
% 0.53/0.60 tff(1,plain,
% 0.53/0.60 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(2,plain,
% 0.53/0.60 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[1])).
% 0.53/0.60 tff(3,plain,
% 0.53/0.60 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(4,plain,
% 0.53/0.60 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[3])).
% 0.53/0.60 tff(5,plain,
% 0.53/0.60 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(6,plain,
% 0.53/0.60 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[5])).
% 0.53/0.60 tff(7,plain,
% 0.53/0.60 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.53/0.60 inference(transitivity,[status(thm)],[6, 4])).
% 0.53/0.60 tff(8,plain,
% 0.53/0.60 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(9,plain,
% 0.53/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[8])).
% 0.53/0.60 tff(10,plain,
% 0.53/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(11,plain,
% 0.53/0.60 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))))),
% 0.53/0.60 inference(bind,[status(th)],[])).
% 0.53/0.60 tff(12,plain,
% 0.53/0.60 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.53/0.60 inference(quant_intro,[status(thm)],[11])).
% 0.53/0.60 tff(13,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m1_filter_2')).
% 0.53/0.60 tff(14,plain,
% 0.53/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.53/0.60 tff(15,plain,
% 0.53/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.53/0.60 tff(16,plain,(
% 0.53/0.60 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.53/0.60 inference(skolemize,[status(sab)],[15])).
% 0.53/0.60 tff(17,plain,
% 0.53/0.60 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.53/0.60 tff(18,plain,
% 0.53/0.60 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.53/0.60 tff(19,plain,
% 0.53/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.53/0.60 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.53/0.60 tff(20,plain,
% 0.53/0.60 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & m1_filter_2(C!2, A!0) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & m1_filter_2(C!2, A!0) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1)))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(21,plain,
% 0.53/0.60 ((((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)) & (m1_filter_2(C!2, A!0) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1)))))) <=> ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & m1_filter_2(C!2, A!0) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1)))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(22,plain,
% 0.53/0.60 (((~(~m1_filter_2(C!2, A!0))) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1))))) <=> (m1_filter_2(C!2, A!0) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1)))))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(23,plain,
% 0.53/0.60 ((~(~((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))) <=> ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))),
% 0.53/0.60 inference(rewrite,[status(thm)],[])).
% 0.53/0.60 tff(24,plain,
% 0.53/0.60 (((~(~((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))) & ((~(~m1_filter_2(C!2, A!0))) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1)))))) <=> (((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)) & (m1_filter_2(C!2, A!0) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1))))))),
% 0.53/0.60 inference(monotonicity,[status(thm)],[23, 22])).
% 0.53/0.60 tff(25,plain,
% 0.53/0.60 (((~(~((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))) & ((~(~m1_filter_2(C!2, A!0))) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1)))))) <=> ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & m1_filter_2(C!2, A!0) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1)))))),
% 0.53/0.60 inference(transitivity,[status(thm)],[24, 21])).
% 0.53/0.60 tff(26,plain,
% 0.53/0.60 ((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(27,plain,
% 0.53/0.61 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & ((~(~((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))) & ((~(~m1_filter_2(C!2, A!0))) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & m1_filter_2(C!2, A!0) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1))))))),
% 0.53/0.61 inference(monotonicity,[status(thm)],[26, 25])).
% 0.53/0.61 tff(28,plain,
% 0.53/0.61 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & ((~(~((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))) & ((~(~m1_filter_2(C!2, A!0))) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & m1_filter_2(C!2, A!0) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1)))))),
% 0.53/0.61 inference(transitivity,[status(thm)],[27, 20])).
% 0.53/0.61 tff(29,plain,
% 0.53/0.61 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~m1_filter_2(C, A)) | ![D: $i] : ((k8_filter_0(A, C) = k8_filter_0(B, D)) | (~((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D))) | (~m1_filter_2(D, B))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~m1_filter_2(C, A)) | ![D: $i] : ((k8_filter_0(A, C) = k8_filter_0(B, D)) | (~((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D))) | (~m1_filter_2(D, B)))))))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(30,plain,
% 0.53/0.61 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ![C: $i] : (m1_filter_2(C, A) => ![D: $i] : (m1_filter_2(D, B) => (((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D)) => (k8_filter_0(A, C) = k8_filter_0(B, D)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~m1_filter_2(C, A)) | ![D: $i] : ((k8_filter_0(A, C) = k8_filter_0(B, D)) | (~((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D))) | (~m1_filter_2(D, B)))))))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(31,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ![C: $i] : (m1_filter_2(C, A) => ![D: $i] : (m1_filter_2(D, B) => (((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D)) => (k8_filter_0(A, C) = k8_filter_0(B, D)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t68_filter_2')).
% 0.53/0.61 tff(32,plain,
% 0.53/0.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~m1_filter_2(C, A)) | ![D: $i] : ((k8_filter_0(A, C) = k8_filter_0(B, D)) | (~((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D))) | (~m1_filter_2(D, B))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.53/0.61 tff(33,plain,
% 0.53/0.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~m1_filter_2(C, A)) | ![D: $i] : ((k8_filter_0(A, C) = k8_filter_0(B, D)) | (~((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D))) | (~m1_filter_2(D, B))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.53/0.61 tff(34,plain,
% 0.53/0.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~m1_filter_2(C, A)) | ![D: $i] : ((k8_filter_0(A, C) = k8_filter_0(B, D)) | (~((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D))) | (~m1_filter_2(D, B))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.53/0.61 tff(35,plain,
% 0.53/0.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~m1_filter_2(C, A)) | ![D: $i] : ((k8_filter_0(A, C) = k8_filter_0(B, D)) | (~((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D))) | (~m1_filter_2(D, B))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.53/0.61 tff(36,plain,
% 0.53/0.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~m1_filter_2(C, A)) | ![D: $i] : ((k8_filter_0(A, C) = k8_filter_0(B, D)) | (~((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D))) | (~m1_filter_2(D, B))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.53/0.61 tff(37,plain,
% 0.53/0.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~m1_filter_2(C, A)) | ![D: $i] : ((k8_filter_0(A, C) = k8_filter_0(B, D)) | (~((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D))) | (~m1_filter_2(D, B))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.53/0.61 tff(38,plain,
% 0.53/0.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) | ![C: $i] : ((~m1_filter_2(C, A)) | ![D: $i] : ((k8_filter_0(A, C) = k8_filter_0(B, D)) | (~((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) & (C = D))) | (~m1_filter_2(D, B))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[37, 29])).
% 0.53/0.61 tff(39,plain,
% 0.53/0.61 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1) & m1_filter_2(C!2, A!0) & (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[38, 28])).
% 0.53/0.61 tff(40,plain,
% 0.53/0.61 (l3_lattices(B!1)),
% 0.53/0.61 inference(and_elim,[status(thm)],[39])).
% 0.53/0.61 tff(41,plain,
% 0.53/0.61 (v10_lattices(B!1)),
% 0.53/0.61 inference(and_elim,[status(thm)],[39])).
% 0.53/0.61 tff(42,plain,
% 0.53/0.61 (~v3_struct_0(B!1)),
% 0.53/0.61 inference(and_elim,[status(thm)],[39])).
% 0.53/0.61 tff(43,plain,
% 0.53/0.61 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1)))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(44,plain,
% 0.53/0.61 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1)))),
% 0.53/0.61 inference(quant_inst,[status(thm)],[])).
% 0.53/0.61 tff(45,plain,
% 0.53/0.61 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.53/0.61 tff(46,plain,
% 0.53/0.61 (![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1))),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[45, 42, 41, 40, 19])).
% 0.53/0.61 tff(47,plain,
% 0.53/0.61 ((~![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1))) | (m1_filter_2(D!3, B!1) <=> m1_filter_0(D!3, B!1))),
% 0.53/0.61 inference(quant_inst,[status(thm)],[])).
% 0.53/0.61 tff(48,plain,
% 0.53/0.61 (m1_filter_2(D!3, B!1) <=> m1_filter_0(D!3, B!1)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.53/0.61 tff(49,plain,
% 0.53/0.61 (~((k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)) | (~((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3))) | (~m1_filter_2(D!3, B!1)))),
% 0.53/0.61 inference(and_elim,[status(thm)],[39])).
% 0.53/0.61 tff(50,plain,
% 0.53/0.61 (m1_filter_2(D!3, B!1)),
% 0.53/0.61 inference(or_elim,[status(thm)],[49])).
% 0.53/0.61 tff(51,plain,
% 0.53/0.61 ((~(m1_filter_2(D!3, B!1) <=> m1_filter_0(D!3, B!1))) | (~m1_filter_2(D!3, B!1)) | m1_filter_0(D!3, B!1)),
% 0.53/0.61 inference(tautology,[status(thm)],[])).
% 0.53/0.61 tff(52,plain,
% 0.53/0.61 ((~(m1_filter_2(D!3, B!1) <=> m1_filter_0(D!3, B!1))) | m1_filter_0(D!3, B!1)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.53/0.61 tff(53,plain,
% 0.53/0.61 (m1_filter_0(D!3, B!1)),
% 0.53/0.61 inference(unit_resolution,[status(thm)],[52, 48])).
% 0.53/0.61 tff(54,plain,
% 0.53/0.61 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E)))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E)))))))))))))),
% 0.53/0.61 inference(bind,[status(th)],[])).
% 0.53/0.61 tff(55,plain,
% 0.53/0.61 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))),
% 0.53/0.61 inference(quant_intro,[status(thm)],[54])).
% 0.53/0.61 tff(56,plain,
% 0.53/0.61 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E)))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E)))))))))))))),
% 0.53/0.61 inference(bind,[status(th)],[])).
% 0.53/0.61 tff(57,plain,
% 0.53/0.61 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))),
% 0.53/0.61 inference(quant_intro,[status(thm)],[56])).
% 0.53/0.61 tff(58,plain,
% 0.53/0.61 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))),
% 0.53/0.61 inference(transitivity,[status(thm)],[57, 55])).
% 0.53/0.61 tff(59,plain,
% 0.53/0.61 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | (((~(C = k8_filter_0(A, B))) | (v1_funct_1(tptp_fun_D_4(C, B, A)) & v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & v1_funct_1(tptp_fun_E_5(C, B, A)) & v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & (tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B)) & (tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))) & ((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))) <=> ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))), (![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | (((~(C = k8_filter_0(A, B))) | (v1_funct_1(tptp_fun_D_4(C, B, A)) & v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & v1_funct_1(tptp_fun_E_5(C, B, A)) & v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & (tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B)) & (tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))) & ((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | (((~(C = k8_filter_0(A, B))) | (v1_funct_1(tptp_fun_D_4(C, B, A)) & v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & v1_funct_1(tptp_fun_E_5(C, B, A)) & v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & (tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B)) & (tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))) & ((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E)))))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E)))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | (((~(C = k8_filter_0(A, B))) | (v1_funct_1(tptp_fun_D_4(C, B, A)) & v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & v1_funct_1(tptp_fun_E_5(C, B, A)) & v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & (tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B)) & (tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))) & ((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))))),
% 0.53/0.61 inference(bind,[status(th)],[])).
% 0.53/0.61 tff(60,plain,
% 0.53/0.61 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | (((~(C = k8_filter_0(A, B))) | (v1_funct_1(tptp_fun_D_4(C, B, A)) & v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & v1_funct_1(tptp_fun_E_5(C, B, A)) & v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & (tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B)) & (tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))) & ((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))),
% 0.53/0.61 inference(quant_intro,[status(thm)],[59])).
% 0.53/0.61 tff(61,plain,
% 0.53/0.61 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | (((~(C = k8_filter_0(A, B))) | (v1_funct_1(tptp_fun_D_4(C, B, A)) & v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & (v1_funct_1(tptp_fun_E_5(C, B, A)) & v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & (tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B)) & (tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))) & ((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | (((~(C = k8_filter_0(A, B))) | (v1_funct_1(tptp_fun_D_4(C, B, A)) & v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & v1_funct_1(tptp_fun_E_5(C, B, A)) & v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & (tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B)) & (tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))) & ((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))))))),
% 0.53/0.61 inference(bind,[status(th)],[])).
% 0.53/0.61 tff(62,plain,
% 0.53/0.61 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | (((~(C = k8_filter_0(A, B))) | (v1_funct_1(tptp_fun_D_4(C, B, A)) & v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & (v1_funct_1(tptp_fun_E_5(C, B, A)) & v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & (tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B)) & (tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))) & ((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | (((~(C = k8_filter_0(A, B))) | (v1_funct_1(tptp_fun_D_4(C, B, A)) & v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & v1_funct_1(tptp_fun_E_5(C, B, A)) & v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & (tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B)) & (tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))) & ((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))))),
% 0.53/0.61 inference(quant_intro,[status(thm)],[61])).
% 0.53/0.61 tff(63,plain,
% 0.53/0.61 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))),
% 0.53/0.61 inference(rewrite,[status(thm)],[])).
% 0.53/0.61 tff(64,plain,
% 0.53/0.61 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) <=> ((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))), rewrite(((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))) <=> ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))), (((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))) <=> (((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))), rewrite((((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))) <=> ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))), (((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))) <=> ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))), (![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))) <=> ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))), ((m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))))) <=> (m1_filter_0(B, A) => ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))), rewrite((m1_filter_0(B, A) => ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))) <=> ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))), ((m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))))) <=> ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))))), (![B: $i] : (m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))))),
% 0.53/0.61 inference(bind,[status(th)],[])).
% 0.53/0.61 tff(65,plain,
% 0.53/0.61 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))),
% 0.53/0.61 inference(quant_intro,[status(thm)],[64])).
% 0.53/0.61 tff(66,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : ((((~v3_struct_0(C)) & v10_lattices(C)) & l3_lattices(C)) => ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) & ?[E: $i] : (((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_filter_0')).
% 0.53/0.61 tff(67,plain,
% 0.53/0.61 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.53/0.61 tff(68,plain,
% 0.53/0.61 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | ((C = k8_filter_0(A, B)) <=> ?[D: $i] : (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B) & ?[E: $i] : (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.53/0.61 tff(69,plain,(
% 0.53/0.61 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | (((~(C = k8_filter_0(A, B))) | (v1_funct_1(tptp_fun_D_4(C, B, A)) & v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & (v1_funct_1(tptp_fun_E_5(C, B, A)) & v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & (tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B)) & (tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))) & ((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))))),
% 0.53/0.61 inference(skolemize,[status(sab)],[68])).
% 0.53/0.61 tff(70,plain,
% 0.53/0.61 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~((~v3_struct_0(C)) & v10_lattices(C) & l3_lattices(C))) | (((~(C = k8_filter_0(A, B))) | (v1_funct_1(tptp_fun_D_4(C, B, A)) & v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B) & v1_funct_1(tptp_fun_E_5(C, B, A)) & v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B) & (tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B)) & (tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A))))) & ((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B) & (D = k1_realset1(u2_lattices(A), B)) & (E = k1_realset1(u1_lattices(A), B)) & (C = g3_lattices(B, D, E))))))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.53/0.61 tff(71,plain,
% 0.53/0.61 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[70, 60])).
% 0.53/0.61 tff(72,plain,
% 0.53/0.61 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))),
% 0.53/0.61 inference(modus_ponens,[status(thm)],[71, 58])).
% 0.53/0.61 tff(73,plain,
% 0.53/0.61 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B))))))))))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(74,plain,
% 0.53/0.62 ((v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, D, E)))))))))))) <=> (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B))))))))))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(75,plain,
% 0.53/0.62 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, D, E))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B)))))))))))))),
% 0.53/0.62 inference(monotonicity,[status(thm)],[74])).
% 0.53/0.62 tff(76,plain,
% 0.53/0.62 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, D, E))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B))))))))))))),
% 0.53/0.62 inference(transitivity,[status(thm)],[75, 73])).
% 0.53/0.62 tff(77,plain,
% 0.53/0.62 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, D, E))))))))))))),
% 0.53/0.62 inference(quant_inst,[status(thm)],[])).
% 0.53/0.62 tff(78,plain,
% 0.53/0.62 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B)))))))))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.53/0.62 tff(79,plain,
% 0.53/0.62 (![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B)))))))))))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[78, 42, 41, 40, 72])).
% 0.53/0.62 tff(80,plain,
% 0.53/0.62 (((~![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B)))))))))))) | ((~m1_filter_0(D!3, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3)))))))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B)))))))))))) | (~m1_filter_0(D!3, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3)))))))))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(81,plain,
% 0.53/0.62 ((~![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B)))))))))))) | ((~m1_filter_0(D!3, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3)))))))))))),
% 0.53/0.62 inference(quant_inst,[status(thm)],[])).
% 0.53/0.62 tff(82,plain,
% 0.53/0.62 ((~![B: $i] : ((~m1_filter_0(B, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, B!1), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, B!1) = k1_realset1(u2_lattices(B!1), B))) | (~(tptp_fun_E_5(C, B, B!1) = k1_realset1(u1_lattices(B!1), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, B!1), tptp_fun_E_5(C, B, B!1)))))))) | (~((C = k8_filter_0(B!1, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), B))) | (~(E = k1_realset1(u1_lattices(B!1), B)))))))))))) | (~m1_filter_0(D!3, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.53/0.62 tff(83,plain,
% 0.53/0.62 ((~m1_filter_0(D!3, B!1)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.53/0.62 tff(84,plain,
% 0.53/0.62 (![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))),
% 0.53/0.62 inference(unit_resolution,[status(thm)],[83, 53])).
% 0.53/0.62 tff(85,plain,
% 0.53/0.62 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B)))))) <=> (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B)))))))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(86,plain,
% 0.53/0.62 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B)))))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))),
% 0.53/0.62 inference(quant_intro,[status(thm)],[85])).
% 0.53/0.62 tff(87,plain,
% 0.53/0.62 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A)) <=> (~(v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) <=> (~(~(v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) <=> (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), rewrite(((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))) <=> (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))) <=> ((v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B)))))))), rewrite(((v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B)))))) <=> (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))) <=> (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(88,plain,
% 0.53/0.62 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))),
% 0.53/0.62 inference(quant_intro,[status(thm)],[87])).
% 0.53/0.62 tff(89,plain,
% 0.53/0.62 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))),
% 0.53/0.62 inference(rewrite,[status(thm)],[])).
% 0.53/0.62 tff(90,plain,
% 0.53/0.62 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A)))), rewrite((((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B))) & l3_lattices(k8_filter_0(A, B))) <=> ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, A)) => (((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B))) & l3_lattices(k8_filter_0(A, B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A)) => ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A)) => ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, A)) => (((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B))) & l3_lattices(k8_filter_0(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))))),
% 0.53/0.62 inference(bind,[status(th)],[])).
% 0.53/0.62 tff(91,plain,
% 0.53/0.62 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, A)) => (((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B))) & l3_lattices(k8_filter_0(A, B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))),
% 0.53/0.62 inference(quant_intro,[status(thm)],[90])).
% 0.53/0.62 tff(92,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, A)) => (((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B))) & l3_lattices(k8_filter_0(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k8_filter_0')).
% 0.53/0.62 tff(93,plain,
% 0.53/0.62 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.53/0.62 tff(94,plain,
% 0.53/0.62 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.53/0.62 tff(95,plain,(
% 0.53/0.62 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, A))) | ((~v3_struct_0(k8_filter_0(A, B))) & v10_lattices(k8_filter_0(A, B)) & l3_lattices(k8_filter_0(A, B))))),
% 0.53/0.62 inference(skolemize,[status(sab)],[94])).
% 0.53/0.62 tff(96,plain,
% 0.53/0.62 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.53/0.62 tff(97,plain,
% 0.53/0.62 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))),
% 0.53/0.62 inference(modus_ponens,[status(thm)],[96, 86])).
% 0.53/0.62 tff(98,plain,
% 0.53/0.62 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~m1_filter_0(D!3, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~m1_filter_0(D!3, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3))))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(99,plain,
% 0.53/0.63 ((v3_struct_0(B!1) | (~m1_filter_0(D!3, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3)))))) <=> (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~m1_filter_0(D!3, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3))))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(100,plain,
% 0.53/0.63 ((~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3))))) <=> (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3)))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(101,plain,
% 0.53/0.63 ((v3_struct_0(B!1) | (~m1_filter_0(D!3, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3)))))) <=> (v3_struct_0(B!1) | (~m1_filter_0(D!3, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3))))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[100])).
% 0.53/0.63 tff(102,plain,
% 0.53/0.63 ((v3_struct_0(B!1) | (~m1_filter_0(D!3, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3)))))) <=> (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~m1_filter_0(D!3, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3))))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[101, 99])).
% 0.53/0.63 tff(103,plain,
% 0.53/0.63 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(B!1) | (~m1_filter_0(D!3, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~m1_filter_0(D!3, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3)))))))),
% 0.53/0.63 inference(monotonicity,[status(thm)],[102])).
% 0.53/0.63 tff(104,plain,
% 0.53/0.63 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(B!1) | (~m1_filter_0(D!3, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~m1_filter_0(D!3, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3))))))),
% 0.53/0.63 inference(transitivity,[status(thm)],[103, 98])).
% 0.53/0.63 tff(105,plain,
% 0.53/0.63 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(B!1) | (~m1_filter_0(D!3, B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3))))))),
% 0.53/0.63 inference(quant_inst,[status(thm)],[])).
% 0.53/0.63 tff(106,plain,
% 0.53/0.63 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~m1_filter_0(D!3, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3)))))),
% 0.53/0.63 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.53/0.63 tff(107,plain,
% 0.53/0.63 ((~m1_filter_0(D!3, B!1)) | (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3)))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[106, 42, 41, 40, 97])).
% 0.53/0.63 tff(108,plain,
% 0.53/0.63 (~(v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3))))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[107, 53])).
% 0.53/0.63 tff(109,plain,
% 0.53/0.63 ((v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3)))) | l3_lattices(k8_filter_0(B!1, D!3))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(110,plain,
% 0.53/0.63 (l3_lattices(k8_filter_0(B!1, D!3))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.53/0.63 tff(111,plain,
% 0.53/0.63 ((v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3)))) | v10_lattices(k8_filter_0(B!1, D!3))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(112,plain,
% 0.53/0.63 (v10_lattices(k8_filter_0(B!1, D!3))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[111, 108])).
% 0.53/0.63 tff(113,plain,
% 0.53/0.63 ((v3_struct_0(k8_filter_0(B!1, D!3)) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~l3_lattices(k8_filter_0(B!1, D!3)))) | (~v3_struct_0(k8_filter_0(B!1, D!3)))),
% 0.53/0.63 inference(tautology,[status(thm)],[])).
% 0.53/0.63 tff(114,plain,
% 0.53/0.63 (~v3_struct_0(k8_filter_0(B!1, D!3))),
% 0.53/0.63 inference(unit_resolution,[status(thm)],[113, 108])).
% 0.53/0.63 tff(115,plain,
% 0.53/0.63 (((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))) | (v3_struct_0(k8_filter_0(B!1, D!3)) | (~l3_lattices(k8_filter_0(B!1, D!3))) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))) | v3_struct_0(k8_filter_0(B!1, D!3)) | (~l3_lattices(k8_filter_0(B!1, D!3))) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)))))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(116,plain,
% 0.53/0.63 ((v3_struct_0(k8_filter_0(B!1, D!3)) | (~l3_lattices(k8_filter_0(B!1, D!3))) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~((~((~(k8_filter_0(B!1, D!3) = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)))))))) | (~((k8_filter_0(B!1, D!3) = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3)))))))))) <=> (v3_struct_0(k8_filter_0(B!1, D!3)) | (~l3_lattices(k8_filter_0(B!1, D!3))) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)))))))),
% 0.53/0.63 inference(rewrite,[status(thm)],[])).
% 0.53/0.63 tff(117,plain,
% 0.53/0.63 (((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))) | (v3_struct_0(k8_filter_0(B!1, D!3)) | (~l3_lattices(k8_filter_0(B!1, D!3))) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~((~((~(k8_filter_0(B!1, D!3) = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)))))))) | (~((k8_filter_0(B!1, D!3) = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))) | (v3_struct_0(k8_filter_0(B!1, D!3)) | (~l3_lattices(k8_filter_0(B!1, D!3))) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))))))))),
% 0.63/0.63 inference(monotonicity,[status(thm)],[116])).
% 0.63/0.63 tff(118,plain,
% 0.63/0.63 (((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))) | (v3_struct_0(k8_filter_0(B!1, D!3)) | (~l3_lattices(k8_filter_0(B!1, D!3))) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~((~((~(k8_filter_0(B!1, D!3) = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)))))))) | (~((k8_filter_0(B!1, D!3) = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))) | v3_struct_0(k8_filter_0(B!1, D!3)) | (~l3_lattices(k8_filter_0(B!1, D!3))) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)))))))),
% 0.63/0.64 inference(transitivity,[status(thm)],[117, 115])).
% 0.63/0.64 tff(119,plain,
% 0.63/0.64 ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))) | (v3_struct_0(k8_filter_0(B!1, D!3)) | (~l3_lattices(k8_filter_0(B!1, D!3))) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~((~((~(k8_filter_0(B!1, D!3) = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)))))))) | (~((k8_filter_0(B!1, D!3) = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(120,plain,
% 0.63/0.64 ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(C, D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, B!1), tptp_fun_E_5(C, D!3, B!1)))))))) | (~((C = k8_filter_0(B!1, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(B!1), D!3))) | (~(E = k1_realset1(u1_lattices(B!1), D!3))))))))))) | v3_struct_0(k8_filter_0(B!1, D!3)) | (~l3_lattices(k8_filter_0(B!1, D!3))) | (~v10_lattices(k8_filter_0(B!1, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.63/0.64 tff(121,plain,
% 0.63/0.64 (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)))))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[120, 114, 112, 110, 84])).
% 0.63/0.64 tff(122,plain,
% 0.63/0.64 (((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))))) | (k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)))),
% 0.63/0.64 inference(tautology,[status(thm)],[])).
% 0.63/0.64 tff(123,plain,
% 0.63/0.64 (k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.63/0.64 tff(124,plain,
% 0.63/0.64 (g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)) = k8_filter_0(B!1, D!3)),
% 0.63/0.64 inference(symmetry,[status(thm)],[123])).
% 0.63/0.64 tff(125,plain,
% 0.63/0.64 (((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))))) | (tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))),
% 0.63/0.64 inference(tautology,[status(thm)],[])).
% 0.63/0.64 tff(126,plain,
% 0.63/0.64 (tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3)),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[125, 121])).
% 0.63/0.64 tff(127,plain,
% 0.63/0.64 (k1_realset1(u1_lattices(B!1), D!3) = tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)),
% 0.63/0.64 inference(symmetry,[status(thm)],[126])).
% 0.63/0.64 tff(128,plain,
% 0.63/0.64 ((g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (C!2 = D!3)),
% 0.63/0.64 inference(or_elim,[status(thm)],[49])).
% 0.63/0.64 tff(129,plain,
% 0.63/0.64 (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))),
% 0.63/0.64 inference(and_elim,[status(thm)],[128])).
% 0.63/0.64 tff(130,plain,
% 0.63/0.64 (g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))),
% 0.63/0.64 inference(symmetry,[status(thm)],[129])).
% 0.63/0.64 tff(131,plain,
% 0.63/0.64 (^[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)))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(132,plain,
% 0.63/0.64 (![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))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[131])).
% 0.63/0.64 tff(133,plain,
% 0.63/0.64 (![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))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(134,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.63/0.64 tff(135,plain,
% 0.63/0.64 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.63/0.64 tff(136,plain,(
% 0.63/0.64 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.63/0.64 inference(skolemize,[status(sab)],[135])).
% 0.63/0.64 tff(137,plain,
% 0.63/0.64 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.63/0.64 tff(138,plain,
% 0.63/0.64 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(139,plain,
% 0.63/0.64 (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.63/0.64 tff(140,plain,
% 0.63/0.64 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(141,plain,
% 0.63/0.64 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[140])).
% 0.63/0.64 tff(142,plain,
% 0.63/0.64 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(143,plain,
% 0.63/0.64 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[142])).
% 0.63/0.64 tff(144,plain,
% 0.63/0.64 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(145,plain,
% 0.63/0.64 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(146,plain,
% 0.63/0.64 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[145])).
% 0.63/0.64 tff(147,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.63/0.64 tff(148,plain,
% 0.63/0.64 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.63/0.64 tff(149,plain,
% 0.63/0.64 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.63/0.64 tff(150,plain,(
% 0.63/0.64 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.63/0.64 inference(skolemize,[status(sab)],[149])).
% 0.63/0.64 tff(151,plain,
% 0.63/0.64 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.63/0.64 tff(152,plain,
% 0.63/0.64 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[151, 141])).
% 0.63/0.64 tff(153,plain,
% 0.63/0.64 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(154,plain,
% 0.63/0.64 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(155,plain,
% 0.63/0.64 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.63/0.64 tff(156,plain,
% 0.63/0.64 (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[155, 40, 152])).
% 0.63/0.64 tff(157,plain,
% 0.63/0.64 (((~l1_lattices(B!1)) | (~l2_lattices(B!1))) | l1_lattices(B!1)),
% 0.63/0.64 inference(tautology,[status(thm)],[])).
% 0.63/0.64 tff(158,plain,
% 0.63/0.64 (l1_lattices(B!1)),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.63/0.64 tff(159,plain,
% 0.63/0.64 (^[A: $i] : refl(((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(160,plain,
% 0.63/0.64 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[159])).
% 0.63/0.64 tff(161,plain,
% 0.63/0.64 (^[A: $i] : rewrite(((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(162,plain,
% 0.63/0.64 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[161])).
% 0.63/0.64 tff(163,plain,
% 0.63/0.64 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(164,plain,
% 0.63/0.64 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(165,plain,
% 0.63/0.64 (![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[164])).
% 0.63/0.64 tff(166,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u1_lattices')).
% 0.63/0.64 tff(167,plain,
% 0.63/0.64 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.63/0.64 tff(168,plain,
% 0.63/0.64 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.63/0.64 tff(169,plain,(
% 0.63/0.64 ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.63/0.64 inference(skolemize,[status(sab)],[168])).
% 0.63/0.64 tff(170,plain,
% 0.63/0.64 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.63/0.64 tff(171,plain,
% 0.63/0.64 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[170, 160])).
% 0.63/0.64 tff(172,plain,
% 0.63/0.64 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(173,plain,
% 0.63/0.64 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(174,plain,
% 0.63/0.64 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.63/0.64 tff(175,plain,
% 0.63/0.64 ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[174, 171])).
% 0.63/0.64 tff(176,plain,
% 0.63/0.64 (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[175, 158])).
% 0.63/0.64 tff(177,plain,
% 0.63/0.64 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.64 inference(tautology,[status(thm)],[])).
% 0.63/0.64 tff(178,plain,
% 0.63/0.64 (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.63/0.64 tff(179,plain,
% 0.63/0.64 ((~(m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.64 inference(tautology,[status(thm)],[])).
% 0.63/0.64 tff(180,plain,
% 0.63/0.64 ((~(m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.63/0.64 tff(181,plain,
% 0.63/0.64 (m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[180, 139])).
% 0.63/0.64 tff(182,plain,
% 0.63/0.64 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.64 inference(tautology,[status(thm)],[])).
% 0.63/0.64 tff(183,plain,
% 0.63/0.64 (v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[182, 176])).
% 0.63/0.64 tff(184,plain,
% 0.63/0.64 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_1(u1_lattices(B!1))),
% 0.63/0.64 inference(tautology,[status(thm)],[])).
% 0.63/0.64 tff(185,plain,
% 0.63/0.64 (v1_funct_1(u1_lattices(B!1))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[184, 176])).
% 0.63/0.64 tff(186,plain,
% 0.63/0.64 (((~l1_lattices(B!1)) | (~l2_lattices(B!1))) | l2_lattices(B!1)),
% 0.63/0.64 inference(tautology,[status(thm)],[])).
% 0.63/0.64 tff(187,plain,
% 0.63/0.64 (l2_lattices(B!1)),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[186, 156])).
% 0.63/0.64 tff(188,plain,
% 0.63/0.64 (^[A: $i] : refl(((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(189,plain,
% 0.63/0.64 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[188])).
% 0.63/0.64 tff(190,plain,
% 0.63/0.64 (^[A: $i] : rewrite(((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(191,plain,
% 0.63/0.64 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[190])).
% 0.63/0.64 tff(192,plain,
% 0.63/0.64 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(193,plain,
% 0.63/0.64 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.63/0.64 inference(bind,[status(th)],[])).
% 0.63/0.64 tff(194,plain,
% 0.63/0.64 (![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.63/0.64 inference(quant_intro,[status(thm)],[193])).
% 0.63/0.64 tff(195,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u2_lattices')).
% 0.63/0.64 tff(196,plain,
% 0.63/0.64 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.63/0.64 tff(197,plain,
% 0.63/0.64 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.63/0.64 tff(198,plain,(
% 0.63/0.64 ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.63/0.64 inference(skolemize,[status(sab)],[197])).
% 0.63/0.64 tff(199,plain,
% 0.63/0.64 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.63/0.64 tff(200,plain,
% 0.63/0.64 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[199, 189])).
% 0.63/0.64 tff(201,plain,
% 0.63/0.64 (((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))) <=> ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.63/0.64 inference(rewrite,[status(thm)],[])).
% 0.63/0.64 tff(202,plain,
% 0.63/0.64 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.63/0.64 inference(quant_inst,[status(thm)],[])).
% 0.63/0.64 tff(203,plain,
% 0.63/0.64 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.63/0.64 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.63/0.64 tff(204,plain,
% 0.63/0.64 ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[203, 200])).
% 0.63/0.64 tff(205,plain,
% 0.63/0.64 (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[204, 187])).
% 0.63/0.64 tff(206,plain,
% 0.63/0.64 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.64 inference(tautology,[status(thm)],[])).
% 0.63/0.64 tff(207,plain,
% 0.63/0.64 (v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.64 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.63/0.65 tff(208,plain,
% 0.63/0.65 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_1(u2_lattices(B!1))),
% 0.63/0.65 inference(tautology,[status(thm)],[])).
% 0.63/0.65 tff(209,plain,
% 0.63/0.65 (v1_funct_1(u2_lattices(B!1))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[208, 205])).
% 0.63/0.65 tff(210,plain,
% 0.63/0.65 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(211,plain,
% 0.63/0.65 (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[210, 137])).
% 0.63/0.65 tff(212,plain,
% 0.63/0.65 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.65 inference(tautology,[status(thm)],[])).
% 0.63/0.65 tff(213,plain,
% 0.63/0.65 (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[212, 205])).
% 0.63/0.65 tff(214,plain,
% 0.63/0.65 ((~(m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.65 inference(tautology,[status(thm)],[])).
% 0.63/0.65 tff(215,plain,
% 0.63/0.65 ((~(m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.63/0.65 tff(216,plain,
% 0.63/0.65 (m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[215, 211])).
% 0.63/0.65 tff(217,plain,
% 0.63/0.65 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(218,plain,
% 0.63/0.65 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[217])).
% 0.63/0.65 tff(219,plain,
% 0.63/0.65 (^[A: $i, B: $i, C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(220,plain,
% 0.63/0.65 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[219])).
% 0.63/0.65 tff(221,plain,
% 0.63/0.65 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.63/0.65 inference(transitivity,[status(thm)],[220, 218])).
% 0.63/0.65 tff(222,plain,
% 0.63/0.65 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : rewrite(((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(223,plain,
% 0.63/0.65 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[222])).
% 0.63/0.65 tff(224,plain,
% 0.63/0.65 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(225,plain,
% 0.63/0.65 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : trans(monotonicity(rewrite((((A = D) & (B = E)) & (C = F)) <=> ((A = D) & (B = E) & (C = F))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))))), rewrite(((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), (![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))))),
% 0.63/0.65 inference(bind,[status(th)],[])).
% 0.63/0.65 tff(226,plain,
% 0.63/0.65 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.63/0.65 inference(quant_intro,[status(thm)],[225])).
% 0.63/0.65 tff(227,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g3_lattices')).
% 0.63/0.65 tff(228,plain,
% 0.63/0.65 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.63/0.65 tff(229,plain,
% 0.63/0.65 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[228, 224])).
% 0.63/0.65 tff(230,plain,(
% 0.63/0.65 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.63/0.65 inference(skolemize,[status(sab)],[229])).
% 0.63/0.65 tff(231,plain,
% 0.63/0.65 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[230, 223])).
% 0.63/0.65 tff(232,plain,
% 0.63/0.65 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[231, 221])).
% 0.63/0.65 tff(233,plain,
% 0.63/0.65 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(234,plain,
% 0.63/0.65 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) <=> ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(235,plain,
% 0.63/0.65 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[234])).
% 0.63/0.65 tff(236,plain,
% 0.63/0.65 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))),
% 0.63/0.65 inference(transitivity,[status(thm)],[235, 233])).
% 0.63/0.65 tff(237,plain,
% 0.63/0.65 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(238,plain,
% 0.63/0.65 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.63/0.65 tff(239,plain,
% 0.63/0.65 ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[238, 232])).
% 0.63/0.65 tff(240,plain,
% 0.63/0.65 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[239, 216, 209, 207, 185, 183, 181])).
% 0.63/0.65 tff(241,plain,
% 0.63/0.65 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(242,plain,
% 0.63/0.65 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(243,plain,
% 0.63/0.65 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.63/0.65 tff(244,plain,
% 0.63/0.65 (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[243, 240, 130])).
% 0.63/0.65 tff(245,plain,
% 0.63/0.65 (((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))) | (u1_lattices(B!1) = u1_lattices(A!0))),
% 0.63/0.65 inference(tautology,[status(thm)],[])).
% 0.63/0.65 tff(246,plain,
% 0.63/0.65 (u1_lattices(B!1) = u1_lattices(A!0)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.63/0.65 tff(247,plain,
% 0.63/0.65 (u1_lattices(A!0) = u1_lattices(B!1)),
% 0.63/0.65 inference(symmetry,[status(thm)],[246])).
% 0.63/0.65 tff(248,plain,
% 0.63/0.65 (k1_realset1(u1_lattices(A!0), D!3) = k1_realset1(u1_lattices(B!1), D!3)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[247])).
% 0.63/0.65 tff(249,plain,
% 0.63/0.65 (C!2 = D!3),
% 0.63/0.65 inference(and_elim,[status(thm)],[128])).
% 0.63/0.65 tff(250,plain,
% 0.63/0.65 (D!3 = C!2),
% 0.63/0.65 inference(symmetry,[status(thm)],[249])).
% 0.63/0.65 tff(251,plain,
% 0.63/0.65 (k8_filter_0(A!0, D!3) = k8_filter_0(A!0, C!2)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[250])).
% 0.63/0.65 tff(252,plain,
% 0.63/0.65 (k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)),
% 0.63/0.65 inference(symmetry,[status(thm)],[251])).
% 0.63/0.65 tff(253,plain,
% 0.63/0.65 (v3_struct_0(k8_filter_0(A!0, C!2)) <=> v3_struct_0(k8_filter_0(A!0, D!3))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[252])).
% 0.63/0.65 tff(254,plain,
% 0.63/0.65 (v3_struct_0(k8_filter_0(A!0, D!3)) <=> v3_struct_0(k8_filter_0(A!0, C!2))),
% 0.63/0.65 inference(symmetry,[status(thm)],[253])).
% 0.63/0.65 tff(255,plain,
% 0.63/0.65 ((~v3_struct_0(k8_filter_0(A!0, D!3))) <=> (~v3_struct_0(k8_filter_0(A!0, C!2)))),
% 0.63/0.65 inference(monotonicity,[status(thm)],[254])).
% 0.63/0.65 tff(256,plain,
% 0.63/0.65 (l3_lattices(A!0)),
% 0.63/0.65 inference(and_elim,[status(thm)],[39])).
% 0.63/0.65 tff(257,plain,
% 0.63/0.65 (v10_lattices(A!0)),
% 0.63/0.65 inference(and_elim,[status(thm)],[39])).
% 0.63/0.65 tff(258,plain,
% 0.63/0.65 (~v3_struct_0(A!0)),
% 0.63/0.65 inference(and_elim,[status(thm)],[39])).
% 0.63/0.65 tff(259,plain,
% 0.63/0.65 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0)))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(260,plain,
% 0.63/0.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0)))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(261,plain,
% 0.63/0.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0))),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.63/0.65 tff(262,plain,
% 0.63/0.65 (![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0))),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[261, 258, 257, 256, 19])).
% 0.63/0.65 tff(263,plain,
% 0.63/0.65 ((~![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0))) | (m1_filter_2(D!3, A!0) <=> m1_filter_0(D!3, A!0))),
% 0.63/0.65 inference(quant_inst,[status(thm)],[])).
% 0.63/0.65 tff(264,plain,
% 0.63/0.65 (m1_filter_2(D!3, A!0) <=> m1_filter_0(D!3, A!0)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[263, 262])).
% 0.63/0.65 tff(265,plain,
% 0.63/0.65 (m1_filter_2(D!3, A!0) <=> m1_filter_2(C!2, A!0)),
% 0.63/0.65 inference(monotonicity,[status(thm)],[250])).
% 0.63/0.65 tff(266,plain,
% 0.63/0.65 (m1_filter_2(C!2, A!0) <=> m1_filter_2(D!3, A!0)),
% 0.63/0.65 inference(symmetry,[status(thm)],[265])).
% 0.63/0.65 tff(267,plain,
% 0.63/0.65 (m1_filter_2(C!2, A!0)),
% 0.63/0.65 inference(and_elim,[status(thm)],[39])).
% 0.63/0.65 tff(268,plain,
% 0.63/0.65 (m1_filter_2(D!3, A!0)),
% 0.63/0.65 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.63/0.65 tff(269,plain,
% 0.63/0.65 ((~(m1_filter_2(D!3, A!0) <=> m1_filter_0(D!3, A!0))) | (~m1_filter_2(D!3, A!0)) | m1_filter_0(D!3, A!0)),
% 0.63/0.65 inference(tautology,[status(thm)],[])).
% 0.63/0.65 tff(270,plain,
% 0.63/0.65 (m1_filter_0(D!3, A!0)),
% 0.63/0.65 inference(unit_resolution,[status(thm)],[269, 268, 264])).
% 0.63/0.65 tff(271,plain,
% 0.63/0.65 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(D!3, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(D!3, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3))))))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(272,plain,
% 0.63/0.65 ((v3_struct_0(A!0) | (~m1_filter_0(D!3, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3)))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(D!3, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3))))))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(273,plain,
% 0.63/0.65 ((~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3))))) <=> (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3)))))),
% 0.63/0.65 inference(rewrite,[status(thm)],[])).
% 0.63/0.65 tff(274,plain,
% 0.63/0.65 ((v3_struct_0(A!0) | (~m1_filter_0(D!3, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3)))))) <=> (v3_struct_0(A!0) | (~m1_filter_0(D!3, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3))))))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[273])).
% 0.63/0.66 tff(275,plain,
% 0.63/0.66 ((v3_struct_0(A!0) | (~m1_filter_0(D!3, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3)))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(D!3, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3))))))),
% 0.63/0.66 inference(transitivity,[status(thm)],[274, 272])).
% 0.63/0.66 tff(276,plain,
% 0.63/0.66 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(A!0) | (~m1_filter_0(D!3, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(D!3, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3)))))))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[275])).
% 0.63/0.66 tff(277,plain,
% 0.63/0.66 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(A!0) | (~m1_filter_0(D!3, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(D!3, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3))))))),
% 0.63/0.66 inference(transitivity,[status(thm)],[276, 271])).
% 0.63/0.66 tff(278,plain,
% 0.63/0.66 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | (v3_struct_0(A!0) | (~m1_filter_0(D!3, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3))))))),
% 0.63/0.66 inference(quant_inst,[status(thm)],[])).
% 0.63/0.66 tff(279,plain,
% 0.63/0.66 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k8_filter_0(A, B)) | (~v10_lattices(k8_filter_0(A, B))) | (~l3_lattices(k8_filter_0(A, B))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(D!3, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3)))))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.63/0.66 tff(280,plain,
% 0.63/0.66 ((~m1_filter_0(D!3, A!0)) | (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3)))))),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[279, 258, 257, 256, 97])).
% 0.63/0.66 tff(281,plain,
% 0.63/0.66 (~(v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3))))),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[280, 270])).
% 0.63/0.66 tff(282,plain,
% 0.63/0.66 ((v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3)))) | (~v3_struct_0(k8_filter_0(A!0, D!3)))),
% 0.63/0.66 inference(tautology,[status(thm)],[])).
% 0.63/0.66 tff(283,plain,
% 0.63/0.66 (~v3_struct_0(k8_filter_0(A!0, D!3))),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[282, 281])).
% 0.63/0.66 tff(284,plain,
% 0.63/0.66 (~v3_struct_0(k8_filter_0(A!0, C!2))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[283, 255])).
% 0.63/0.66 tff(285,plain,
% 0.63/0.66 (v10_lattices(k8_filter_0(A!0, C!2)) <=> v10_lattices(k8_filter_0(A!0, D!3))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[252])).
% 0.63/0.66 tff(286,plain,
% 0.63/0.66 (v10_lattices(k8_filter_0(A!0, D!3)) <=> v10_lattices(k8_filter_0(A!0, C!2))),
% 0.63/0.66 inference(symmetry,[status(thm)],[285])).
% 0.63/0.66 tff(287,plain,
% 0.63/0.66 ((v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3)))) | v10_lattices(k8_filter_0(A!0, D!3))),
% 0.63/0.66 inference(tautology,[status(thm)],[])).
% 0.63/0.66 tff(288,plain,
% 0.63/0.66 (v10_lattices(k8_filter_0(A!0, D!3))),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[287, 281])).
% 0.63/0.66 tff(289,plain,
% 0.63/0.66 (v10_lattices(k8_filter_0(A!0, C!2))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[288, 286])).
% 0.63/0.66 tff(290,plain,
% 0.63/0.66 (l3_lattices(k8_filter_0(A!0, C!2)) <=> l3_lattices(k8_filter_0(A!0, D!3))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[252])).
% 0.63/0.66 tff(291,plain,
% 0.63/0.66 (l3_lattices(k8_filter_0(A!0, D!3)) <=> l3_lattices(k8_filter_0(A!0, C!2))),
% 0.63/0.66 inference(symmetry,[status(thm)],[290])).
% 0.63/0.66 tff(292,plain,
% 0.63/0.66 ((v3_struct_0(k8_filter_0(A!0, D!3)) | (~v10_lattices(k8_filter_0(A!0, D!3))) | (~l3_lattices(k8_filter_0(A!0, D!3)))) | l3_lattices(k8_filter_0(A!0, D!3))),
% 0.63/0.66 inference(tautology,[status(thm)],[])).
% 0.63/0.66 tff(293,plain,
% 0.63/0.66 (l3_lattices(k8_filter_0(A!0, D!3))),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[292, 281])).
% 0.63/0.66 tff(294,plain,
% 0.63/0.66 (l3_lattices(k8_filter_0(A!0, C!2))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[293, 291])).
% 0.63/0.66 tff(295,plain,
% 0.63/0.66 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B))))))))))))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(296,plain,
% 0.63/0.66 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, D, E)))))))))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B))))))))))))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(297,plain,
% 0.63/0.66 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, D, E))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B)))))))))))))),
% 0.63/0.66 inference(monotonicity,[status(thm)],[296])).
% 0.63/0.66 tff(298,plain,
% 0.63/0.66 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, D, E))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B))))))))))))),
% 0.63/0.66 inference(transitivity,[status(thm)],[297, 295])).
% 0.63/0.66 tff(299,plain,
% 0.63/0.66 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, D, E))))))))))))),
% 0.63/0.66 inference(quant_inst,[status(thm)],[])).
% 0.63/0.66 tff(300,plain,
% 0.63/0.66 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A))) | (~v1_funct_2(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A))) | (~v1_funct_2(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A) = k1_realset1(u2_lattices(A), B))) | (~(tptp_fun_E_5(C, B, A) = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A), tptp_fun_E_5(C, B, A)))))))) | (~((C = k8_filter_0(A, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(D = k1_realset1(u2_lattices(A), B))) | (~(E = k1_realset1(u1_lattices(A), B))) | (~(C = g3_lattices(B, D, E))))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B)))))))))))),
% 0.63/0.66 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.63/0.66 tff(301,plain,
% 0.63/0.66 (![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B)))))))))))),
% 0.63/0.66 inference(unit_resolution,[status(thm)],[300, 258, 257, 256, 72])).
% 0.63/0.66 tff(302,plain,
% 0.63/0.66 (((~![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B)))))))))))) | ((~m1_filter_0(D!3, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3)))))))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B)))))))))))) | (~m1_filter_0(D!3, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3)))))))))))),
% 0.63/0.66 inference(rewrite,[status(thm)],[])).
% 0.63/0.66 tff(303,plain,
% 0.63/0.66 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B)))))))))))) | ((~m1_filter_0(D!3, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3)))))))))))),
% 0.63/0.66 inference(quant_inst,[status(thm)],[])).
% 0.63/0.66 tff(304,plain,
% 0.63/0.66 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, B))) | (~((~v1_funct_1(tptp_fun_D_4(C, B, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_D_4(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(tptp_fun_E_5(C, B, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(tptp_fun_E_5(C, B, A!0), k2_zfmisc_1(B, B), B)) | (~(tptp_fun_D_4(C, B, A!0) = k1_realset1(u2_lattices(A!0), B))) | (~(tptp_fun_E_5(C, B, A!0) = k1_realset1(u1_lattices(A!0), B))) | (~(C = g3_lattices(B, tptp_fun_D_4(C, B, A!0), tptp_fun_E_5(C, B, A!0)))))))) | (~((C = k8_filter_0(A!0, B)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(D, k2_zfmisc_1(B, B), B)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(B, B), B)) | (~m2_relset_1(E, k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), B))) | (~(E = k1_realset1(u1_lattices(A!0), B)))))))))))) | (~m1_filter_0(D!3, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))),
% 0.63/0.67 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.63/0.67 tff(305,plain,
% 0.63/0.67 ((~m1_filter_0(D!3, A!0)) | ![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[304, 301])).
% 0.63/0.67 tff(306,plain,
% 0.63/0.67 (![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))),
% 0.63/0.67 inference(unit_resolution,[status(thm)],[305, 270])).
% 0.63/0.67 tff(307,plain,
% 0.63/0.67 (((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))) | (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E))))))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))) | v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E))))))))))),
% 0.66/0.67 inference(rewrite,[status(thm)],[])).
% 0.66/0.67 tff(308,plain,
% 0.66/0.67 ((v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3)))))))))) <=> (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E))))))))))),
% 0.66/0.67 inference(rewrite,[status(thm)],[])).
% 0.66/0.67 tff(309,plain,
% 0.66/0.67 (((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))) | (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))) | (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E)))))))))))),
% 0.66/0.67 inference(monotonicity,[status(thm)],[308])).
% 0.66/0.67 tff(310,plain,
% 0.66/0.67 (((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))) | (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))) <=> ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))) | v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E))))))))))),
% 0.66/0.68 inference(transitivity,[status(thm)],[309, 307])).
% 0.66/0.68 tff(311,plain,
% 0.66/0.68 ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))) | (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))),
% 0.66/0.68 inference(quant_inst,[status(thm)],[])).
% 0.66/0.68 tff(312,plain,
% 0.66/0.68 ((~![C: $i] : (v3_struct_0(C) | (~l3_lattices(C)) | (~v10_lattices(C)) | (~((~((~(C = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(C, D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(C, D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(C, D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(C, D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(C = g3_lattices(D!3, tptp_fun_D_4(C, D!3, A!0), tptp_fun_E_5(C, D!3, A!0)))))))) | (~((C = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(C = g3_lattices(D!3, D, E))) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))))))))))) | v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E)))))))))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.66/0.68 tff(313,plain,
% 0.66/0.68 (v3_struct_0(k8_filter_0(A!0, C!2)) | (~l3_lattices(k8_filter_0(A!0, C!2))) | (~v10_lattices(k8_filter_0(A!0, C!2))) | (~((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E)))))))))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[312, 306])).
% 0.66/0.68 tff(314,plain,
% 0.66/0.68 (~((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E))))))))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[313, 294, 289, 284])).
% 0.66/0.68 tff(315,plain,
% 0.66/0.68 (((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3)) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(D, k2_zfmisc_1(D!3, D!3), D!3)) | ![E: $i] : ((~v1_funct_1(E)) | (~v1_funct_2(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(E, k2_zfmisc_1(D!3, D!3), D!3)) | (~(D = k1_realset1(u2_lattices(A!0), D!3))) | (~(E = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, D, E)))))))) | ((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))),
% 0.66/0.68 inference(tautology,[status(thm)],[])).
% 0.66/0.68 tff(316,plain,
% 0.66/0.68 ((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))))))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[315, 314])).
% 0.66/0.68 tff(317,plain,
% 0.66/0.68 ((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))))))),
% 0.66/0.68 inference(tautology,[status(thm)],[])).
% 0.66/0.68 tff(318,plain,
% 0.66/0.68 ((~((~(k8_filter_0(A!0, C!2) = k8_filter_0(A!0, D!3))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))))) | (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))))))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[317, 252])).
% 0.66/0.68 tff(319,plain,
% 0.66/0.68 (~((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[318, 316])).
% 0.66/0.68 tff(320,plain,
% 0.66/0.68 (((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))))) | (tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))),
% 0.66/0.68 inference(tautology,[status(thm)],[])).
% 0.66/0.68 tff(321,plain,
% 0.66/0.68 (tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3)),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[320, 319])).
% 0.66/0.68 tff(322,plain,
% 0.66/0.68 (tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1)),
% 0.66/0.68 inference(transitivity,[status(thm)],[321, 248, 127])).
% 0.66/0.68 tff(323,plain,
% 0.66/0.68 (((~v1_funct_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))) | (~(tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u1_lattices(B!1), D!3))) | (~(k8_filter_0(B!1, D!3) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))))) | (tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3))),
% 0.66/0.68 inference(tautology,[status(thm)],[])).
% 0.66/0.68 tff(324,plain,
% 0.66/0.68 (tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1) = k1_realset1(u2_lattices(B!1), D!3)),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[323, 121])).
% 0.66/0.68 tff(325,plain,
% 0.66/0.68 (k1_realset1(u2_lattices(B!1), D!3) = tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1)),
% 0.66/0.68 inference(symmetry,[status(thm)],[324])).
% 0.66/0.68 tff(326,plain,
% 0.66/0.68 (((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))) | (u2_lattices(B!1) = u2_lattices(A!0))),
% 0.66/0.68 inference(tautology,[status(thm)],[])).
% 0.66/0.68 tff(327,plain,
% 0.66/0.68 (u2_lattices(B!1) = u2_lattices(A!0)),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[326, 244])).
% 0.66/0.68 tff(328,plain,
% 0.66/0.68 (u2_lattices(A!0) = u2_lattices(B!1)),
% 0.66/0.68 inference(symmetry,[status(thm)],[327])).
% 0.66/0.68 tff(329,plain,
% 0.66/0.68 (k1_realset1(u2_lattices(A!0), D!3) = k1_realset1(u2_lattices(B!1), D!3)),
% 0.66/0.68 inference(monotonicity,[status(thm)],[328])).
% 0.66/0.68 tff(330,plain,
% 0.66/0.68 (((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))))) | (tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))),
% 0.66/0.69 inference(tautology,[status(thm)],[])).
% 0.66/0.69 tff(331,plain,
% 0.66/0.69 (tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3)),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[330, 319])).
% 0.66/0.69 tff(332,plain,
% 0.66/0.69 (tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1)),
% 0.66/0.69 inference(transitivity,[status(thm)],[331, 329, 325])).
% 0.66/0.69 tff(333,plain,
% 0.66/0.69 (g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(B!1, D!3), D!3, B!1), tptp_fun_E_5(k8_filter_0(B!1, D!3), D!3, B!1))),
% 0.66/0.69 inference(monotonicity,[status(thm)],[332, 322])).
% 0.66/0.69 tff(334,plain,
% 0.66/0.69 (((~v1_funct_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~v1_funct_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))) | (~v1_funct_2(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~m2_relset_1(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0), k2_zfmisc_1(D!3, D!3), D!3)) | (~(tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u2_lattices(A!0), D!3))) | (~(tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0) = k1_realset1(u1_lattices(A!0), D!3))) | (~(k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))))) | (k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0)))),
% 0.66/0.69 inference(tautology,[status(thm)],[])).
% 0.66/0.69 tff(335,plain,
% 0.66/0.69 (k8_filter_0(A!0, C!2) = g3_lattices(D!3, tptp_fun_D_4(k8_filter_0(A!0, C!2), D!3, A!0), tptp_fun_E_5(k8_filter_0(A!0, C!2), D!3, A!0))),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[334, 319])).
% 0.66/0.69 tff(336,plain,
% 0.66/0.69 (k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3)),
% 0.66/0.69 inference(transitivity,[status(thm)],[335, 333, 124])).
% 0.66/0.69 tff(337,plain,
% 0.66/0.69 (~(k8_filter_0(A!0, C!2) = k8_filter_0(B!1, D!3))),
% 0.66/0.69 inference(or_elim,[status(thm)],[49])).
% 0.66/0.69 tff(338,plain,
% 0.66/0.69 ($false),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[337, 336])).
% 0.66/0.69 % SZS output end Proof
%------------------------------------------------------------------------------