%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT288+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:11 AM UTC 2025
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT288+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 19 20:00:55 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(r2_hidden_type, type, (
% 0.13/0.40 r2_hidden: ( $i * $i ) > $o)).
% 0.13/0.40 tff(a_1_1_lopclset_type, type, (
% 0.13/0.40 a_1_1_lopclset: $i > $i)).
% 0.13/0.40 tff(tptp_fun_A_0_type, type, (
% 0.13/0.40 tptp_fun_A_0: $i)).
% 0.13/0.40 tff(tptp_fun_C_2_type, type, (
% 0.13/0.40 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.13/0.40 tff(a_2_0_lopclset_type, type, (
% 0.13/0.40 a_2_0_lopclset: ( $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_B_1_type, type, (
% 0.13/0.40 tptp_fun_B_1: $i)).
% 0.13/0.40 tff(k7_lopclset_type, type, (
% 0.13/0.40 k7_lopclset: $i > $i)).
% 0.13/0.40 tff(v17_lattices_type, type, (
% 0.13/0.40 v17_lattices: $i > $o)).
% 0.13/0.40 tff(v10_lattices_type, type, (
% 0.13/0.40 v10_lattices: $i > $o)).
% 0.13/0.40 tff(l3_lattices_type, type, (
% 0.13/0.40 l3_lattices: $i > $o)).
% 0.13/0.40 tff(v3_struct_0_type, type, (
% 0.13/0.40 v3_struct_0: $i > $o)).
% 0.13/0.40 tff(v3_realset2_type, type, (
% 0.13/0.40 v3_realset2: $i > $o)).
% 0.13/0.40 tff(r1_tarski_type, type, (
% 0.13/0.40 r1_tarski: ( $i * $i ) > $o)).
% 0.13/0.40 tff(m1_subset_1_type, type, (
% 0.13/0.40 m1_subset_1: ( $i * $i ) > $o)).
% 0.13/0.40 tff(u1_struct_0_type, type, (
% 0.13/0.40 u1_struct_0: $i > $i)).
% 0.13/0.40 tff(m1_filter_0_type, type, (
% 0.13/0.40 m1_filter_0: ( $i * $i ) > $o)).
% 0.13/0.40 tff(v1_filter_0_type, type, (
% 0.13/0.40 v1_filter_0: ( $i * $i ) > $o)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(4,plain,
% 0.13/0.40 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(6,plain,
% 0.13/0.40 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.40 tff(8,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5_lopclset')).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.13/0.40 tff(11,plain,(
% 0.13/0.40 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.13/0.40 inference(skolemize,[status(sab)],[10])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.13/0.40 tff(13,plain,
% 0.13/0.40 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 ((~![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(17,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t19_lopclset')).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (l3_lattices(A!0)),
% 0.20/0.41 inference(and_elim,[status(thm)],[22])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (~v3_realset2(A!0)),
% 0.20/0.41 inference(and_elim,[status(thm)],[22])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (v17_lattices(A!0)),
% 0.20/0.41 inference(and_elim,[status(thm)],[22])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (v10_lattices(A!0)),
% 0.20/0.41 inference(and_elim,[status(thm)],[22])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (~v3_struct_0(A!0)),
% 0.20/0.41 inference(and_elim,[status(thm)],[22])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 ((v3_realset2(A!0) | v3_struct_0(A!0) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0))) <=> (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (k7_lopclset(A!0) = a_1_1_lopclset(A!0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[33, 27, 26, 25, 24, 23, 13])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (a_1_1_lopclset(A!0) = k7_lopclset(A!0)),
% 0.20/0.41 inference(symmetry,[status(thm)],[34])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))),
% 0.20/0.41 inference(symmetry,[status(thm)],[36])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 ((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))) <=> (~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (^[A: $i, B: $i] : refl((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (^[A: $i, B: $i] : rewrite((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[42, 40])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))), rewrite((r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))) <=> (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))) <=> (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))), rewrite((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (^[A: $i, B: $i] : rewrite((r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.41 tff(49,axiom,(![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.20/0.41 tff(52,plain,(
% 0.20/0.41 ![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[51])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 ((~![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))) | (~((~((~r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))) | ![C: $i] : ((~r2_hidden(C, a_2_0_lopclset(A!0, B!1))) | r2_hidden(C, k7_lopclset(A!0))))) | (~(r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (~((~((~r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))) | ![C: $i] : ((~r2_hidden(C, a_2_0_lopclset(A!0, B!1))) | r2_hidden(C, k7_lopclset(A!0))))) | (~(r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (((~((~r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))) | ![C: $i] : ((~r2_hidden(C, a_2_0_lopclset(A!0, B!1))) | r2_hidden(C, k7_lopclset(A!0))))) | (~(r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))))))) | (r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)))),
% 0.20/0.42 inference(and_elim,[status(thm)],[22])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (~r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))),
% 0.20/0.42 inference(or_elim,[status(thm)],[59])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ((~(r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)))))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 ((~(r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)))))) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[62, 58])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))) | (~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[65, 38])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (^[A: $i, B: $i] : refl((v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B))))) <=> ![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)) <=> (~(v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B))))), ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) <=> (~(~(v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B))))))), rewrite((~(~(v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)))), ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) <=> (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B))))), trans(trans(monotonicity(rewrite((v1_filter_0(A, B) & m1_filter_0(A, B)) <=> (~((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))))), ((r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B))) <=> (r2_hidden(A, a_1_1_lopclset(B)) <=> (~((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))))))), rewrite((r2_hidden(A, a_1_1_lopclset(B)) <=> (~((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))))) <=> (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B))))), ((r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B))) <=> (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))))), rewrite((~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))) <=> (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B))))), ((r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B))) <=> (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B)))) <=> ((v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B))) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B))))))), rewrite(((v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B))) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B)))) <=> (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B)))) <=> ![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[69])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(72,plain,
% 0.20/0.42 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B))), (((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B)) & (~v3_realset2(B))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B)) & (~v3_realset2(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)))), (((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B))))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B))) & l3_lattices(B)))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B))) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)))), rewrite((r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : ((m1_filter_0(C, B) & (A = C)) & v1_filter_0(C, B))) <=> (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B)))), (((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) => (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : ((m1_filter_0(C, B) & (A = C)) & v1_filter_0(C, B)))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)) => (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B)))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)) => (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B))))), (((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) => (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : ((m1_filter_0(C, B) & (A = C)) & v1_filter_0(C, B)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(73,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) => (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : ((m1_filter_0(C, B) & (A = C)) & v1_filter_0(C, B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.42 tff(74,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) => (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : ((m1_filter_0(C, B) & (A = C)) & v1_filter_0(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fraenkel_a_1_1_lopclset')).
% 0.20/0.42 tff(75,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.42 tff(76,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.20/0.42 tff(77,plain,(
% 0.20/0.42 ![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> (v1_filter_0(A, B) & m1_filter_0(A, B))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[76])).
% 0.20/0.42 tff(78,plain,
% 0.20/0.42 (![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 68])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (((~![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 ((~![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~(((~v1_filter_0(A, B)) | (~m1_filter_0(A, B))) <=> r2_hidden(A, a_1_1_lopclset(B)))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[82, 27, 26, 25, 24, 23, 79])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : refl((v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C))))) <=> ![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) <=> (~(v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B))))), ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) <=> (~(~(v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B))))))), rewrite((~(~(v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)))), ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) <=> (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B))))), trans(trans(monotonicity(rewrite((r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B)) <=> (~((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))))), ((r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B))) <=> (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (~((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))))))), rewrite((r2_hidden(A, a_2_0_lopclset(B, C)) <=> (~((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))))) <=> (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C))))), ((r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B))) <=> (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))), rewrite((~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))) <=> (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C))))), ((r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B))) <=> (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B)))) <=> ((v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B))) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C))))))), rewrite(((v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B))) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B)))) <=> (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B)))) <=> ![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B))), (((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B)) & (~v3_realset2(B))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B)) & (~v3_realset2(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)))), (((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B))))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B))) & l3_lattices(B)))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B))) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)))), (((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))), (((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))))), rewrite((r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (((m1_filter_0(D, B) & (A = D)) & v1_filter_0(D, B)) & r2_hidden(C, D))) <=> (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B)))), ((((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (((m1_filter_0(D, B) & (A = D)) & v1_filter_0(D, B)) & r2_hidden(C, D)))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B)))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B))))), ((((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (((m1_filter_0(D, B) & (A = D)) & v1_filter_0(D, B)) & r2_hidden(C, D)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (((m1_filter_0(D, B) & (A = D)) & v1_filter_0(D, B)) & r2_hidden(C, D)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.42 tff(91,axiom,(![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (((m1_filter_0(D, B) & (A = D)) & v1_filter_0(D, B)) & r2_hidden(C, D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fraenkel_a_2_0_lopclset')).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.20/0.42 tff(94,plain,(
% 0.20/0.42 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> (r2_hidden(C, A) & m1_filter_0(A, B) & v1_filter_0(A, B))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[93])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 0.20/0.43 inference(or_elim,[status(thm)],[59])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 ((v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))))) <=> (v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 ((~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))) <=> (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 ((((~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) <=> (((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 ((~(((~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))) <=> (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[101])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 ((~(((~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))) <=> (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[102, 100])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 ((v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))))) <=> (v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 ((v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))))) <=> (v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[104, 99])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 (((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[106, 98])).
% 0.20/0.43 tff(108,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(109,plain,
% 0.20/0.43 ((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~(((~r2_hidden(C, A)) | (~m1_filter_0(A, B)) | (~v1_filter_0(A, B))) <=> r2_hidden(A, a_2_0_lopclset(B, C)))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (~(((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[109, 27, 26, 25, 24, 23, 97, 96])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[111, 63])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 ((((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))))) | (~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 ((((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (~((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[114, 110])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~r2_hidden(B!1, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 ((~((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)))) | (~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 (~((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[120, 119, 117])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 ((((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))) | ((~v1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0)) | (~m1_filter_0(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), A!0))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[122, 121, 83])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[123, 66])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------