%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT300+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:14:14 AM UTC 2025
% Result : Theorem 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT300+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 20:07:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.43 % SZS status Theorem
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(r2_hidden_type, type, (
% 0.20/0.43 r2_hidden: ( $i * $i ) > $o)).
% 0.20/0.43 tff(tptp_fun_B_1_type, type, (
% 0.20/0.43 tptp_fun_B_1: $i)).
% 0.20/0.43 tff(tptp_fun_C_6_type, type, (
% 0.20/0.43 tptp_fun_C_6: ( $i * $i ) > $i)).
% 0.20/0.43 tff(tptp_fun_A_0_type, type, (
% 0.20/0.43 tptp_fun_A_0: $i)).
% 0.20/0.43 tff(m1_subset_1_type, type, (
% 0.20/0.43 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.43 tff(m1_struct_0_type, type, (
% 0.20/0.43 m1_struct_0: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(k1_zfmisc_1_type, type, (
% 0.20/0.43 k1_zfmisc_1: $i > $i)).
% 0.20/0.43 tff(u1_struct_0_type, type, (
% 0.20/0.43 u1_struct_0: $i > $i)).
% 0.20/0.43 tff(m2_lattice4_type, type, (
% 0.20/0.43 m2_lattice4: ( $i * $i ) > $o)).
% 0.20/0.43 tff(v1_xboole_0_type, type, (
% 0.20/0.43 v1_xboole_0: $i > $o)).
% 0.20/0.43 tff(m2_filter_2_type, type, (
% 0.20/0.43 m2_filter_2: ( $i * $i ) > $o)).
% 0.20/0.43 tff(v10_lattices_type, type, (
% 0.20/0.43 v10_lattices: $i > $o)).
% 0.20/0.43 tff(l3_lattices_type, type, (
% 0.20/0.43 l3_lattices: $i > $o)).
% 0.20/0.43 tff(v3_struct_0_type, type, (
% 0.20/0.43 v3_struct_0: $i > $o)).
% 0.20/0.43 tff(l1_struct_0_type, type, (
% 0.20/0.43 l1_struct_0: $i > $o)).
% 0.20/0.43 tff(l2_lattices_type, type, (
% 0.20/0.43 l2_lattices: $i > $o)).
% 0.20/0.43 tff(l1_lattices_type, type, (
% 0.20/0.43 l1_lattices: $i > $o)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (^[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(((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(7,plain,
% 0.20/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.44 tff(8,plain,
% 0.20/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(9,plain,
% 0.20/0.44 (^[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] : rewrite((m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(10,plain,
% 0.20/0.44 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.44 tff(11,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 0.20/0.44 tff(12,plain,
% 0.20/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.44 tff(13,plain,
% 0.20/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.44 tff(14,plain,(
% 0.20/0.44 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[13])).
% 0.20/0.44 tff(15,plain,
% 0.20/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.44 tff(16,plain,
% 0.20/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.44 tff(17,plain,
% 0.20/0.44 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m2_filter_2(B!1, A!0) & ![C: $i] : (~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m2_filter_2(B!1, A!0) & ![C: $i] : (~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(18,plain,
% 0.20/0.44 ((m2_filter_2(B!1, A!0) & ![C: $i] : (~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1)))) <=> (m2_filter_2(B!1, A!0) & ![C: $i] : (~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(19,plain,
% 0.20/0.44 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m2_filter_2(B!1, A!0) & ![C: $i] : (~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m2_filter_2(B!1, A!0) & ![C: $i] : (~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.44 tff(20,plain,
% 0.20/0.44 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m2_filter_2(B!1, A!0) & ![C: $i] : (~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m2_filter_2(B!1, A!0) & ![C: $i] : (~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.44 tff(21,plain,
% 0.20/0.44 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ?[C: $i] : (m1_subset_1(C, u1_struct_0(A)) & r2_hidden(C, B))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ?[C: $i] : (m1_subset_1(C, u1_struct_0(A)) & r2_hidden(C, B)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(22,plain,
% 0.20/0.44 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ?[C: $i] : (m1_subset_1(C, u1_struct_0(A)) & r2_hidden(C, B))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ?[C: $i] : (m1_subset_1(C, u1_struct_0(A)) & r2_hidden(C, B)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(23,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ?[C: $i] : (m1_subset_1(C, u1_struct_0(A)) & r2_hidden(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_filter_2')).
% 0.20/0.44 tff(24,plain,
% 0.20/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ?[C: $i] : (m1_subset_1(C, u1_struct_0(A)) & r2_hidden(C, B))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.44 tff(25,plain,
% 0.20/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ?[C: $i] : (m1_subset_1(C, u1_struct_0(A)) & r2_hidden(C, B))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.44 tff(26,plain,
% 0.20/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ?[C: $i] : (m1_subset_1(C, u1_struct_0(A)) & r2_hidden(C, B))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.44 tff(27,plain,
% 0.20/0.44 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ?[C: $i] : (m1_subset_1(C, u1_struct_0(A)) & r2_hidden(C, B))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.44 tff(28,plain,
% 0.20/0.44 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m2_filter_2(B!1, A!0) & ![C: $i] : (~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.44 tff(29,plain,
% 0.20/0.44 (l3_lattices(A!0)),
% 0.20/0.44 inference(and_elim,[status(thm)],[28])).
% 0.20/0.44 tff(30,plain,
% 0.20/0.44 (v10_lattices(A!0)),
% 0.20/0.44 inference(and_elim,[status(thm)],[28])).
% 0.20/0.44 tff(31,plain,
% 0.20/0.44 (~v3_struct_0(A!0)),
% 0.20/0.44 inference(and_elim,[status(thm)],[28])).
% 0.20/0.44 tff(32,plain,
% 0.20/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(33,plain,
% 0.20/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(34,plain,
% 0.20/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.44 tff(35,plain,
% 0.20/0.44 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[34, 31, 30, 29, 16])).
% 0.20/0.44 tff(36,plain,
% 0.20/0.44 (m2_filter_2(B!1, A!0)),
% 0.20/0.44 inference(and_elim,[status(thm)],[28])).
% 0.20/0.44 tff(37,plain,
% 0.20/0.44 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(38,plain,
% 0.20/0.44 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(39,plain,
% 0.20/0.44 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.44 tff(40,plain,
% 0.20/0.44 (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[39, 36, 35])).
% 0.20/0.44 tff(41,plain,
% 0.20/0.44 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | m2_lattice4(B!1, A!0)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(42,plain,
% 0.20/0.44 (m2_lattice4(B!1, A!0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.20/0.44 tff(43,plain,
% 0.20/0.44 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(44,plain,
% 0.20/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.44 tff(45,plain,
% 0.20/0.44 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(46,plain,
% 0.20/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.44 tff(47,plain,
% 0.20/0.44 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(48,plain,
% 0.20/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.44 tff(49,plain,
% 0.20/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[48, 46])).
% 0.20/0.44 tff(50,plain,
% 0.20/0.44 (^[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] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(51,plain,
% 0.20/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.44 tff(52,plain,
% 0.20/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(53,plain,
% 0.20/0.44 (^[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] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(54,plain,
% 0.20/0.44 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.44 tff(55,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 0.20/0.44 tff(56,plain,
% 0.20/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.44 tff(57,plain,
% 0.20/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.44 tff(58,plain,(
% 0.20/0.44 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[57])).
% 0.20/0.44 tff(59,plain,
% 0.20/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.44 tff(60,plain,
% 0.20/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[59, 49])).
% 0.20/0.44 tff(61,plain,
% 0.20/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[60, 44])).
% 0.20/0.44 tff(62,plain,
% 0.20/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[64, 31, 30, 29, 61])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[68, 65, 42])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | (~v1_xboole_0(B!1))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (~v1_xboole_0(B!1)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[70, 40])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.44 tff(79,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.44 tff(82,plain,(
% 0.20/0.44 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[81])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(87,plain,
% 0.20/0.45 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.45 tff(88,plain,
% 0.20/0.45 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[87, 29, 84])).
% 0.20/0.45 tff(89,plain,
% 0.20/0.45 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(90,plain,
% 0.20/0.45 (l2_lattices(A!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.45 tff(91,plain,
% 0.20/0.45 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(92,plain,
% 0.20/0.45 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.45 tff(93,plain,
% 0.20/0.45 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(94,plain,
% 0.20/0.45 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.45 tff(96,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 0.20/0.45 tff(97,plain,
% 0.20/0.45 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.20/0.45 tff(99,plain,(
% 0.20/0.45 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[98])).
% 0.20/0.45 tff(100,plain,
% 0.20/0.45 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 (l1_struct_0(A!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[103, 100, 90])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 (^[A: $i, B: $i] : rewrite((v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 (^[A: $i, B: $i] : rewrite((v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(110,plain,
% 0.20/0.45 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[110, 108])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B))) <=> ((v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B))))), rewrite(((v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B))) <=> (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B))) <=> (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B))) <=> (((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B))))), rewrite((((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B))) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))), ((((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B))) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[115])).
% 0.20/0.45 tff(117,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m1_struct_0')).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.20/0.45 tff(120,plain,(
% 0.20/0.45 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[119])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[122, 106])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (m1_struct_0(C, A!0, B!1) <=> m1_subset_1(C, B!1)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))) | v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (m1_struct_0(C, A!0, B!1) <=> m1_subset_1(C, B!1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (m1_struct_0(C, A!0, B!1) <=> m1_subset_1(C, B!1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (m1_struct_0(C, A, B) <=> m1_subset_1(C, B)))) | v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (m1_struct_0(C, A!0, B!1) <=> m1_subset_1(C, B!1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 (![C: $i] : (m1_struct_0(C, A!0, B!1) <=> m1_subset_1(C, B!1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[126, 31, 123, 104, 71, 69])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 ((~![C: $i] : (m1_struct_0(C, A!0, B!1) <=> m1_subset_1(C, B!1))) | (m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1) <=> m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1) <=> m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.20/0.45 tff(130,plain,
% 0.20/0.45 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[130])).
% 0.20/0.45 tff(132,plain,
% 0.20/0.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_struct_0(tptp_fun_C_6(B, A), A, B)) <=> ((v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_struct_0(tptp_fun_C_6(B, A), A, B)))), rewrite(((v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_struct_0(tptp_fun_C_6(B, A), A, B)) <=> (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_struct_0(tptp_fun_C_6(B, A), A, B)) <=> (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_struct_0(tptp_fun_C_6(B, A), A, B)) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[132])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ?[C: $i] : m1_struct_0(C, A, B)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ?[C: $i] : m1_struct_0(C, A, B))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ?[C: $i] : m1_struct_0(C, A, B)) <=> (((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ?[C: $i] : m1_struct_0(C, A, B)))), rewrite((((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ?[C: $i] : m1_struct_0(C, A, B)) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ?[C: $i] : m1_struct_0(C, A, B))), ((((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ?[C: $i] : m1_struct_0(C, A, B)) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ?[C: $i] : m1_struct_0(C, A, B))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ?[C: $i] : m1_struct_0(C, A, B)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ?[C: $i] : m1_struct_0(C, A, B))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.45 tff(137,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ?[C: $i] : m1_struct_0(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','existence_m1_struct_0')).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ?[C: $i] : m1_struct_0(C, A, B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ?[C: $i] : m1_struct_0(C, A, B))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.20/0.45 tff(140,plain,(
% 0.20/0.45 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_struct_0(tptp_fun_C_6(B, A), A, B))),
% 0.20/0.45 inference(skolemize,[status(sab)],[139])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 ((v1_xboole_0(B!1) | v3_struct_0(A!0) | m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1) | (~l1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1) | (~l1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[144])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1) | (~l1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1))),
% 0.20/0.45 inference(transitivity,[status(thm)],[145, 143])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1) | (~l1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m1_struct_0(tptp_fun_C_6(B, A), A, B) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[148, 31, 142, 104, 71, 69])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 ((~(m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1) <=> m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1))) | (~m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1)) | m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 ((~(m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1) <=> m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1))) | m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[151, 129])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B))) <=> (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 (![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[153])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 (![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(156,plain,
% 0.20/0.46 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.46 tff(158,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 (![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 (![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.20/0.46 tff(161,plain,(
% 0.20/0.46 ![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[160])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 (![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 (((~![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(B!1) | (~m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)) | r2_hidden(tptp_fun_C_6(B!1, A!0), B!1))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))) | v1_xboole_0(B!1) | (~m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)) | r2_hidden(tptp_fun_C_6(B!1, A!0), B!1))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 ((v1_xboole_0(B!1) | r2_hidden(tptp_fun_C_6(B!1, A!0), B!1) | (~m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1))) <=> (v1_xboole_0(B!1) | (~m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)) | r2_hidden(tptp_fun_C_6(B!1, A!0), B!1))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 (((~![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(B!1) | r2_hidden(tptp_fun_C_6(B!1, A!0), B!1) | (~m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(B!1) | (~m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)) | r2_hidden(tptp_fun_C_6(B!1, A!0), B!1)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[164])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 (((~![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(B!1) | r2_hidden(tptp_fun_C_6(B!1, A!0), B!1) | (~m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))) | v1_xboole_0(B!1) | (~m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)) | r2_hidden(tptp_fun_C_6(B!1, A!0), B!1))),
% 0.20/0.46 inference(transitivity,[status(thm)],[165, 163])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(B!1) | r2_hidden(tptp_fun_C_6(B!1, A!0), B!1) | (~m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (v1_xboole_0(B) | r2_hidden(A, B) | (~m1_subset_1(A, B)))) | v1_xboole_0(B!1) | (~m1_subset_1(tptp_fun_C_6(B!1, A!0), B!1)) | r2_hidden(tptp_fun_C_6(B!1, A!0), B!1)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 (r2_hidden(tptp_fun_C_6(B!1, A!0), B!1)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[168, 162, 71, 152])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 (^[A: $i, B: $i] : rewrite((v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(171,plain,
% 0.20/0.46 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[172])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (^[A: $i, B: $i] : rewrite((v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[174])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[175, 173])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A)))) <=> ((v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A)))))), rewrite(((v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A)))) <=> (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A)))) <=> (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A)))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[177])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), (((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), quant_intro(proof_bind(^[C: $i] : rewrite((m1_struct_0(C, A, B) => m1_subset_1(C, u1_struct_0(A))) <=> ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))), (![C: $i] : (m1_struct_0(C, A, B) => m1_subset_1(C, u1_struct_0(A))) <=> ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m1_struct_0(C, A, B) => m1_subset_1(C, u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m1_struct_0(C, A, B) => m1_subset_1(C, u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m1_struct_0(C, A, B) => m1_subset_1(C, u1_struct_0(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[180])).
% 0.20/0.46 tff(182,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & l1_struct_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m1_struct_0(C, A, B) => m1_subset_1(C, u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_struct_0')).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.20/0.46 tff(185,plain,(
% 0.20/0.46 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l1_struct_0(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[184])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[186, 176])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[187, 171])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_struct_0(C, A!0, B!1)) | m1_subset_1(C, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))) | v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_struct_0(C, A!0, B!1)) | m1_subset_1(C, u1_struct_0(A!0))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_struct_0(C, A!0, B!1)) | m1_subset_1(C, u1_struct_0(A!0))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~l1_struct_0(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m1_struct_0(C, A, B)) | m1_subset_1(C, u1_struct_0(A))))) | v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_struct_0(C, A!0, B!1)) | m1_subset_1(C, u1_struct_0(A!0)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 (![C: $i] : ((~m1_struct_0(C, A!0, B!1)) | m1_subset_1(C, u1_struct_0(A!0)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[191, 31, 188, 104, 71, 69])).
% 0.20/0.46 tff(193,plain,
% 0.20/0.46 (((~![C: $i] : ((~m1_struct_0(C, A!0, B!1)) | m1_subset_1(C, u1_struct_0(A!0)))) | ((~m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1)) | m1_subset_1(tptp_fun_C_6(B!1, A!0), u1_struct_0(A!0)))) <=> ((~![C: $i] : ((~m1_struct_0(C, A!0, B!1)) | m1_subset_1(C, u1_struct_0(A!0)))) | (~m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1)) | m1_subset_1(tptp_fun_C_6(B!1, A!0), u1_struct_0(A!0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(194,plain,
% 0.20/0.46 ((~![C: $i] : ((~m1_struct_0(C, A!0, B!1)) | m1_subset_1(C, u1_struct_0(A!0)))) | ((~m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1)) | m1_subset_1(tptp_fun_C_6(B!1, A!0), u1_struct_0(A!0)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(195,plain,
% 0.20/0.46 ((~![C: $i] : ((~m1_struct_0(C, A!0, B!1)) | m1_subset_1(C, u1_struct_0(A!0)))) | (~m1_struct_0(tptp_fun_C_6(B!1, A!0), A!0, B!1)) | m1_subset_1(tptp_fun_C_6(B!1, A!0), u1_struct_0(A!0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.20/0.46 tff(196,plain,
% 0.20/0.46 (m1_subset_1(tptp_fun_C_6(B!1, A!0), u1_struct_0(A!0))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[195, 192, 149])).
% 0.20/0.46 tff(197,plain,
% 0.20/0.46 (^[C: $i] : refl(((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1))) <=> ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(198,plain,
% 0.20/0.46 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[197])).
% 0.20/0.46 tff(199,plain,
% 0.20/0.46 (^[C: $i] : trans(monotonicity(rewrite((m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1)) <=> (~((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1))))), ((~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1))) <=> (~(~((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1))))))), rewrite((~(~((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1))))) <=> ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)))), ((~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1))) <=> ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(200,plain,
% 0.20/0.46 (![C: $i] : (~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[199])).
% 0.20/0.46 tff(201,plain,
% 0.20/0.46 (![C: $i] : (~(m1_subset_1(C, u1_struct_0(A!0)) & r2_hidden(C, B!1)))),
% 0.20/0.46 inference(and_elim,[status(thm)],[28])).
% 0.20/0.46 tff(202,plain,
% 0.20/0.46 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.20/0.46 tff(203,plain,
% 0.20/0.46 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.20/0.46 tff(204,plain,
% 0.20/0.46 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)))) | ((~m1_subset_1(tptp_fun_C_6(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_6(B!1, A!0), B!1)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)))) | (~m1_subset_1(tptp_fun_C_6(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_6(B!1, A!0), B!1)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(205,plain,
% 0.20/0.46 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)))) | ((~m1_subset_1(tptp_fun_C_6(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_6(B!1, A!0), B!1)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(206,plain,
% 0.20/0.46 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)))) | (~m1_subset_1(tptp_fun_C_6(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_6(B!1, A!0), B!1))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.46 tff(207,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[206, 203, 196, 169])).
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------