%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU169+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:27:07 AM UTC 2025
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU169+2 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:09:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(in_type, type, (
% 0.19/0.40 in: ( $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_B_17_type, type, (
% 0.19/0.40 tptp_fun_B_17: $i)).
% 0.19/0.40 tff(tptp_fun_C_13_type, type, (
% 0.19/0.40 tptp_fun_C_13: ( $i * $i ) > $i)).
% 0.19/0.40 tff(powerset_type, type, (
% 0.19/0.40 powerset: $i > $i)).
% 0.19/0.40 tff(tptp_fun_A_18_type, type, (
% 0.19/0.40 tptp_fun_A_18: $i)).
% 0.19/0.40 tff(tptp_fun_D_14_type, type, (
% 0.19/0.40 tptp_fun_D_14: ( $i * $i ) > $i)).
% 0.19/0.40 tff(union_type, type, (
% 0.19/0.40 union: $i > $i)).
% 0.19/0.40 tff(tptp_fun_C_19_type, type, (
% 0.19/0.40 tptp_fun_C_19: $i)).
% 0.19/0.40 tff(tptp_fun_D_12_type, type, (
% 0.19/0.40 tptp_fun_D_12: ( $i * $i ) > $i)).
% 0.19/0.40 tff(element_type, type, (
% 0.19/0.40 element: ( $i * $i ) > $o)).
% 0.19/0.40 tff(empty_type, type, (
% 0.19/0.40 empty: $i > $o)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (^[A: $i, B: $i] : refl((~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))) <=> (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))) <=> ![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (^[A: $i, B: $i] : rewrite(((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (^[A: $i, B: $i] : rewrite((((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B)))) <=> ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (![A: $i, B: $i] : (((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.40 tff(8,axiom,(![A: $i, B: $i] : (((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_subset_1')).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.40 tff(11,plain,(
% 0.19/0.40 ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 ((~![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))) | (~((~(empty(powerset(A!18)) | (element(B!17, powerset(A!18)) <=> in(B!17, powerset(A!18))))) | (~((~empty(powerset(A!18))) | (element(B!17, powerset(A!18)) <=> empty(B!17))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (~((~(empty(powerset(A!18)) | (element(B!17, powerset(A!18)) <=> in(B!17, powerset(A!18))))) | (~((~empty(powerset(A!18))) | (element(B!17, powerset(A!18)) <=> empty(B!17)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (((~(empty(powerset(A!18)) | (element(B!17, powerset(A!18)) <=> in(B!17, powerset(A!18))))) | (~((~empty(powerset(A!18))) | (element(B!17, powerset(A!18)) <=> empty(B!17))))) | (empty(powerset(A!18)) | (element(B!17, powerset(A!18)) <=> in(B!17, powerset(A!18))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (empty(powerset(A!18)) | (element(B!17, powerset(A!18)) <=> in(B!17, powerset(A!18)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (^[A: $i] : refl((~empty(powerset(A))) <=> (~empty(powerset(A))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (![A: $i] : (~empty(powerset(A))) <=> ![A: $i] : (~empty(powerset(A)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![A: $i] : (~empty(powerset(A))) <=> ![A: $i] : (~empty(powerset(A)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(21,axiom,(![A: $i] : (~empty(powerset(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_subset_1')).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (![A: $i] : (~empty(powerset(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.41 tff(23,plain,(
% 0.19/0.41 ![A: $i] : (~empty(powerset(A)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[22])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (![A: $i] : (~empty(powerset(A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 ((~![A: $i] : (~empty(powerset(A)))) | (~empty(powerset(A!18)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (~empty(powerset(A!18))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 ((~(empty(powerset(A!18)) | (element(B!17, powerset(A!18)) <=> in(B!17, powerset(A!18))))) | empty(powerset(A!18)) | (element(B!17, powerset(A!18)) <=> in(B!17, powerset(A!18)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 (element(B!17, powerset(A!18)) <=> in(B!17, powerset(A!18))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[27, 26, 17])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))) <=> (~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 ((~![A: $i, B: $i] : (element(B, powerset(A)) => ![C: $i] : (in(C, B) => in(C, A)))) <=> (~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(31,axiom,(~![A: $i, B: $i] : (element(B, powerset(A)) => ![C: $i] : (in(C, B) => in(C, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l3_subset_1')).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 29])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (element(B!17, powerset(A!18))),
% 0.19/0.41 inference(and_elim,[status(thm)],[35])).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 ((~(element(B!17, powerset(A!18)) <=> in(B!17, powerset(A!18)))) | (~element(B!17, powerset(A!18))) | in(B!17, powerset(A!18))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 ((~(element(B!17, powerset(A!18)) <=> in(B!17, powerset(A!18)))) | in(B!17, powerset(A!18))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (in(B!17, powerset(A!18))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[38, 28])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (~((~in(C!19, B!17)) | in(C!19, A!18))),
% 0.19/0.41 inference(and_elim,[status(thm)],[35])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (~in(C!19, A!18)),
% 0.19/0.41 inference(or_elim,[status(thm)],[40])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (in(C!19, B!17)),
% 0.19/0.41 inference(or_elim,[status(thm)],[40])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))) | (~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[43, 42, 41, 39])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18)))) | ((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (![A: $i] : (union(powerset(A)) = A) <=> ![A: $i] : (union(powerset(A)) = A)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![A: $i] : (union(powerset(A)) = A) <=> ![A: $i] : (union(powerset(A)) = A)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(49,axiom,(![A: $i] : (union(powerset(A)) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t99_zfmisc_1')).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (![A: $i] : (union(powerset(A)) = A)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.41 tff(51,plain,(
% 0.19/0.41 ![A: $i] : (union(powerset(A)) = A)),
% 0.19/0.41 inference(skolemize,[status(sab)],[50])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![A: $i] : (union(powerset(A)) = A)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 ((~![A: $i] : (union(powerset(A)) = A)) | (union(powerset(A!18)) = A!18)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (union(powerset(A!18)) = A!18),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (A!18 = union(powerset(A!18))),
% 0.19/0.41 inference(symmetry,[status(thm)],[54])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 ((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18)))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[56, 55, 46])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~((A!18 = union(powerset(A!18))) | (~((~(in(tptp_fun_C_13(A!18, powerset(A!18)), A!18) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), tptp_fun_D_14(A!18, powerset(A!18)))) | (~in(tptp_fun_D_14(A!18, powerset(A!18)), powerset(A!18))))))) | (~((~in(B!17, powerset(A!18))) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), A!18)) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), B!17))))))))) | ((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 ((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~((A!18 = union(powerset(A!18))) | (~((~(in(tptp_fun_C_13(A!18, powerset(A!18)), A!18) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), tptp_fun_D_14(A!18, powerset(A!18)))) | (~in(tptp_fun_D_14(A!18, powerset(A!18)), powerset(A!18))))))) | (~((~in(B!17, powerset(A!18))) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), A!18)) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), B!17))))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (^[A: $i, B: $i, D_31: $i, C: $i, D: $i] : rewrite((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~((~in(C, D)) | (~in(D, A)) | in(C, B))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | (~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31)))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) <=> ![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~((~in(C, D)) | (~in(D, A)) | in(C, B))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | (~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (^[A: $i, B: $i, D_31: $i, C: $i, D: $i] : refl((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) <=> ![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31)))))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![A: $i, B: $i] : ![D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) <=> ![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31)))))))))))),
% 0.19/0.41 inference(pull_quant,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant((in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))) <=> ![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))), ((~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))) <=> (~![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))))), pull_quant((~![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))) <=> ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))), ((~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))) <=> ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), pull_quant(((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> (~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant((~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i] : ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant(![C: $i] : ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) <=> ((~(B = union(A))) | ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), pull_quant(((~(B = union(A))) | ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))) <=> ![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) <=> ![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), ((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) <=> (~![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))))), pull_quant((~![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) <=> ?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), ((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) <=> ?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))) <=> ![D: $i] : ((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))), ((~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))) <=> (~![D: $i] : ((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))), pull_quant((~![D: $i] : ((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))), ((~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))), (((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))) <=> ((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))), pull_quant(((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))), (((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))), ((~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))) <=> (~?[D: $i] : ((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))), pull_quant((~?[D: $i] : ((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))), ((~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))) <=> ((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))), pull_quant(((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))) <=> (~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))))), pull_quant((~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))) <=> (?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))))), pull_quant((?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))) <=> ?[D_31: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))) <=> ?[D_31: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))))) <=> (~?[D_31: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))))), pull_quant((~?[D_31: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) <=> ![D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))))) <=> ![D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31)))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))))) <=> ![A: $i, B: $i] : ![D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31)))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))))) <=> ![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31)))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[66, 64])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))))) <=> ![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31)))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[67, 63])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (^[A: $i, B: $i] : rewrite((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))))) <=> ![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31)))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[70, 68])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_12(C, A)) & in(tptp_fun_D_12(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) <=> ((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A)) & in(tptp_fun_D_14(B, A), A)) <=> (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A))))), ((in(tptp_fun_C_13(B, A), B) | (in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A)) & in(tptp_fun_D_14(B, A), A))) <=> (in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A))))))), rewrite((in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A))))) <=> (in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))), ((in(tptp_fun_C_13(B, A), B) | (in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A)) & in(tptp_fun_D_14(B, A), A))) <=> (in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A))))))), rewrite(((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_13(B, A), D) & in(D, A)))) <=> ((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))), (((in(tptp_fun_C_13(B, A), B) | (in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A)) & in(tptp_fun_D_14(B, A), A))) & ((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_13(B, A), D) & in(D, A))))) <=> ((in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A))))) & ((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))), rewrite(((in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A))))) & ((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))) <=> (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))), (((in(tptp_fun_C_13(B, A), B) | (in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A)) & in(tptp_fun_D_14(B, A), A))) & ((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_13(B, A), D) & in(D, A))))) <=> (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_13(B, A), B) | (in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A)) & in(tptp_fun_D_14(B, A), A))) & ((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_13(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))), rewrite(((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_13(B, A), B) | (in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A)) & in(tptp_fun_D_14(B, A), A))) & ((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_13(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_12(C, A)) & in(tptp_fun_D_12(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_13(B, A), B) | (in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A)) & in(tptp_fun_D_14(B, A), A))) & ((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_13(B, A), D) & in(D, A))))))) <=> (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))))), rewrite((((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_12(C, A)) & in(tptp_fun_D_12(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_13(B, A), B) | (in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A)) & in(tptp_fun_D_14(B, A), A))) & ((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_13(B, A), D) & in(D, A))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_12(C, A)) & in(tptp_fun_D_12(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_13(B, A), B) | (in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A)) & in(tptp_fun_D_14(B, A), A))) & ((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_13(B, A), D) & in(D, A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A)))) <=> ![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(75,axiom,(![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_tarski')).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.43 tff(77,plain,(
% 0.19/0.43 ![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_12(C, A)) & in(tptp_fun_D_12(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_13(B, A), B) | (in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A)) & in(tptp_fun_D_14(B, A), A))) & ((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_13(B, A), D) & in(D, A)))))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[76])).
% 0.19/0.43 tff(78,plain,
% 0.19/0.43 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_13(B, A), D)))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 (![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | ((~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31)))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 (![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~((~in(C, D)) | (~in(D, A)) | in(C, B))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | (~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[79, 61])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 (((~![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~((~in(C, D)) | (~in(D, A)) | in(C, B))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | (~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) | (~((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~((A!18 = union(powerset(A!18))) | (~((~(in(tptp_fun_C_13(A!18, powerset(A!18)), A!18) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), tptp_fun_D_14(A!18, powerset(A!18)))) | (~in(tptp_fun_D_14(A!18, powerset(A!18)), powerset(A!18))))))) | (~((~in(B!17, powerset(A!18))) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), A!18)) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), B!17))))))))))) <=> ((~![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~((~in(C, D)) | (~in(D, A)) | in(C, B))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | (~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) | (~((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~((A!18 = union(powerset(A!18))) | (~((~(in(tptp_fun_C_13(A!18, powerset(A!18)), A!18) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), tptp_fun_D_14(A!18, powerset(A!18)))) | (~in(tptp_fun_D_14(A!18, powerset(A!18)), powerset(A!18))))))) | (~((~in(B!17, powerset(A!18))) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), A!18)) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), B!17)))))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 ((~((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~((A!18 = union(powerset(A!18))) | (~((~(in(tptp_fun_C_13(A!18, powerset(A!18)), A!18) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), tptp_fun_D_14(A!18, powerset(A!18)))) | (~in(tptp_fun_D_14(A!18, powerset(A!18)), powerset(A!18))))))) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), A!18)) | (~in(B!17, powerset(A!18))) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), B!17)))))))))) <=> (~((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~((A!18 = union(powerset(A!18))) | (~((~(in(tptp_fun_C_13(A!18, powerset(A!18)), A!18) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), tptp_fun_D_14(A!18, powerset(A!18)))) | (~in(tptp_fun_D_14(A!18, powerset(A!18)), powerset(A!18))))))) | (~((~in(B!17, powerset(A!18))) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), A!18)) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), B!17))))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (((~![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~((~in(C, D)) | (~in(D, A)) | in(C, B))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | (~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) | (~((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~((A!18 = union(powerset(A!18))) | (~((~(in(tptp_fun_C_13(A!18, powerset(A!18)), A!18) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), tptp_fun_D_14(A!18, powerset(A!18)))) | (~in(tptp_fun_D_14(A!18, powerset(A!18)), powerset(A!18))))))) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), A!18)) | (~in(B!17, powerset(A!18))) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), B!17))))))))))) <=> ((~![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~((~in(C, D)) | (~in(D, A)) | in(C, B))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | (~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) | (~((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~((A!18 = union(powerset(A!18))) | (~((~(in(tptp_fun_C_13(A!18, powerset(A!18)), A!18) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), tptp_fun_D_14(A!18, powerset(A!18)))) | (~in(tptp_fun_D_14(A!18, powerset(A!18)), powerset(A!18))))))) | (~((~in(B!17, powerset(A!18))) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), A!18)) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), B!17)))))))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.44 tff(84,plain,
% 0.19/0.44 (((~![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~((~in(C, D)) | (~in(D, A)) | in(C, B))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | (~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) | (~((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~((A!18 = union(powerset(A!18))) | (~((~(in(tptp_fun_C_13(A!18, powerset(A!18)), A!18) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), tptp_fun_D_14(A!18, powerset(A!18)))) | (~in(tptp_fun_D_14(A!18, powerset(A!18)), powerset(A!18))))))) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), A!18)) | (~in(B!17, powerset(A!18))) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), B!17))))))))))) <=> ((~![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~((~in(C, D)) | (~in(D, A)) | in(C, B))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | (~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) | (~((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~((A!18 = union(powerset(A!18))) | (~((~(in(tptp_fun_C_13(A!18, powerset(A!18)), A!18) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), tptp_fun_D_14(A!18, powerset(A!18)))) | (~in(tptp_fun_D_14(A!18, powerset(A!18)), powerset(A!18))))))) | (~((~in(B!17, powerset(A!18))) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), A!18)) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), B!17)))))))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[83, 81])).
% 0.19/0.44 tff(85,plain,
% 0.19/0.44 ((~![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~((~in(C, D)) | (~in(D, A)) | in(C, B))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | (~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) | (~((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~((A!18 = union(powerset(A!18))) | (~((~(in(tptp_fun_C_13(A!18, powerset(A!18)), A!18) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), tptp_fun_D_14(A!18, powerset(A!18)))) | (~in(tptp_fun_D_14(A!18, powerset(A!18)), powerset(A!18))))))) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), A!18)) | (~in(B!17, powerset(A!18))) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), B!17))))))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(86,plain,
% 0.19/0.44 ((~![A: $i, B: $i, D_31: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_12(C, A))) | (~in(tptp_fun_D_12(C, A), A)))))) | (~((~in(C, D)) | (~in(D, A)) | in(C, B))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_13(B, A), B) | (~((~in(tptp_fun_C_13(B, A), tptp_fun_D_14(B, A))) | (~in(tptp_fun_D_14(B, A), A)))))) | (~((~in(tptp_fun_C_13(B, A), B)) | (~in(D_31, A)) | (~in(tptp_fun_C_13(B, A), D_31))))))))))) | (~((~((~(A!18 = union(powerset(A!18)))) | (~((~((~in(C!19, A!18)) | (~((~in(C!19, tptp_fun_D_12(C!19, powerset(A!18)))) | (~in(tptp_fun_D_12(C!19, powerset(A!18)), powerset(A!18))))))) | (~((~in(C!19, B!17)) | (~in(B!17, powerset(A!18))) | in(C!19, A!18))))))) | (~((A!18 = union(powerset(A!18))) | (~((~(in(tptp_fun_C_13(A!18, powerset(A!18)), A!18) | (~((~in(tptp_fun_C_13(A!18, powerset(A!18)), tptp_fun_D_14(A!18, powerset(A!18)))) | (~in(tptp_fun_D_14(A!18, powerset(A!18)), powerset(A!18))))))) | (~((~in(B!17, powerset(A!18))) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), A!18)) | (~in(tptp_fun_C_13(A!18, powerset(A!18)), B!17))))))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[86, 80, 59])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------