%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM396+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:20:53 AM UTC 2025
% Result : Theorem 0.18s 0.46s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM396+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 01:02:24 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.18/0.46 % SZS status Theorem
% 0.18/0.46 % SZS output start Proof
% 0.18/0.46 tff(tptp_fun_A_18_type, type, (
% 0.18/0.46 tptp_fun_A_18: $i)).
% 0.18/0.46 tff(tptp_fun_C_3_type, type, (
% 0.18/0.46 tptp_fun_C_3: $i > $i)).
% 0.18/0.46 tff(set_union2_type, type, (
% 0.18/0.46 set_union2: ( $i * $i ) > $i)).
% 0.18/0.46 tff(singleton_type, type, (
% 0.18/0.46 singleton: $i > $i)).
% 0.18/0.46 tff(in_type, type, (
% 0.18/0.46 in: ( $i * $i ) > $o)).
% 0.18/0.46 tff(tptp_fun_B_4_type, type, (
% 0.18/0.46 tptp_fun_B_4: $i > $i)).
% 0.18/0.46 tff(epsilon_connected_type, type, (
% 0.18/0.46 epsilon_connected: $i > $o)).
% 0.18/0.46 tff(succ_type, type, (
% 0.18/0.46 succ: $i > $i)).
% 0.18/0.46 tff(epsilon_transitive_type, type, (
% 0.18/0.46 epsilon_transitive: $i > $o)).
% 0.18/0.46 tff(subset_type, type, (
% 0.18/0.46 subset: ( $i * $i ) > $o)).
% 0.18/0.46 tff(tptp_fun_B_1_type, type, (
% 0.18/0.46 tptp_fun_B_1: $i > $i)).
% 0.18/0.46 tff(tptp_fun_C_0_type, type, (
% 0.18/0.46 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.18/0.46 tff(tptp_fun_D_2_type, type, (
% 0.18/0.46 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.18/0.46 tff(ordinal_type, type, (
% 0.18/0.46 ordinal: $i > $o)).
% 0.18/0.46 tff(1,plain,
% 0.18/0.46 ((tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18))))),
% 0.18/0.46 inference(commutativity,[status(thm)],[])).
% 0.18/0.46 tff(2,plain,
% 0.18/0.46 (^[A: $i] : refl((succ(A) = set_union2(A, singleton(A))) <=> (succ(A) = set_union2(A, singleton(A))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(3,plain,
% 0.18/0.46 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.46 tff(4,plain,
% 0.18/0.46 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(5,axiom,(![A: $i] : (succ(A) = set_union2(A, singleton(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_ordinal1')).
% 0.18/0.46 tff(6,plain,
% 0.18/0.46 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.46 tff(7,plain,(
% 0.18/0.46 ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[6])).
% 0.18/0.46 tff(8,plain,
% 0.18/0.46 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.46 tff(9,plain,
% 0.18/0.46 ((~![A: $i] : (succ(A) = set_union2(A, singleton(A)))) | (succ(A!18) = set_union2(A!18, singleton(A!18)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(10,plain,
% 0.18/0.46 (succ(A!18) = set_union2(A!18, singleton(A!18))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.18/0.46 tff(11,plain,
% 0.18/0.46 (set_union2(A!18, singleton(A!18)) = succ(A!18)),
% 0.18/0.46 inference(symmetry,[status(thm)],[10])).
% 0.18/0.46 tff(12,plain,
% 0.18/0.46 (epsilon_transitive(set_union2(A!18, singleton(A!18))) <=> epsilon_transitive(succ(A!18))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[11])).
% 0.18/0.46 tff(13,plain,
% 0.18/0.46 (epsilon_transitive(succ(A!18)) <=> epsilon_transitive(set_union2(A!18, singleton(A!18)))),
% 0.18/0.46 inference(symmetry,[status(thm)],[12])).
% 0.18/0.46 tff(14,plain,
% 0.18/0.46 ((~epsilon_transitive(succ(A!18))) <=> (~epsilon_transitive(set_union2(A!18, singleton(A!18))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[13])).
% 0.18/0.46 tff(15,assumption,(~epsilon_transitive(succ(A!18))), introduced(assumption)).
% 0.18/0.46 tff(16,plain,
% 0.18/0.46 (~epsilon_transitive(set_union2(A!18, singleton(A!18)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.46 tff(17,plain,
% 0.18/0.46 (^[A: $i] : refl((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(18,plain,
% 0.18/0.46 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[17])).
% 0.18/0.46 tff(19,plain,
% 0.18/0.46 (^[A: $i] : rewrite((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(20,plain,
% 0.18/0.46 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.46 tff(21,plain,
% 0.18/0.46 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[20, 18])).
% 0.18/0.46 tff(22,plain,
% 0.18/0.46 (^[A: $i] : trans(monotonicity(rewrite(((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))) <=> (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))), rewrite((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(23,plain,
% 0.18/0.46 (![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.46 tff(24,plain,
% 0.18/0.46 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(25,plain,
% 0.18/0.46 (^[A: $i] : rewrite((epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(26,plain,
% 0.18/0.46 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[25])).
% 0.18/0.46 tff(27,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.18/0.46 tff(28,plain,
% 0.18/0.46 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.46 tff(29,plain,
% 0.18/0.46 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.18/0.46 tff(30,plain,(
% 0.18/0.46 ![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))),
% 0.18/0.46 inference(skolemize,[status(sab)],[29])).
% 0.18/0.46 tff(31,plain,
% 0.18/0.46 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.18/0.46 tff(32,plain,
% 0.18/0.46 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.18/0.46 tff(33,plain,
% 0.18/0.46 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))) | (~((~((~epsilon_transitive(set_union2(A!18, singleton(A!18)))) | ![B: $i] : ((~in(B, set_union2(A!18, singleton(A!18)))) | subset(B, set_union2(A!18, singleton(A!18)))))) | (~(epsilon_transitive(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))))))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(34,plain,
% 0.18/0.46 (~((~((~epsilon_transitive(set_union2(A!18, singleton(A!18)))) | ![B: $i] : ((~in(B, set_union2(A!18, singleton(A!18)))) | subset(B, set_union2(A!18, singleton(A!18)))))) | (~(epsilon_transitive(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))))))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.18/0.46 tff(35,plain,
% 0.18/0.46 (((~((~epsilon_transitive(set_union2(A!18, singleton(A!18)))) | ![B: $i] : ((~in(B, set_union2(A!18, singleton(A!18)))) | subset(B, set_union2(A!18, singleton(A!18)))))) | (~(epsilon_transitive(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))))))) | (epsilon_transitive(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))))))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(36,plain,
% 0.18/0.46 (epsilon_transitive(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.18/0.46 tff(37,plain,
% 0.18/0.46 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(38,plain,
% 0.18/0.46 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[37])).
% 0.18/0.46 tff(39,plain,
% 0.18/0.46 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.47 inference(pull_quant,[status(thm)],[])).
% 0.18/0.47 tff(40,plain,
% 0.18/0.47 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(41,plain,
% 0.18/0.47 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[40])).
% 0.18/0.47 tff(42,plain,
% 0.18/0.47 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[41, 39])).
% 0.18/0.47 tff(43,plain,
% 0.18/0.47 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[42, 38])).
% 0.18/0.47 tff(44,plain,
% 0.18/0.47 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(45,plain,
% 0.18/0.47 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.47 tff(46,plain,
% 0.18/0.47 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[45, 43])).
% 0.18/0.47 tff(47,plain,
% 0.18/0.47 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))) <=> (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite(((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(48,plain,
% 0.18/0.47 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[47])).
% 0.18/0.47 tff(49,plain,
% 0.18/0.47 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(50,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 0.18/0.47 tff(51,plain,
% 0.18/0.47 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.47 tff(52,plain,(
% 0.18/0.47 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.18/0.47 inference(skolemize,[status(sab)],[51])).
% 0.18/0.47 tff(53,plain,
% 0.18/0.47 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.18/0.47 tff(54,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.18/0.47 tff(55,plain,
% 0.18/0.47 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(56,plain,
% 0.18/0.47 ((~(~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(57,plain,
% 0.18/0.47 (((~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))) | $false) <=> (~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(58,plain,
% 0.18/0.47 ((~$true) <=> $false),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(59,plain,
% 0.18/0.47 (($true | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))) <=> $true),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(60,plain,
% 0.18/0.47 ((~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18))) <=> (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(61,plain,
% 0.18/0.47 ((singleton(A!18) = singleton(A!18)) <=> $true),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(62,plain,
% 0.18/0.47 (((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[61, 60])).
% 0.18/0.47 tff(63,plain,
% 0.18/0.47 (((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))) <=> $true),
% 0.18/0.47 inference(transitivity,[status(thm)],[62, 59])).
% 0.18/0.47 tff(64,plain,
% 0.18/0.47 ((~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18))))) <=> (~$true)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[63])).
% 0.18/0.47 tff(65,plain,
% 0.18/0.47 ((~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18))))) <=> $false),
% 0.18/0.47 inference(transitivity,[status(thm)],[64, 58])).
% 0.18/0.47 tff(66,plain,
% 0.18/0.47 ((~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))) <=> (~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(67,plain,
% 0.18/0.47 (($false | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(68,plain,
% 0.18/0.47 ((~(singleton(A!18) = singleton(A!18))) <=> (~$true)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[61])).
% 0.18/0.47 tff(69,plain,
% 0.18/0.47 ((~(singleton(A!18) = singleton(A!18))) <=> $false),
% 0.18/0.47 inference(transitivity,[status(thm)],[68, 58])).
% 0.18/0.47 tff(70,plain,
% 0.18/0.47 (((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))) <=> ($false | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[69])).
% 0.18/0.47 tff(71,plain,
% 0.18/0.47 (((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.47 inference(transitivity,[status(thm)],[70, 67])).
% 0.18/0.47 tff(72,plain,
% 0.18/0.47 ((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))) <=> (~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[71])).
% 0.18/0.47 tff(73,plain,
% 0.18/0.47 ((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))) <=> (~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[72, 66])).
% 0.18/0.47 tff(74,plain,
% 0.18/0.47 (((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))) <=> ((~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))) | $false)),
% 0.18/0.47 inference(monotonicity,[status(thm)],[73, 65])).
% 0.18/0.47 tff(75,plain,
% 0.18/0.47 (((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))) <=> (~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[74, 57])).
% 0.18/0.47 tff(76,plain,
% 0.18/0.47 ((~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18))))))) <=> (~(~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[75])).
% 0.18/0.47 tff(77,plain,
% 0.18/0.47 ((~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18))))))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.47 inference(transitivity,[status(thm)],[76, 56])).
% 0.18/0.47 tff(78,plain,
% 0.18/0.47 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[77])).
% 0.18/0.47 tff(79,plain,
% 0.18/0.47 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.47 inference(transitivity,[status(thm)],[78, 55])).
% 0.18/0.47 tff(80,plain,
% 0.18/0.47 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(81,plain,
% 0.18/0.47 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.47 tff(82,plain,
% 0.18/0.47 (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[81, 54])).
% 0.18/0.47 tff(83,plain,
% 0.18/0.47 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(84,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.47 tff(85,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.18/0.47 inference(pull_quant,[status(thm)],[])).
% 0.18/0.47 tff(86,plain,
% 0.18/0.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(87,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.47 tff(88,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[87, 85])).
% 0.18/0.47 tff(89,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[88, 84])).
% 0.18/0.47 tff(90,plain,
% 0.18/0.47 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(91,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[90])).
% 0.18/0.47 tff(92,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[91, 89])).
% 0.18/0.47 tff(93,plain,
% 0.18/0.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))) <=> (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(94,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[93])).
% 0.18/0.48 tff(95,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(96,plain,
% 0.18/0.48 (^[A: $i, B: $i, C: $i] : rewrite(((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(97,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[96])).
% 0.18/0.48 tff(98,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.18/0.48 tff(99,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.48 tff(100,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[99, 95])).
% 0.18/0.48 tff(101,plain,(
% 0.18/0.48 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))),
% 0.18/0.48 inference(skolemize,[status(sab)],[100])).
% 0.18/0.48 tff(102,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[101, 94])).
% 0.18/0.48 tff(103,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[102, 92])).
% 0.18/0.48 tff(104,plain,
% 0.18/0.48 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(105,plain,
% 0.18/0.48 ((~(~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(106,plain,
% 0.18/0.48 (((~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | $false) <=> (~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(107,plain,
% 0.18/0.48 (($true | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))) <=> $true),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(108,plain,
% 0.18/0.48 ((~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))) <=> (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(109,plain,
% 0.18/0.48 ((in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(110,plain,
% 0.18/0.48 ((~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))) <=> (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[109])).
% 0.18/0.48 tff(111,plain,
% 0.18/0.48 ((~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))) <=> (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[110, 108])).
% 0.18/0.48 tff(112,plain,
% 0.18/0.48 ((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) <=> $true),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(113,plain,
% 0.18/0.48 (((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))) <=> ($true | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[112, 111])).
% 0.18/0.48 tff(114,plain,
% 0.18/0.48 (((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))) <=> $true),
% 0.18/0.48 inference(transitivity,[status(thm)],[113, 107])).
% 0.18/0.48 tff(115,plain,
% 0.18/0.48 ((~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))))) <=> (~$true)),
% 0.18/0.48 inference(monotonicity,[status(thm)],[114])).
% 0.18/0.48 tff(116,plain,
% 0.18/0.48 ((~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))))) <=> $false),
% 0.18/0.48 inference(transitivity,[status(thm)],[115, 58])).
% 0.18/0.48 tff(117,plain,
% 0.18/0.48 ((~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))) <=> (~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(118,plain,
% 0.18/0.48 (($false | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(119,plain,
% 0.18/0.48 ((in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(120,plain,
% 0.18/0.48 ((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) <=> (~$true)),
% 0.18/0.48 inference(monotonicity,[status(thm)],[112])).
% 0.18/0.48 tff(121,plain,
% 0.18/0.48 ((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) <=> $false),
% 0.18/0.48 inference(transitivity,[status(thm)],[120, 58])).
% 0.18/0.48 tff(122,plain,
% 0.18/0.48 (((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)))) <=> ($false | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[121, 119])).
% 0.18/0.48 tff(123,plain,
% 0.18/0.48 (((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[122, 118])).
% 0.18/0.48 tff(124,plain,
% 0.18/0.48 ((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))))) <=> (~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[123])).
% 0.18/0.48 tff(125,plain,
% 0.18/0.48 ((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))))) <=> (~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[124, 117])).
% 0.18/0.48 tff(126,plain,
% 0.18/0.48 (((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))) <=> ((~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | $false)),
% 0.18/0.48 inference(monotonicity,[status(thm)],[125, 116])).
% 0.18/0.48 tff(127,plain,
% 0.18/0.48 (((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))) <=> (~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[126, 106])).
% 0.18/0.48 tff(128,plain,
% 0.18/0.48 ((~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))))))) <=> (~(~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[127])).
% 0.18/0.48 tff(129,plain,
% 0.18/0.48 ((~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))))))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[128, 105])).
% 0.18/0.48 tff(130,plain,
% 0.18/0.48 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[129])).
% 0.18/0.49 tff(131,plain,
% 0.18/0.49 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[130, 104])).
% 0.18/0.49 tff(132,plain,
% 0.18/0.49 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(133,plain,
% 0.18/0.49 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.18/0.49 tff(134,plain,
% 0.18/0.49 (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[133, 103])).
% 0.18/0.49 tff(135,assumption,(~((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))))), introduced(assumption)).
% 0.18/0.49 tff(136,plain,
% 0.18/0.49 (((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(137,plain,
% 0.18/0.49 (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.18/0.49 tff(138,plain,
% 0.18/0.49 ((~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | (~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(139,plain,
% 0.18/0.49 ((~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.18/0.49 tff(140,plain,
% 0.18/0.49 (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[139, 134])).
% 0.18/0.49 tff(141,plain,
% 0.18/0.49 (((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(142,plain,
% 0.18/0.49 (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[141, 135])).
% 0.18/0.49 tff(143,assumption,(subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)), introduced(assumption)).
% 0.18/0.49 tff(144,assumption,(~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))), introduced(assumption)).
% 0.18/0.49 tff(145,plain,
% 0.18/0.49 (^[A: $i, B: $i] : refl(subset(A, set_union2(A, B)) <=> subset(A, set_union2(A, B)))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(146,plain,
% 0.18/0.49 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[145])).
% 0.18/0.49 tff(147,plain,
% 0.18/0.49 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(148,axiom,(![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_xboole_1')).
% 0.18/0.49 tff(149,plain,
% 0.18/0.49 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.18/0.49 tff(150,plain,(
% 0.18/0.49 ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.18/0.49 inference(skolemize,[status(sab)],[149])).
% 0.18/0.49 tff(151,plain,
% 0.18/0.49 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.18/0.49 tff(152,plain,
% 0.18/0.49 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(A!18, set_union2(A!18, singleton(A!18)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(153,plain,
% 0.18/0.49 (subset(A!18, set_union2(A!18, singleton(A!18)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.18/0.49 tff(154,plain,
% 0.18/0.49 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C))) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(155,plain,
% 0.18/0.49 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(B, C)) <=> (~((~subset(A, B)) | (~subset(B, C))))), ((~(subset(A, B) & subset(B, C))) <=> (~(~((~subset(A, B)) | (~subset(B, C))))))), rewrite((~(~((~subset(A, B)) | (~subset(B, C))))) <=> ((~subset(A, B)) | (~subset(B, C)))), ((~(subset(A, B) & subset(B, C))) <=> ((~subset(A, B)) | (~subset(B, C))))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (((~subset(A, B)) | (~subset(B, C))) | subset(A, C)))), rewrite((((~subset(A, B)) | (~subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(156,plain,
% 0.18/0.49 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[155])).
% 0.18/0.49 tff(157,plain,
% 0.18/0.49 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(158,plain,
% 0.18/0.49 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(159,plain,
% 0.18/0.49 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[158])).
% 0.18/0.49 tff(160,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_xboole_1')).
% 0.18/0.49 tff(161,plain,
% 0.18/0.49 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.18/0.49 tff(162,plain,
% 0.18/0.49 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.18/0.49 tff(163,plain,(
% 0.18/0.49 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.18/0.49 inference(skolemize,[status(sab)],[162])).
% 0.18/0.49 tff(164,plain,
% 0.18/0.49 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.18/0.49 tff(165,plain,
% 0.18/0.49 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[164, 154])).
% 0.18/0.49 tff(166,plain,
% 0.18/0.49 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | ((~subset(A!18, set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) | (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (~subset(A!18, set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) | (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(167,plain,
% 0.18/0.49 ((subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) | (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)) | (~subset(A!18, set_union2(A!18, singleton(A!18))))) <=> ((~subset(A!18, set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) | (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(168,plain,
% 0.18/0.49 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) | (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)) | (~subset(A!18, set_union2(A!18, singleton(A!18)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | ((~subset(A!18, set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) | (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[167])).
% 0.18/0.49 tff(169,plain,
% 0.18/0.49 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) | (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)) | (~subset(A!18, set_union2(A!18, singleton(A!18)))))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (~subset(A!18, set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) | (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)))),
% 0.18/0.49 inference(transitivity,[status(thm)],[168, 166])).
% 0.18/0.49 tff(170,plain,
% 0.18/0.49 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) | (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)) | (~subset(A!18, set_union2(A!18, singleton(A!18)))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(171,plain,
% 0.18/0.49 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(A, B)) | (~subset(B, C)))) | (~subset(A!18, set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) | (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.18/0.49 tff(172,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[171, 165, 153, 144, 143])).
% 0.18/0.49 tff(173,plain,((~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(174,plain,
% 0.18/0.49 (~subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[173, 142])).
% 0.18/0.49 tff(175,plain,
% 0.18/0.49 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))) | (~((~((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))) | (~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_1(A!18), A!18)) | subset(tptp_fun_B_1(A!18), A!18)))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(176,plain,
% 0.18/0.49 (~((~((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))) | (~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_1(A!18), A!18)) | subset(tptp_fun_B_1(A!18), A!18))))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[175, 32])).
% 0.18/0.49 tff(177,plain,
% 0.18/0.49 (((~((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))) | (~(epsilon_transitive(A!18) | (~((~in(tptp_fun_B_1(A!18), A!18)) | subset(tptp_fun_B_1(A!18), A!18)))))) | ((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(178,plain,
% 0.18/0.49 ((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.18/0.49 tff(179,plain,
% 0.18/0.49 ((~![A: $i] : ((~ordinal(A)) | ordinal(succ(A)))) <=> (~![A: $i] : ((~ordinal(A)) | ordinal(succ(A))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(180,plain,
% 0.18/0.49 ((~![A: $i] : (ordinal(A) => ordinal(succ(A)))) <=> (~![A: $i] : ((~ordinal(A)) | ordinal(succ(A))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(181,axiom,(~![A: $i] : (ordinal(A) => ordinal(succ(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t29_ordinal1')).
% 0.18/0.49 tff(182,plain,
% 0.18/0.49 (~![A: $i] : ((~ordinal(A)) | ordinal(succ(A)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.18/0.49 tff(183,plain,
% 0.18/0.49 (~![A: $i] : ((~ordinal(A)) | ordinal(succ(A)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[182, 179])).
% 0.18/0.49 tff(184,plain,
% 0.18/0.49 (~![A: $i] : ((~ordinal(A)) | ordinal(succ(A)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.18/0.49 tff(185,plain,
% 0.18/0.49 (~![A: $i] : ((~ordinal(A)) | ordinal(succ(A)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[184, 179])).
% 0.18/0.49 tff(186,plain,(
% 0.18/0.49 ~((~ordinal(A!18)) | ordinal(succ(A!18)))),
% 0.18/0.49 inference(skolemize,[status(sab)],[185])).
% 0.18/0.49 tff(187,plain,
% 0.18/0.49 (ordinal(A!18)),
% 0.18/0.49 inference(or_elim,[status(thm)],[186])).
% 0.18/0.49 tff(188,plain,
% 0.18/0.49 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(189,plain,
% 0.18/0.49 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[188])).
% 0.18/0.49 tff(190,plain,
% 0.18/0.49 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(191,plain,
% 0.18/0.49 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[190])).
% 0.18/0.49 tff(192,plain,
% 0.18/0.49 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(193,plain,
% 0.18/0.49 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(194,plain,
% 0.18/0.49 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[193])).
% 0.18/0.49 tff(195,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_ordinal1')).
% 0.18/0.49 tff(196,plain,
% 0.18/0.49 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.18/0.49 tff(197,plain,
% 0.18/0.49 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.18/0.49 tff(198,plain,(
% 0.18/0.49 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.49 inference(skolemize,[status(sab)],[197])).
% 0.18/0.49 tff(199,plain,
% 0.18/0.49 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.18/0.49 tff(200,plain,
% 0.18/0.49 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[199, 189])).
% 0.18/0.49 tff(201,plain,
% 0.18/0.49 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(A!18)) | (~((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(A!18)) | (~((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18)))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(202,plain,
% 0.18/0.49 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(A!18)) | (~((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18)))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(203,plain,
% 0.18/0.49 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(A!18)) | (~((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.18/0.49 tff(204,plain,
% 0.18/0.49 (~((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[203, 200, 187])).
% 0.18/0.49 tff(205,plain,
% 0.18/0.49 (((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) | epsilon_transitive(A!18)),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(206,plain,
% 0.18/0.49 (epsilon_transitive(A!18)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.18/0.49 tff(207,plain,
% 0.18/0.49 ((~((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))) | (~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(208,plain,
% 0.18/0.49 ((~((~epsilon_transitive(A!18)) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18)))) | ![B: $i] : ((~in(B, A!18)) | subset(B, A!18))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.18/0.49 tff(209,plain,
% 0.18/0.49 (![B: $i] : ((~in(B, A!18)) | subset(B, A!18))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[208, 178])).
% 0.18/0.49 tff(210,plain,
% 0.18/0.49 (((~![B: $i] : ((~in(B, A!18)) | subset(B, A!18))) | ((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))) <=> ((~![B: $i] : ((~in(B, A!18)) | subset(B, A!18))) | (~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(211,plain,
% 0.18/0.49 ((~![B: $i] : ((~in(B, A!18)) | subset(B, A!18))) | ((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(212,plain,
% 0.18/0.49 ((~![B: $i] : ((~in(B, A!18)) | subset(B, A!18))) | (~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.18/0.49 tff(213,plain,
% 0.18/0.49 (~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[212, 209, 174])).
% 0.18/0.49 tff(214,plain,
% 0.18/0.49 ((~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)))) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(215,plain,
% 0.18/0.49 (in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[214, 213, 140])).
% 0.18/0.49 tff(216,plain,
% 0.18/0.49 ((~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))) | (~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18))) | (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(217,plain,
% 0.18/0.49 ((~(in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18))) | (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.18/0.49 tff(218,plain,
% 0.18/0.49 (tptp_fun_B_1(set_union2(A!18, singleton(A!18))) = A!18),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[217, 82])).
% 0.18/0.49 tff(219,plain,
% 0.18/0.49 (subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> subset(A!18, set_union2(A!18, singleton(A!18)))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[218])).
% 0.18/0.49 tff(220,plain,
% 0.18/0.49 (subset(A!18, set_union2(A!18, singleton(A!18))) <=> subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))),
% 0.18/0.49 inference(symmetry,[status(thm)],[219])).
% 0.18/0.49 tff(221,plain,
% 0.18/0.49 (subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[153, 220])).
% 0.18/0.49 tff(222,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[142, 221])).
% 0.18/0.49 tff(223,plain,((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(224,plain,
% 0.18/0.49 ((~(epsilon_transitive(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))))))) | epsilon_transitive(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(225,plain,
% 0.18/0.49 ((~(epsilon_transitive(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | subset(tptp_fun_B_1(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))))))) | epsilon_transitive(set_union2(A!18, singleton(A!18)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.18/0.49 tff(226,plain,
% 0.18/0.49 (epsilon_transitive(set_union2(A!18, singleton(A!18)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[225, 36])).
% 0.18/0.49 tff(227,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[226, 16])).
% 0.18/0.49 tff(228,plain,(epsilon_transitive(succ(A!18))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(229,plain,
% 0.18/0.49 (^[A: $i] : refl((~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(230,plain,
% 0.18/0.49 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[229])).
% 0.18/0.49 tff(231,plain,
% 0.18/0.49 (^[A: $i] : trans(trans(monotonicity(rewrite((epsilon_transitive(A) & epsilon_connected(A)) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))), ((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))), rewrite((ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))), ((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))))), rewrite((~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))), ((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(232,plain,
% 0.18/0.49 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[231])).
% 0.18/0.49 tff(233,plain,
% 0.18/0.49 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(234,axiom,(![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_ordinal1')).
% 0.18/0.49 tff(235,plain,
% 0.18/0.49 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.18/0.49 tff(236,plain,(
% 0.18/0.49 ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.18/0.49 inference(skolemize,[status(sab)],[235])).
% 0.18/0.49 tff(237,plain,
% 0.18/0.49 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[236, 232])).
% 0.18/0.49 tff(238,plain,
% 0.18/0.49 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[237, 230])).
% 0.18/0.49 tff(239,plain,
% 0.18/0.49 ((~![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))) | (~(((~epsilon_transitive(succ(A!18))) | (~epsilon_connected(succ(A!18)))) <=> ordinal(succ(A!18))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(240,plain,
% 0.18/0.49 (~(((~epsilon_transitive(succ(A!18))) | (~epsilon_connected(succ(A!18)))) <=> ordinal(succ(A!18)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.18/0.49 tff(241,plain,
% 0.18/0.49 (~ordinal(succ(A!18))),
% 0.18/0.49 inference(or_elim,[status(thm)],[186])).
% 0.18/0.49 tff(242,plain,
% 0.18/0.49 ((((~epsilon_transitive(succ(A!18))) | (~epsilon_connected(succ(A!18)))) <=> ordinal(succ(A!18))) | ((~epsilon_transitive(succ(A!18))) | (~epsilon_connected(succ(A!18)))) | ordinal(succ(A!18))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(243,plain,
% 0.18/0.49 ((((~epsilon_transitive(succ(A!18))) | (~epsilon_connected(succ(A!18)))) <=> ordinal(succ(A!18))) | ((~epsilon_transitive(succ(A!18))) | (~epsilon_connected(succ(A!18))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.18/0.49 tff(244,plain,
% 0.18/0.49 ((~epsilon_transitive(succ(A!18))) | (~epsilon_connected(succ(A!18)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[243, 240])).
% 0.18/0.49 tff(245,plain,
% 0.18/0.49 ((~((~epsilon_transitive(succ(A!18))) | (~epsilon_connected(succ(A!18))))) | (~epsilon_transitive(succ(A!18))) | (~epsilon_connected(succ(A!18)))),
% 0.18/0.49 inference(tautology,[status(thm)],[])).
% 0.18/0.49 tff(246,plain,
% 0.18/0.49 ((~epsilon_transitive(succ(A!18))) | (~epsilon_connected(succ(A!18)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.18/0.49 tff(247,plain,
% 0.18/0.49 (~epsilon_connected(succ(A!18))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[246, 228])).
% 0.18/0.49 tff(248,plain,
% 0.18/0.49 (epsilon_connected(set_union2(A!18, singleton(A!18))) <=> epsilon_connected(succ(A!18))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[11])).
% 0.18/0.49 tff(249,plain,
% 0.18/0.49 (epsilon_connected(succ(A!18)) <=> epsilon_connected(set_union2(A!18, singleton(A!18)))),
% 0.18/0.49 inference(symmetry,[status(thm)],[248])).
% 0.18/0.49 tff(250,plain,
% 0.18/0.49 ((~epsilon_connected(succ(A!18))) <=> (~epsilon_connected(set_union2(A!18, singleton(A!18))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[249])).
% 0.18/0.49 tff(251,assumption,(~epsilon_connected(succ(A!18))), introduced(assumption)).
% 0.18/0.49 tff(252,plain,
% 0.18/0.49 (~epsilon_connected(set_union2(A!18, singleton(A!18)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.18/0.49 tff(253,plain,
% 0.18/0.49 (^[A: $i] : refl((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A)))))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A)))))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(254,plain,
% 0.18/0.49 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A)))))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[253])).
% 0.18/0.49 tff(255,plain,
% 0.18/0.49 (^[A: $i] : rewrite((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A)))))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A)))))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(256,plain,
% 0.18/0.49 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A)))))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[255])).
% 0.18/0.50 tff(257,plain,
% 0.18/0.50 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A)))))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[256, 254])).
% 0.18/0.50 tff(258,plain,
% 0.18/0.50 (^[A: $i] : trans(monotonicity(rewrite(((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) <=> ((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))), rewrite((epsilon_connected(A) | (in(tptp_fun_B_4(A), A) & in(tptp_fun_C_3(A), A) & (~in(tptp_fun_B_4(A), tptp_fun_C_3(A))) & (~(tptp_fun_B_4(A) = tptp_fun_C_3(A))) & (~in(tptp_fun_C_3(A), tptp_fun_B_4(A))))) <=> (epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A)))))), ((((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_4(A), A) & in(tptp_fun_C_3(A), A) & (~in(tptp_fun_B_4(A), tptp_fun_C_3(A))) & (~(tptp_fun_B_4(A) = tptp_fun_C_3(A))) & (~in(tptp_fun_C_3(A), tptp_fun_B_4(A)))))) <=> (((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A)))) & (epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A)))))))), rewrite((((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A)))) & (epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A)))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))), ((((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_4(A), A) & in(tptp_fun_C_3(A), A) & (~in(tptp_fun_B_4(A), tptp_fun_C_3(A))) & (~(tptp_fun_B_4(A) = tptp_fun_C_3(A))) & (~in(tptp_fun_C_3(A), tptp_fun_B_4(A)))))) <=> (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(259,plain,
% 0.18/0.50 (![A: $i] : (((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_4(A), A) & in(tptp_fun_C_3(A), A) & (~in(tptp_fun_B_4(A), tptp_fun_C_3(A))) & (~(tptp_fun_B_4(A) = tptp_fun_C_3(A))) & (~in(tptp_fun_C_3(A), tptp_fun_B_4(A)))))) <=> ![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[258])).
% 0.18/0.50 tff(260,plain,
% 0.18/0.50 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) <=> ![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(261,plain,
% 0.18/0.50 (^[A: $i] : rewrite((epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B))))) <=> (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(262,plain,
% 0.18/0.50 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B))))) <=> ![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[261])).
% 0.18/0.50 tff(263,axiom,(![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_ordinal1')).
% 0.18/0.50 tff(264,plain,
% 0.18/0.50 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.18/0.50 tff(265,plain,
% 0.18/0.50 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[264, 260])).
% 0.18/0.50 tff(266,plain,(
% 0.18/0.50 ![A: $i] : (((~epsilon_connected(A)) | ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) & (epsilon_connected(A) | (in(tptp_fun_B_4(A), A) & in(tptp_fun_C_3(A), A) & (~in(tptp_fun_B_4(A), tptp_fun_C_3(A))) & (~(tptp_fun_B_4(A) = tptp_fun_C_3(A))) & (~in(tptp_fun_C_3(A), tptp_fun_B_4(A))))))),
% 0.18/0.50 inference(skolemize,[status(sab)],[265])).
% 0.18/0.50 tff(267,plain,
% 0.18/0.50 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[266, 259])).
% 0.18/0.50 tff(268,plain,
% 0.18/0.50 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[267, 257])).
% 0.18/0.50 tff(269,plain,
% 0.18/0.50 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(set_union2(A!18, singleton(A!18)))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, set_union2(A!18, singleton(A!18)))) | (~in(C, set_union2(A!18, singleton(A!18))))))) | (~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(set_union2(A!18, singleton(A!18)))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, set_union2(A!18, singleton(A!18)))) | (~in(C, set_union2(A!18, singleton(A!18))))))) | (~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(270,plain,
% 0.18/0.50 ((~((~((~epsilon_connected(set_union2(A!18, singleton(A!18)))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, set_union2(A!18, singleton(A!18)))) | (~in(C, set_union2(A!18, singleton(A!18))))))) | (~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))))))))) <=> (~((~((~epsilon_connected(set_union2(A!18, singleton(A!18)))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, set_union2(A!18, singleton(A!18)))) | (~in(C, set_union2(A!18, singleton(A!18))))))) | (~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(271,plain,
% 0.18/0.50 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(set_union2(A!18, singleton(A!18)))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, set_union2(A!18, singleton(A!18)))) | (~in(C, set_union2(A!18, singleton(A!18))))))) | (~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(set_union2(A!18, singleton(A!18)))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, set_union2(A!18, singleton(A!18)))) | (~in(C, set_union2(A!18, singleton(A!18))))))) | (~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))))))))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[270])).
% 0.18/0.50 tff(272,plain,
% 0.18/0.50 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(set_union2(A!18, singleton(A!18)))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, set_union2(A!18, singleton(A!18)))) | (~in(C, set_union2(A!18, singleton(A!18))))))) | (~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(set_union2(A!18, singleton(A!18)))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, set_union2(A!18, singleton(A!18)))) | (~in(C, set_union2(A!18, singleton(A!18))))))) | (~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))))))))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[271, 269])).
% 0.18/0.50 tff(273,plain,
% 0.18/0.50 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(set_union2(A!18, singleton(A!18)))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, set_union2(A!18, singleton(A!18)))) | (~in(C, set_union2(A!18, singleton(A!18))))))) | (~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))))))))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(274,plain,
% 0.18/0.50 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(set_union2(A!18, singleton(A!18)))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, set_union2(A!18, singleton(A!18)))) | (~in(C, set_union2(A!18, singleton(A!18))))))) | (~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.18/0.50 tff(275,plain,
% 0.18/0.50 (~((~((~epsilon_connected(set_union2(A!18, singleton(A!18)))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, set_union2(A!18, singleton(A!18)))) | (~in(C, set_union2(A!18, singleton(A!18))))))) | (~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))))))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[274, 268])).
% 0.18/0.50 tff(276,plain,
% 0.18/0.50 (((~((~epsilon_connected(set_union2(A!18, singleton(A!18)))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, set_union2(A!18, singleton(A!18)))) | (~in(C, set_union2(A!18, singleton(A!18))))))) | (~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))))))) | (epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(277,plain,
% 0.18/0.50 (epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[276, 275])).
% 0.18/0.50 tff(278,assumption,((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))), introduced(assumption)).
% 0.18/0.50 tff(279,plain,
% 0.18/0.50 ((~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))))))) | epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(280,plain,
% 0.18/0.50 ((~(epsilon_connected(set_union2(A!18, singleton(A!18))) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))))))) | epsilon_connected(set_union2(A!18, singleton(A!18)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[279, 278])).
% 0.18/0.50 tff(281,plain,
% 0.18/0.50 (epsilon_connected(set_union2(A!18, singleton(A!18)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[280, 277])).
% 0.18/0.50 tff(282,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[281, 252])).
% 0.18/0.50 tff(283,plain,(epsilon_connected(succ(A!18)) | (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.50 tff(284,plain,
% 0.18/0.50 (~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[283, 247])).
% 0.18/0.50 tff(285,plain,
% 0.18/0.50 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(286,plain,
% 0.18/0.50 ((~(~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(287,plain,
% 0.18/0.50 (((~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))) | $false) <=> (~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(288,plain,
% 0.18/0.50 ((~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))) <=> (~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(289,plain,
% 0.18/0.50 (($false | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(290,plain,
% 0.18/0.50 (((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))) <=> ($false | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[69])).
% 0.18/0.50 tff(291,plain,
% 0.18/0.50 (((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.50 inference(transitivity,[status(thm)],[290, 289])).
% 0.18/0.50 tff(292,plain,
% 0.18/0.51 ((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))) <=> (~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[291])).
% 0.18/0.51 tff(293,plain,
% 0.18/0.51 ((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))) <=> (~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.51 inference(transitivity,[status(thm)],[292, 288])).
% 0.18/0.51 tff(294,plain,
% 0.18/0.51 (((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))) <=> ((~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))) | $false)),
% 0.18/0.51 inference(monotonicity,[status(thm)],[293, 65])).
% 0.18/0.51 tff(295,plain,
% 0.18/0.51 (((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))) <=> (~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.51 inference(transitivity,[status(thm)],[294, 287])).
% 0.18/0.51 tff(296,plain,
% 0.18/0.51 ((~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18))))))) <=> (~(~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[295])).
% 0.18/0.51 tff(297,plain,
% 0.18/0.51 ((~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18))))))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.51 inference(transitivity,[status(thm)],[296, 286])).
% 0.18/0.51 tff(298,plain,
% 0.18/0.51 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[297])).
% 0.18/0.51 tff(299,plain,
% 0.18/0.51 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.51 inference(transitivity,[status(thm)],[298, 285])).
% 0.18/0.51 tff(300,plain,
% 0.18/0.51 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(301,plain,
% 0.18/0.51 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.18/0.51 tff(302,plain,
% 0.18/0.51 (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[301, 54])).
% 0.18/0.51 tff(303,plain,
% 0.18/0.51 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(304,plain,
% 0.18/0.51 ((~(~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(305,plain,
% 0.18/0.51 (((~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | $false) <=> (~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(306,plain,
% 0.18/0.51 ((~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))) <=> (~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(307,plain,
% 0.18/0.51 (($false | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(308,plain,
% 0.18/0.51 ((in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(309,plain,
% 0.18/0.51 (((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18)))) <=> ($false | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[121, 308])).
% 0.18/0.51 tff(310,plain,
% 0.18/0.51 (((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18)))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[309, 307])).
% 0.18/0.51 tff(311,plain,
% 0.18/0.51 ((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))))) <=> (~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[310])).
% 0.18/0.51 tff(312,plain,
% 0.18/0.51 ((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))))) <=> (~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[311, 306])).
% 0.18/0.51 tff(313,plain,
% 0.18/0.51 (((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))) <=> ((~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | $false)),
% 0.18/0.51 inference(monotonicity,[status(thm)],[312, 116])).
% 0.18/0.51 tff(314,plain,
% 0.18/0.51 (((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))) <=> (~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[313, 305])).
% 0.18/0.51 tff(315,plain,
% 0.18/0.51 ((~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))))))) <=> (~(~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[314])).
% 0.18/0.51 tff(316,plain,
% 0.18/0.51 ((~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))))))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[315, 304])).
% 0.18/0.51 tff(317,plain,
% 0.18/0.51 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[316])).
% 0.18/0.51 tff(318,plain,
% 0.18/0.51 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[317, 303])).
% 0.18/0.51 tff(319,plain,
% 0.18/0.51 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(320,plain,
% 0.18/0.51 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.18/0.52 tff(321,plain,
% 0.18/0.52 (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[320, 103])).
% 0.18/0.52 tff(322,assumption,(~((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))))), introduced(assumption)).
% 0.18/0.52 tff(323,plain,
% 0.18/0.52 (((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(324,plain,
% 0.18/0.52 (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[323, 322])).
% 0.18/0.52 tff(325,plain,
% 0.18/0.52 ((~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(326,plain,
% 0.18/0.52 ((~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[325, 324])).
% 0.18/0.52 tff(327,plain,
% 0.18/0.52 (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[326, 321])).
% 0.18/0.52 tff(328,plain,
% 0.18/0.52 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(329,plain,
% 0.18/0.52 ((~(~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(330,plain,
% 0.18/0.52 (((~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | $false) <=> (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(331,plain,
% 0.18/0.52 ((~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))) <=> (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(332,plain,
% 0.18/0.52 (($false | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(333,plain,
% 0.18/0.52 ((in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(334,plain,
% 0.18/0.52 (((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)))) <=> ($false | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[121, 333])).
% 0.18/0.52 tff(335,plain,
% 0.18/0.52 (((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[334, 332])).
% 0.18/0.52 tff(336,plain,
% 0.18/0.52 ((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18))))) <=> (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[335])).
% 0.18/0.52 tff(337,plain,
% 0.18/0.52 ((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18))))) <=> (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[336, 331])).
% 0.18/0.52 tff(338,plain,
% 0.18/0.52 (((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))) <=> ((~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | $false)),
% 0.18/0.52 inference(monotonicity,[status(thm)],[337, 116])).
% 0.18/0.52 tff(339,plain,
% 0.18/0.52 (((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))) <=> (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[338, 330])).
% 0.18/0.52 tff(340,plain,
% 0.18/0.52 ((~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))))))) <=> (~(~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[339])).
% 0.18/0.52 tff(341,plain,
% 0.18/0.52 ((~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18)))))))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[340, 329])).
% 0.18/0.52 tff(342,plain,
% 0.18/0.52 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[341])).
% 0.18/0.52 tff(343,plain,
% 0.18/0.52 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[342, 328])).
% 0.18/0.52 tff(344,plain,
% 0.18/0.52 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18))))) | (~((set_union2(A!18, singleton(A!18)) = set_union2(A!18, singleton(A!18))) | (~(in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), singleton(A!18)) | in(tptp_fun_D_2(set_union2(A!18, singleton(A!18)), singleton(A!18), A!18), A!18))))))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(345,plain,
% 0.18/0.52 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.18/0.52 tff(346,plain,
% 0.18/0.52 (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[345, 103])).
% 0.18/0.52 tff(347,plain,
% 0.18/0.52 (((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(348,plain,
% 0.18/0.52 (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[347, 322])).
% 0.18/0.52 tff(349,plain,
% 0.18/0.52 ((~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(350,plain,
% 0.18/0.52 ((~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[349, 348])).
% 0.18/0.52 tff(351,plain,
% 0.18/0.52 (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[350, 346])).
% 0.18/0.52 tff(352,assumption,(~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))), introduced(assumption)).
% 0.18/0.52 tff(353,plain,
% 0.18/0.52 ((~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(354,plain,
% 0.18/0.52 ((~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[353, 352])).
% 0.18/0.52 tff(355,plain,
% 0.18/0.52 (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[354, 351])).
% 0.18/0.52 tff(356,plain,
% 0.18/0.52 (((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(357,plain,
% 0.18/0.52 (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[356, 322])).
% 0.18/0.52 tff(358,plain,
% 0.18/0.52 (((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(359,plain,
% 0.18/0.52 (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[358, 322])).
% 0.18/0.52 tff(360,plain,
% 0.18/0.52 (((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))) | (~(tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(361,plain,
% 0.18/0.52 (~(tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[360, 322])).
% 0.18/0.52 tff(362,plain,
% 0.18/0.52 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_3(A!18), A!18)) | (~in(tptp_fun_B_4(A!18), A!18)) | in(tptp_fun_C_3(A!18), tptp_fun_B_4(A!18)) | (tptp_fun_B_4(A!18) = tptp_fun_C_3(A!18)) | in(tptp_fun_B_4(A!18), tptp_fun_C_3(A!18))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_3(A!18), A!18)) | (~in(tptp_fun_B_4(A!18), A!18)) | in(tptp_fun_C_3(A!18), tptp_fun_B_4(A!18)) | (tptp_fun_B_4(A!18) = tptp_fun_C_3(A!18)) | in(tptp_fun_B_4(A!18), tptp_fun_C_3(A!18)))))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(363,plain,
% 0.18/0.53 ((~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~(epsilon_connected(A!18) | (~(in(tptp_fun_B_4(A!18), tptp_fun_C_3(A!18)) | (tptp_fun_B_4(A!18) = tptp_fun_C_3(A!18)) | in(tptp_fun_C_3(A!18), tptp_fun_B_4(A!18)) | (~in(tptp_fun_B_4(A!18), A!18)) | (~in(tptp_fun_C_3(A!18), A!18)))))))) <=> (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_3(A!18), A!18)) | (~in(tptp_fun_B_4(A!18), A!18)) | in(tptp_fun_C_3(A!18), tptp_fun_B_4(A!18)) | (tptp_fun_B_4(A!18) = tptp_fun_C_3(A!18)) | in(tptp_fun_B_4(A!18), tptp_fun_C_3(A!18))))))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(364,plain,
% 0.18/0.53 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~(epsilon_connected(A!18) | (~(in(tptp_fun_B_4(A!18), tptp_fun_C_3(A!18)) | (tptp_fun_B_4(A!18) = tptp_fun_C_3(A!18)) | in(tptp_fun_C_3(A!18), tptp_fun_B_4(A!18)) | (~in(tptp_fun_B_4(A!18), A!18)) | (~in(tptp_fun_C_3(A!18), A!18))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_3(A!18), A!18)) | (~in(tptp_fun_B_4(A!18), A!18)) | in(tptp_fun_C_3(A!18), tptp_fun_B_4(A!18)) | (tptp_fun_B_4(A!18) = tptp_fun_C_3(A!18)) | in(tptp_fun_B_4(A!18), tptp_fun_C_3(A!18)))))))))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[363])).
% 0.18/0.53 tff(365,plain,
% 0.18/0.53 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~(epsilon_connected(A!18) | (~(in(tptp_fun_B_4(A!18), tptp_fun_C_3(A!18)) | (tptp_fun_B_4(A!18) = tptp_fun_C_3(A!18)) | in(tptp_fun_C_3(A!18), tptp_fun_B_4(A!18)) | (~in(tptp_fun_B_4(A!18), A!18)) | (~in(tptp_fun_C_3(A!18), A!18))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_3(A!18), A!18)) | (~in(tptp_fun_B_4(A!18), A!18)) | in(tptp_fun_C_3(A!18), tptp_fun_B_4(A!18)) | (tptp_fun_B_4(A!18) = tptp_fun_C_3(A!18)) | in(tptp_fun_B_4(A!18), tptp_fun_C_3(A!18)))))))))),
% 0.18/0.53 inference(transitivity,[status(thm)],[364, 362])).
% 0.18/0.53 tff(366,plain,
% 0.18/0.53 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~(epsilon_connected(A!18) | (~(in(tptp_fun_B_4(A!18), tptp_fun_C_3(A!18)) | (tptp_fun_B_4(A!18) = tptp_fun_C_3(A!18)) | in(tptp_fun_C_3(A!18), tptp_fun_B_4(A!18)) | (~in(tptp_fun_B_4(A!18), A!18)) | (~in(tptp_fun_C_3(A!18), A!18))))))))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(367,plain,
% 0.18/0.53 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A)) | (~in(C, A))))) | (~(epsilon_connected(A) | (~(in(tptp_fun_B_4(A), tptp_fun_C_3(A)) | (tptp_fun_B_4(A) = tptp_fun_C_3(A)) | in(tptp_fun_C_3(A), tptp_fun_B_4(A)) | (~in(tptp_fun_B_4(A), A)) | (~in(tptp_fun_C_3(A), A))))))))) | (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_3(A!18), A!18)) | (~in(tptp_fun_B_4(A!18), A!18)) | in(tptp_fun_C_3(A!18), tptp_fun_B_4(A!18)) | (tptp_fun_B_4(A!18) = tptp_fun_C_3(A!18)) | in(tptp_fun_B_4(A!18), tptp_fun_C_3(A!18))))))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[366, 365])).
% 0.18/0.53 tff(368,plain,
% 0.18/0.53 (~((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_3(A!18), A!18)) | (~in(tptp_fun_B_4(A!18), A!18)) | in(tptp_fun_C_3(A!18), tptp_fun_B_4(A!18)) | (tptp_fun_B_4(A!18) = tptp_fun_C_3(A!18)) | in(tptp_fun_B_4(A!18), tptp_fun_C_3(A!18)))))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[367, 268])).
% 0.18/0.53 tff(369,plain,
% 0.18/0.53 (((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~(epsilon_connected(A!18) | (~((~in(tptp_fun_C_3(A!18), A!18)) | (~in(tptp_fun_B_4(A!18), A!18)) | in(tptp_fun_C_3(A!18), tptp_fun_B_4(A!18)) | (tptp_fun_B_4(A!18) = tptp_fun_C_3(A!18)) | in(tptp_fun_B_4(A!18), tptp_fun_C_3(A!18))))))) | ((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(370,plain,
% 0.18/0.53 ((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18)))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[369, 368])).
% 0.18/0.53 tff(371,plain,
% 0.18/0.53 (((~epsilon_transitive(A!18)) | (~epsilon_connected(A!18))) | epsilon_connected(A!18)),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(372,plain,
% 0.18/0.53 (epsilon_connected(A!18)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[371, 204])).
% 0.18/0.53 tff(373,plain,
% 0.18/0.53 ((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | (~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18)))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(374,plain,
% 0.18/0.53 ((~((~epsilon_connected(A!18)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18))))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18)))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[373, 372])).
% 0.18/0.53 tff(375,plain,
% 0.18/0.53 (![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18)))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[374, 370])).
% 0.18/0.53 tff(376,plain,
% 0.18/0.53 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(377,plain,
% 0.18/0.53 ((in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(378,plain,
% 0.18/0.53 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[377])).
% 0.18/0.53 tff(379,plain,
% 0.18/0.53 (((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18)))) <=> ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18)))),
% 0.18/0.53 inference(transitivity,[status(thm)],[378, 376])).
% 0.18/0.53 tff(380,plain,
% 0.18/0.53 ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18)))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18)))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(381,plain,
% 0.18/0.53 ((~![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, A!18)) | (~in(C, A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.18/0.53 tff(382,plain,
% 0.18/0.53 ((~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[381, 375, 361, 359, 357])).
% 0.18/0.53 tff(383,plain,
% 0.18/0.53 (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[382, 355])).
% 0.18/0.53 tff(384,plain,
% 0.18/0.53 ((~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(385,plain,
% 0.18/0.53 (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[384, 383, 327])).
% 0.18/0.53 tff(386,plain,
% 0.18/0.53 ((~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))) | (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))) | (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(387,plain,
% 0.18/0.53 ((~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))) | (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[386, 385])).
% 0.18/0.53 tff(388,plain,
% 0.18/0.53 (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[387, 302])).
% 0.18/0.53 tff(389,plain,
% 0.18/0.53 (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) <=> in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18)),
% 0.18/0.53 inference(monotonicity,[status(thm)],[388])).
% 0.18/0.53 tff(390,plain,
% 0.18/0.53 (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), A!18) <=> in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))),
% 0.18/0.53 inference(symmetry,[status(thm)],[389])).
% 0.18/0.53 tff(391,plain,
% 0.18/0.53 (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[355, 390])).
% 0.18/0.53 tff(392,plain,
% 0.18/0.53 ($false),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[357, 391])).
% 0.18/0.53 tff(393,plain,(((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), tptp_fun_C_3(set_union2(A!18, singleton(A!18))))) | in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.53 tff(394,plain,
% 0.18/0.53 (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[393, 284])).
% 0.18/0.53 tff(395,assumption,(~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))), introduced(assumption)).
% 0.18/0.53 tff(396,plain,
% 0.18/0.53 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(397,plain,
% 0.18/0.53 ((~(~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(398,plain,
% 0.18/0.53 (((~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))) | $false) <=> (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(399,plain,
% 0.18/0.53 ((~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))) <=> (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(400,plain,
% 0.18/0.53 (($false | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(401,plain,
% 0.18/0.53 (((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))) <=> ($false | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[69])).
% 0.18/0.53 tff(402,plain,
% 0.18/0.53 (((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.53 inference(transitivity,[status(thm)],[401, 400])).
% 0.18/0.53 tff(403,plain,
% 0.18/0.53 ((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))) <=> (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[402])).
% 0.18/0.53 tff(404,plain,
% 0.18/0.53 ((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))) <=> (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.53 inference(transitivity,[status(thm)],[403, 399])).
% 0.18/0.53 tff(405,plain,
% 0.18/0.53 (((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))) <=> ((~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))) | $false)),
% 0.18/0.53 inference(monotonicity,[status(thm)],[404, 65])).
% 0.18/0.53 tff(406,plain,
% 0.18/0.53 (((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))) <=> (~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.53 inference(transitivity,[status(thm)],[405, 398])).
% 0.18/0.53 tff(407,plain,
% 0.18/0.53 ((~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18))))))) <=> (~(~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[406])).
% 0.18/0.53 tff(408,plain,
% 0.18/0.53 ((~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18))))))) <=> (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.53 inference(transitivity,[status(thm)],[407, 397])).
% 0.18/0.53 tff(409,plain,
% 0.18/0.53 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[408])).
% 0.18/0.53 tff(410,plain,
% 0.18/0.53 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))),
% 0.18/0.53 inference(transitivity,[status(thm)],[409, 396])).
% 0.18/0.53 tff(411,plain,
% 0.18/0.53 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(A!18) = singleton(A!18))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)))) | (~((singleton(A!18) = singleton(A!18)) | (~(in(tptp_fun_C_0(singleton(A!18), A!18), singleton(A!18)) <=> (tptp_fun_C_0(singleton(A!18), A!18) = A!18)))))))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(412,plain,
% 0.18/0.53 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.18/0.54 tff(413,plain,
% 0.18/0.54 ($false),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[412, 54, 395])).
% 0.18/0.54 tff(414,plain,(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.54 tff(415,plain,
% 0.18/0.54 ((~(in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18))) | (~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(416,plain,
% 0.18/0.54 ((~in(tptp_fun_B_4(set_union2(A!18, singleton(A!18))), singleton(A!18))) | (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18)),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[415, 414])).
% 0.18/0.54 tff(417,plain,
% 0.18/0.54 (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = A!18),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[416, 394])).
% 0.18/0.54 tff(418,plain,
% 0.18/0.54 (A!18 = tptp_fun_B_4(set_union2(A!18, singleton(A!18)))),
% 0.18/0.54 inference(symmetry,[status(thm)],[417])).
% 0.18/0.54 tff(419,plain,
% 0.18/0.54 ((tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = tptp_fun_B_4(set_union2(A!18, singleton(A!18))))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[418])).
% 0.18/0.54 tff(420,plain,
% 0.18/0.54 ((tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18) <=> (tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18))))),
% 0.18/0.54 inference(transitivity,[status(thm)],[419, 1])).
% 0.18/0.54 tff(421,plain,
% 0.18/0.54 ((tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18)))) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)),
% 0.18/0.54 inference(symmetry,[status(thm)],[420])).
% 0.18/0.54 tff(422,plain,
% 0.18/0.54 ((~(tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18))))) <=> (~(tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[421])).
% 0.18/0.54 tff(423,plain,
% 0.18/0.54 (~(tptp_fun_B_4(set_union2(A!18, singleton(A!18))) = tptp_fun_C_3(set_union2(A!18, singleton(A!18))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[360, 284])).
% 0.18/0.54 tff(424,plain,
% 0.18/0.54 (~(tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18)),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.18/0.54 tff(425,plain,
% 0.18/0.54 (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[323, 284])).
% 0.18/0.54 tff(426,plain,
% 0.18/0.54 ((~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), set_union2(A!18, singleton(A!18))) <=> (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))))) | (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[325, 425])).
% 0.18/0.54 tff(427,plain,
% 0.18/0.54 (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18) | in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[426, 321])).
% 0.18/0.54 tff(428,plain,
% 0.18/0.54 (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18)))) <=> in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18)),
% 0.18/0.54 inference(monotonicity,[status(thm)],[417])).
% 0.18/0.54 tff(429,plain,
% 0.18/0.54 ((~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18))))) <=> (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18))),
% 0.18/0.54 inference(monotonicity,[status(thm)],[428])).
% 0.18/0.54 tff(430,plain,
% 0.18/0.54 (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), tptp_fun_B_4(set_union2(A!18, singleton(A!18))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[358, 284])).
% 0.18/0.54 tff(431,plain,
% 0.18/0.54 (~in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), A!18)),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.18/0.54 tff(432,plain,
% 0.18/0.54 (in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[384, 431, 427])).
% 0.18/0.54 tff(433,plain,
% 0.18/0.54 (~(in(tptp_fun_C_3(set_union2(A!18, singleton(A!18))), singleton(A!18)) <=> (tptp_fun_C_3(set_union2(A!18, singleton(A!18))) = A!18))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[386, 432, 424])).
% 0.18/0.54 tff(434,plain,
% 0.18/0.54 ($false),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[301, 54, 433])).
% 0.18/0.54 % SZS output end Proof
% 0.18/0.54 % E exiting
%------------------------------------------------------------------------------