%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM397+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 1.08s 1.30s
% Output : Proof 1.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM397+1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Jun 20 01:01:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 1.08/1.30 % SZS status Theorem
% 1.08/1.30 % SZS output start Proof
% 1.08/1.30 tff(subset_type, type, (
% 1.08/1.30 subset: ( $i * $i ) > $o)).
% 1.08/1.30 tff(tptp_fun_A_19_type, type, (
% 1.08/1.30 tptp_fun_A_19: $i)).
% 1.08/1.30 tff(tptp_fun_D_3_type, type, (
% 1.08/1.30 tptp_fun_D_3: ( $i * $i ) > $i)).
% 1.08/1.30 tff(tptp_fun_B_0_type, type, (
% 1.08/1.30 tptp_fun_B_0: $i > $i)).
% 1.08/1.30 tff(union_type, type, (
% 1.08/1.30 union: $i > $i)).
% 1.08/1.30 tff(element_type, type, (
% 1.08/1.30 element: ( $i * $i ) > $o)).
% 1.08/1.30 tff(powerset_type, type, (
% 1.08/1.30 powerset: $i > $i)).
% 1.08/1.30 tff(in_type, type, (
% 1.08/1.30 in: ( $i * $i ) > $o)).
% 1.08/1.30 tff(epsilon_transitive_type, type, (
% 1.08/1.30 epsilon_transitive: $i > $o)).
% 1.08/1.30 tff(epsilon_connected_type, type, (
% 1.08/1.30 epsilon_connected: $i > $o)).
% 1.08/1.30 tff(tptp_fun_C_1_type, type, (
% 1.08/1.30 tptp_fun_C_1: $i > $i)).
% 1.08/1.30 tff(tptp_fun_B_2_type, type, (
% 1.08/1.30 tptp_fun_B_2: $i > $i)).
% 1.08/1.30 tff(ordinal_type, type, (
% 1.08/1.30 ordinal: $i > $o)).
% 1.08/1.30 tff(tptp_fun_C_4_type, type, (
% 1.08/1.30 tptp_fun_C_4: ( $i * $i ) > $i)).
% 1.08/1.30 tff(tptp_fun_D_5_type, type, (
% 1.08/1.30 tptp_fun_D_5: ( $i * $i ) > $i)).
% 1.08/1.30 tff(empty_set_type, type, (
% 1.08/1.30 empty_set: $i)).
% 1.08/1.30 tff(empty_type, type, (
% 1.08/1.30 empty: $i > $o)).
% 1.08/1.30 tff(relation_type, type, (
% 1.08/1.30 relation: $i > $o)).
% 1.08/1.30 tff(relation_empty_yielding_type, type, (
% 1.08/1.30 relation_empty_yielding: $i > $o)).
% 1.08/1.30 tff(one_to_one_type, type, (
% 1.08/1.30 one_to_one: $i > $o)).
% 1.08/1.30 tff(function_type, type, (
% 1.08/1.30 function: $i > $o)).
% 1.08/1.30 tff(1,plain,
% 1.08/1.30 (^[A: $i] : refl((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 1.08/1.30 inference(bind,[status(th)],[])).
% 1.08/1.30 tff(2,plain,
% 1.08/1.30 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 1.08/1.30 inference(quant_intro,[status(thm)],[1])).
% 1.08/1.30 tff(3,plain,
% 1.08/1.30 (^[A: $i] : rewrite((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))))),
% 1.08/1.30 inference(bind,[status(th)],[])).
% 1.08/1.30 tff(4,plain,
% 1.08/1.30 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 1.08/1.30 inference(quant_intro,[status(thm)],[3])).
% 1.08/1.30 tff(5,plain,
% 1.08/1.30 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 1.08/1.30 inference(transitivity,[status(thm)],[4, 2])).
% 1.08/1.30 tff(6,plain,
% 1.08/1.30 (^[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_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))))), rewrite((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))))),
% 1.08/1.30 inference(bind,[status(th)],[])).
% 1.08/1.30 tff(7,plain,
% 1.08/1.30 (![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 1.08/1.30 inference(quant_intro,[status(thm)],[6])).
% 1.08/1.30 tff(8,plain,
% 1.08/1.30 (![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)))),
% 1.08/1.30 inference(rewrite,[status(thm)],[])).
% 1.08/1.30 tff(9,plain,
% 1.08/1.30 (^[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))))),
% 1.08/1.30 inference(bind,[status(th)],[])).
% 1.08/1.30 tff(10,plain,
% 1.08/1.30 (![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)))),
% 1.08/1.30 inference(quant_intro,[status(thm)],[9])).
% 1.08/1.30 tff(11,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_ordinal1')).
% 1.08/1.30 tff(12,plain,
% 1.08/1.30 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 1.08/1.30 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.08/1.30 tff(13,plain,
% 1.08/1.30 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 1.08/1.30 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.08/1.30 tff(14,plain,(
% 1.08/1.30 ![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))),
% 1.08/1.30 inference(skolemize,[status(sab)],[13])).
% 1.08/1.30 tff(15,plain,
% 1.08/1.30 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 1.08/1.30 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.08/1.30 tff(16,plain,
% 1.08/1.30 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))),
% 1.08/1.30 inference(modus_ponens,[status(thm)],[15, 5])).
% 1.08/1.30 tff(17,plain,
% 1.08/1.30 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(union(A!19))) | ![B: $i] : ((~in(B, union(A!19))) | subset(B, union(A!19))))) | (~(epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))))))))),
% 1.08/1.30 inference(quant_inst,[status(thm)],[])).
% 1.08/1.30 tff(18,plain,
% 1.08/1.30 (~((~((~epsilon_transitive(union(A!19))) | ![B: $i] : ((~in(B, union(A!19))) | subset(B, union(A!19))))) | (~(epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))))))),
% 1.08/1.30 inference(unit_resolution,[status(thm)],[17, 16])).
% 1.08/1.30 tff(19,plain,
% 1.08/1.30 (((~((~epsilon_transitive(union(A!19))) | ![B: $i] : ((~in(B, union(A!19))) | subset(B, union(A!19))))) | (~(epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))))))) | (epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))))),
% 1.08/1.30 inference(tautology,[status(thm)],[])).
% 1.08/1.30 tff(20,plain,
% 1.08/1.30 (epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))))),
% 1.08/1.30 inference(unit_resolution,[status(thm)],[19, 18])).
% 1.08/1.30 tff(21,assumption,((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))))))), introduced(assumption)).
% 1.08/1.30 tff(22,plain,
% 1.08/1.30 (^[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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))))),
% 1.08/1.30 inference(bind,[status(th)],[])).
% 1.08/1.30 tff(23,plain,
% 1.08/1.30 (![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 1.08/1.30 inference(quant_intro,[status(thm)],[22])).
% 1.08/1.30 tff(24,plain,
% 1.08/1.30 (^[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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A)))))))))),
% 1.08/1.30 inference(bind,[status(th)],[])).
% 1.08/1.30 tff(25,plain,
% 1.08/1.30 (![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 1.08/1.30 inference(quant_intro,[status(thm)],[24])).
% 1.08/1.30 tff(26,plain,
% 1.08/1.30 (![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 1.08/1.30 inference(transitivity,[status(thm)],[25, 23])).
% 1.08/1.30 tff(27,plain,
% 1.08/1.30 (^[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_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A))))) <=> (epsilon_connected(A) | (~(in(tptp_fun_B_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(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_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(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_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))))),
% 1.08/1.30 inference(bind,[status(th)],[])).
% 1.08/1.30 tff(28,plain,
% 1.08/1.30 (![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_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 1.08/1.30 inference(quant_intro,[status(thm)],[27])).
% 1.08/1.30 tff(29,plain,
% 1.08/1.30 (![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)))))),
% 1.08/1.30 inference(rewrite,[status(thm)],[])).
% 1.08/1.30 tff(30,plain,
% 1.08/1.30 (^[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))))))),
% 1.08/1.30 inference(bind,[status(th)],[])).
% 1.08/1.30 tff(31,plain,
% 1.08/1.30 (![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)))))),
% 1.08/1.30 inference(quant_intro,[status(thm)],[30])).
% 1.08/1.30 tff(32,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/sandbox2/benchmark/theBenchmark.p','d3_ordinal1')).
% 1.08/1.30 tff(33,plain,
% 1.08/1.30 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 1.08/1.30 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.08/1.30 tff(34,plain,
% 1.08/1.30 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 1.08/1.30 inference(modus_ponens,[status(thm)],[33, 29])).
% 1.08/1.30 tff(35,plain,(
% 1.08/1.30 ![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_2(A), A) & in(tptp_fun_C_1(A), A) & (~in(tptp_fun_B_2(A), tptp_fun_C_1(A))) & (~(tptp_fun_B_2(A) = tptp_fun_C_1(A))) & (~in(tptp_fun_C_1(A), tptp_fun_B_2(A))))))),
% 1.08/1.30 inference(skolemize,[status(sab)],[34])).
% 1.08/1.30 tff(36,plain,
% 1.08/1.30 (![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 1.08/1.30 inference(modus_ponens,[status(thm)],[35, 28])).
% 1.08/1.30 tff(37,plain,
% 1.08/1.30 (![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))),
% 1.08/1.30 inference(modus_ponens,[status(thm)],[36, 26])).
% 1.08/1.30 tff(38,plain,
% 1.08/1.30 (((~![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))))))))) <=> ((~![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))))))))))),
% 1.08/1.30 inference(rewrite,[status(thm)],[])).
% 1.08/1.30 tff(39,plain,
% 1.08/1.30 ((~((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19))))))))) <=> (~((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))))))))),
% 1.08/1.30 inference(rewrite,[status(thm)],[])).
% 1.08/1.30 tff(40,plain,
% 1.08/1.30 (((~![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))))))))) <=> ((~![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))))))))))),
% 1.08/1.30 inference(monotonicity,[status(thm)],[39])).
% 1.08/1.30 tff(41,plain,
% 1.08/1.30 (((~![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))))))))) <=> ((~![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))))))))))),
% 1.08/1.31 inference(transitivity,[status(thm)],[40, 38])).
% 1.08/1.31 tff(42,plain,
% 1.08/1.31 ((~![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~(in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19)))))))))),
% 1.08/1.31 inference(quant_inst,[status(thm)],[])).
% 1.08/1.31 tff(43,plain,
% 1.08/1.31 ((~![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_2(A), tptp_fun_C_1(A)) | (tptp_fun_B_2(A) = tptp_fun_C_1(A)) | in(tptp_fun_C_1(A), tptp_fun_B_2(A)) | (~in(tptp_fun_B_2(A), A)) | (~in(tptp_fun_C_1(A), A))))))))) | (~((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))))))))),
% 1.08/1.31 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.08/1.31 tff(44,plain,
% 1.08/1.31 ($false),
% 1.08/1.31 inference(unit_resolution,[status(thm)],[43, 37, 21])).
% 1.08/1.31 tff(45,plain,(~((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))))))))), inference(lemma,lemma(discharge,[]))).
% 1.08/1.31 tff(46,plain,
% 1.08/1.31 (((~((~epsilon_connected(union(A!19))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(B, union(A!19))) | (~in(C, union(A!19)))))) | (~(epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))))))) | (epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))))))),
% 1.08/1.31 inference(tautology,[status(thm)],[])).
% 1.08/1.31 tff(47,plain,
% 1.08/1.31 (epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))))),
% 1.08/1.31 inference(unit_resolution,[status(thm)],[46, 45])).
% 1.08/1.31 tff(48,plain,
% 1.08/1.31 ((tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) <=> (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19)))),
% 1.08/1.31 inference(commutativity,[status(thm)],[])).
% 1.08/1.31 tff(49,plain,
% 1.08/1.31 ((tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) <=> (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19)))),
% 1.08/1.31 inference(symmetry,[status(thm)],[48])).
% 1.08/1.31 tff(50,plain,
% 1.08/1.31 ((~(tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19)))) <=> (~(tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))))),
% 1.08/1.31 inference(monotonicity,[status(thm)],[49])).
% 1.08/1.31 tff(51,assumption,(~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))))), introduced(assumption)).
% 1.08/1.31 tff(52,plain,
% 1.08/1.31 (((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))) | (~(tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))))),
% 1.08/1.31 inference(tautology,[status(thm)],[])).
% 1.08/1.31 tff(53,plain,
% 1.08/1.31 (~(tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19)))),
% 1.08/1.31 inference(unit_resolution,[status(thm)],[52, 51])).
% 1.08/1.31 tff(54,plain,
% 1.08/1.31 (~(tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19)))),
% 1.08/1.31 inference(modus_ponens,[status(thm)],[53, 50])).
% 1.08/1.31 tff(55,plain,
% 1.08/1.31 (((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))))),
% 1.08/1.31 inference(tautology,[status(thm)],[])).
% 1.08/1.31 tff(56,plain,
% 1.08/1.31 (~in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))),
% 1.08/1.31 inference(unit_resolution,[status(thm)],[55, 51])).
% 1.08/1.31 tff(57,plain,
% 1.08/1.31 (((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))) | (~in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))))),
% 1.08/1.31 inference(tautology,[status(thm)],[])).
% 1.08/1.31 tff(58,plain,
% 1.08/1.31 (~in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19)))),
% 1.08/1.31 inference(unit_resolution,[status(thm)],[57, 51])).
% 1.08/1.31 tff(59,plain,
% 1.08/1.31 (((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))) | in(tptp_fun_B_2(union(A!19)), union(A!19))),
% 1.08/1.31 inference(tautology,[status(thm)],[])).
% 1.08/1.31 tff(60,plain,
% 1.08/1.31 (in(tptp_fun_B_2(union(A!19)), union(A!19))),
% 1.08/1.31 inference(unit_resolution,[status(thm)],[59, 51])).
% 1.08/1.31 tff(61,plain,
% 1.08/1.31 (^[A: $i, B: $i, D_20: $i, C: $i, D: $i] : rewrite((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 1.08/1.31 inference(bind,[status(th)],[])).
% 1.08/1.31 tff(62,plain,
% 1.08/1.31 (![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) <=> ![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))),
% 1.08/1.31 inference(quant_intro,[status(thm)],[61])).
% 1.08/1.31 tff(63,plain,
% 1.08/1.31 (^[A: $i, B: $i, D_20: $i, C: $i, D: $i] : refl((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))))),
% 1.08/1.31 inference(bind,[status(th)],[])).
% 1.08/1.31 tff(64,plain,
% 1.08/1.31 (![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) <=> ![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 1.08/1.31 inference(quant_intro,[status(thm)],[63])).
% 1.08/1.31 tff(65,plain,
% 1.08/1.31 (![A: $i, B: $i] : ![D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) <=> ![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 1.08/1.31 inference(pull_quant,[status(thm)],[])).
% 1.08/1.31 tff(66,plain,
% 1.08/1.31 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant((in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))) <=> ![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))), ((~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))) <=> (~![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))))), pull_quant((~![D: $i] : (in(C, B) | ((~in(C, D)) | (~in(D, A))))) <=> ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))), ((~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))) <=> ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), pull_quant(((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> (~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant((~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i] : ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant(![C: $i] : ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) <=> ((~(B = union(A))) | ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), pull_quant(((~(B = union(A))) | ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))) <=> ![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) <=> ![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), ((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) <=> (~![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))))), pull_quant((~![C: $i, D: $i] : ((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) <=> ?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), ((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) <=> ?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))) <=> ![D: $i] : ((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))), ((~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))) <=> (~![D: $i] : ((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))), pull_quant((~![D: $i] : ((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))), ((~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))), (((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))) <=> ((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))), pull_quant(((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))), (((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))), ((~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))) <=> (~?[D: $i] : ((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))), pull_quant((~?[D: $i] : ((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))), ((~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))) <=> ((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))), pull_quant(((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))) <=> (~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))), pull_quant((~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))) <=> (?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))))), pull_quant((?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))) <=> ?[D_20: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))) <=> ?[D_20: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> (~?[D_20: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))))), pull_quant((~?[D_20: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) <=> ![D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> ![D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))))),
% 1.08/1.31 inference(bind,[status(th)],[])).
% 1.08/1.31 tff(67,plain,
% 1.08/1.31 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> ![A: $i, B: $i] : ![D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 1.08/1.31 inference(quant_intro,[status(thm)],[66])).
% 1.08/1.31 tff(68,plain,
% 1.08/1.31 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> ![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 1.08/1.31 inference(transitivity,[status(thm)],[67, 65])).
% 1.08/1.31 tff(69,plain,
% 1.08/1.31 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> ![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 1.08/1.31 inference(transitivity,[status(thm)],[68, 64])).
% 1.08/1.31 tff(70,plain,
% 1.08/1.31 (^[A: $i, B: $i] : rewrite((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))))),
% 1.08/1.31 inference(bind,[status(th)],[])).
% 1.08/1.31 tff(71,plain,
% 1.08/1.31 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))))),
% 1.08/1.31 inference(quant_intro,[status(thm)],[70])).
% 1.08/1.31 tff(72,plain,
% 1.08/1.31 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))) <=> ![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 1.08/1.31 inference(transitivity,[status(thm)],[71, 69])).
% 1.08/1.31 tff(73,plain,
% 1.08/1.31 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_3(C, A)) & in(tptp_fun_D_3(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) <=> ((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A)) <=> (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A))))), ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) <=> (in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A))))))), rewrite((in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A))))) <=> (in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))), ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) <=> (in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A))))))), rewrite(((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A)))) <=> ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))), (((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A))))) <=> ((in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A))))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))), rewrite(((in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A))))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))) <=> (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))), (((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A))))) <=> (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))), rewrite(((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_3(C, A)) & in(tptp_fun_D_3(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A))))))) <=> (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))))), rewrite((((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_3(C, A)) & in(tptp_fun_D_3(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))))))),
% 1.08/1.31 inference(bind,[status(th)],[])).
% 1.08/1.31 tff(74,plain,
% 1.08/1.31 (![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_3(C, A)) & in(tptp_fun_D_3(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))))),
% 1.08/1.31 inference(quant_intro,[status(thm)],[73])).
% 1.08/1.31 tff(75,plain,
% 1.08/1.31 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A)))) <=> ![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 1.08/1.31 inference(rewrite,[status(thm)],[])).
% 1.08/1.31 tff(76,axiom,(![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_tarski')).
% 1.08/1.31 tff(77,plain,
% 1.08/1.31 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 1.08/1.31 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.08/1.31 tff(78,plain,(
% 1.08/1.31 ![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_3(C, A)) & in(tptp_fun_D_3(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_4(B, A), B) | (in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A)) & in(tptp_fun_D_5(B, A), A))) & ((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_4(B, A), D) & in(D, A)))))))),
% 1.08/1.31 inference(skolemize,[status(sab)],[77])).
% 1.08/1.31 tff(79,plain,
% 1.08/1.31 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_4(B, A), D)))))))))))),
% 1.08/1.31 inference(modus_ponens,[status(thm)],[78, 74])).
% 1.08/1.31 tff(80,plain,
% 1.08/1.31 (![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | ((~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20)))))))))))),
% 1.08/1.31 inference(modus_ponens,[status(thm)],[79, 72])).
% 1.08/1.31 tff(81,plain,
% 1.08/1.31 (![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))),
% 1.08/1.31 inference(modus_ponens,[status(thm)],[80, 62])).
% 1.08/1.31 tff(82,plain,
% 1.08/1.31 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))))))),
% 1.08/1.32 inference(rewrite,[status(thm)],[])).
% 1.08/1.32 tff(83,plain,
% 1.08/1.32 ((~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set)))))))))) <=> (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))))))),
% 1.08/1.32 inference(rewrite,[status(thm)],[])).
% 1.08/1.32 tff(84,plain,
% 1.08/1.32 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))))))),
% 1.08/1.32 inference(monotonicity,[status(thm)],[83])).
% 1.08/1.32 tff(85,plain,
% 1.08/1.32 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))))))),
% 1.08/1.32 inference(transitivity,[status(thm)],[84, 82])).
% 1.08/1.32 tff(86,plain,
% 1.08/1.32 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set))))))))))),
% 1.08/1.32 inference(quant_inst,[status(thm)],[])).
% 1.08/1.32 tff(87,plain,
% 1.08/1.32 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))))))),
% 1.08/1.32 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.08/1.32 tff(88,plain,
% 1.08/1.32 (~((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))))),
% 1.08/1.32 inference(unit_resolution,[status(thm)],[87, 81])).
% 1.08/1.32 tff(89,plain,
% 1.08/1.32 (((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~(in(tptp_fun_B_2(union(A!19)), union(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))))) | ((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))),
% 1.08/1.32 inference(tautology,[status(thm)],[])).
% 1.08/1.32 tff(90,plain,
% 1.08/1.32 ((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19))))),
% 1.08/1.32 inference(unit_resolution,[status(thm)],[89, 88])).
% 1.08/1.32 tff(91,assumption,(in(tptp_fun_B_2(union(A!19)), union(A!19))), introduced(assumption)).
% 1.08/1.32 tff(92,plain,
% 1.08/1.32 ((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19))))),
% 1.08/1.32 inference(tautology,[status(thm)],[])).
% 1.08/1.32 tff(93,plain,
% 1.08/1.32 ((~((~in(tptp_fun_B_2(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19))))),
% 1.08/1.32 inference(unit_resolution,[status(thm)],[92, 91])).
% 1.08/1.32 tff(94,plain,
% 1.08/1.32 (~((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)))),
% 1.08/1.32 inference(unit_resolution,[status(thm)],[93, 90])).
% 1.08/1.32 tff(95,plain,
% 1.08/1.32 (((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19))) | in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)),
% 1.08/1.32 inference(tautology,[status(thm)],[])).
% 1.08/1.32 tff(96,plain,
% 1.08/1.32 (in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)),
% 1.08/1.32 inference(unit_resolution,[status(thm)],[95, 94])).
% 1.08/1.32 tff(97,plain,
% 1.08/1.32 ((~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))) <=> (~![A: $i] : ((~ordinal(A)) | ordinal(union(A))))),
% 1.08/1.32 inference(rewrite,[status(thm)],[])).
% 1.08/1.32 tff(98,plain,
% 1.08/1.32 ((~![A: $i] : (ordinal(A) => ordinal(union(A)))) <=> (~![A: $i] : ((~ordinal(A)) | ordinal(union(A))))),
% 1.08/1.32 inference(rewrite,[status(thm)],[])).
% 1.08/1.32 tff(99,axiom,(~![A: $i] : (ordinal(A) => ordinal(union(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t30_ordinal1')).
% 1.08/1.32 tff(100,plain,
% 1.08/1.32 (~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))),
% 1.08/1.32 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.08/1.32 tff(101,plain,
% 1.08/1.32 (~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))),
% 1.08/1.32 inference(modus_ponens,[status(thm)],[100, 97])).
% 1.08/1.32 tff(102,plain,
% 1.08/1.32 (~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))),
% 1.08/1.32 inference(modus_ponens,[status(thm)],[101, 97])).
% 1.08/1.32 tff(103,plain,
% 1.08/1.32 (~![A: $i] : ((~ordinal(A)) | ordinal(union(A)))),
% 1.08/1.32 inference(modus_ponens,[status(thm)],[102, 97])).
% 1.08/1.32 tff(104,plain,(
% 1.08/1.32 ~((~ordinal(A!19)) | ordinal(union(A!19)))),
% 1.08/1.32 inference(skolemize,[status(sab)],[103])).
% 1.08/1.32 tff(105,plain,
% 1.08/1.32 (ordinal(A!19)),
% 1.08/1.32 inference(or_elim,[status(thm)],[104])).
% 1.08/1.32 tff(106,plain,
% 1.08/1.32 (^[A: $i, B: $i] : refl((ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B))))),
% 1.08/1.32 inference(bind,[status(th)],[])).
% 1.08/1.32 tff(107,plain,
% 1.08/1.32 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 1.08/1.32 inference(quant_intro,[status(thm)],[106])).
% 1.08/1.32 tff(108,plain,
% 1.08/1.32 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 1.08/1.32 inference(rewrite,[status(thm)],[])).
% 1.08/1.32 tff(109,plain,
% 1.08/1.32 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) => ordinal(A)) <=> (ordinal(A) | (~in(A, B)))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> (ordinal(B) => (ordinal(A) | (~in(A, B)))))), rewrite((ordinal(B) => (ordinal(A) | (~in(A, B)))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B)))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> (ordinal(A) | (~in(A, B)) | (~ordinal(B)))))),
% 1.08/1.32 inference(bind,[status(th)],[])).
% 1.08/1.32 tff(110,plain,
% 1.08/1.32 (![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A))) <=> ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 1.08/1.32 inference(quant_intro,[status(thm)],[109])).
% 1.08/1.32 tff(111,axiom,(![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_ordinal1')).
% 1.08/1.32 tff(112,plain,
% 1.08/1.32 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 1.08/1.32 inference(modus_ponens,[status(thm)],[111, 110])).
% 1.08/1.32 tff(113,plain,
% 1.08/1.32 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 1.08/1.32 inference(modus_ponens,[status(thm)],[112, 108])).
% 1.08/1.32 tff(114,plain,(
% 1.08/1.32 ![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 1.08/1.32 inference(skolemize,[status(sab)],[113])).
% 1.08/1.32 tff(115,plain,
% 1.08/1.32 (![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))),
% 1.08/1.32 inference(modus_ponens,[status(thm)],[114, 107])).
% 1.08/1.32 tff(116,plain,
% 1.08/1.32 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)))),
% 1.08/1.32 inference(rewrite,[status(thm)],[])).
% 1.08/1.32 tff(117,plain,
% 1.08/1.32 ((ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | (~ordinal(A!19))) <=> ((~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)))),
% 1.08/1.32 inference(rewrite,[status(thm)],[])).
% 1.08/1.32 tff(118,plain,
% 1.08/1.32 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | (~ordinal(A!19)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))))),
% 1.08/1.32 inference(monotonicity,[status(thm)],[117])).
% 1.08/1.32 tff(119,plain,
% 1.08/1.32 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | (~ordinal(A!19)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)))),
% 1.08/1.32 inference(transitivity,[status(thm)],[118, 116])).
% 1.08/1.32 tff(120,plain,
% 1.08/1.32 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | (~ordinal(A!19)))),
% 1.08/1.32 inference(quant_inst,[status(thm)],[])).
% 1.08/1.32 tff(121,plain,
% 1.08/1.32 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))),
% 1.08/1.32 inference(modus_ponens,[status(thm)],[120, 119])).
% 1.08/1.32 tff(122,plain,
% 1.08/1.32 (ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))),
% 1.08/1.32 inference(unit_resolution,[status(thm)],[121, 115, 105, 96])).
% 1.08/1.32 tff(123,plain,
% 1.08/1.32 (((~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19), A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))),
% 1.08/1.32 inference(tautology,[status(thm)],[])).
% 1.08/1.32 tff(124,plain,
% 1.08/1.32 (in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))),
% 1.08/1.32 inference(unit_resolution,[status(thm)],[123, 94])).
% 1.08/1.32 tff(125,assumption,(~ordinal(tptp_fun_B_2(union(A!19)))), introduced(assumption)).
% 1.08/1.32 tff(126,plain,
% 1.08/1.32 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ordinal(tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))))),
% 1.08/1.32 inference(rewrite,[status(thm)],[])).
% 1.08/1.32 tff(127,plain,
% 1.08/1.32 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))))),
% 1.08/1.32 inference(quant_inst,[status(thm)],[])).
% 1.08/1.32 tff(128,plain,
% 1.08/1.32 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ordinal(tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_B_2(union(A!19)), A!19)))),
% 1.08/1.32 inference(modus_ponens,[status(thm)],[127, 126])).
% 1.08/1.32 tff(129,plain,
% 1.08/1.32 ($false),
% 1.08/1.32 inference(unit_resolution,[status(thm)],[128, 115, 125, 124, 122])).
% 1.08/1.32 tff(130,plain,(ordinal(tptp_fun_B_2(union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19)))), inference(lemma,lemma(discharge,[]))).
% 1.08/1.32 tff(131,plain,
% 1.08/1.32 (ordinal(tptp_fun_B_2(union(A!19)))),
% 1.08/1.32 inference(unit_resolution,[status(thm)],[130, 60])).
% 1.08/1.32 tff(132,assumption,(![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))), introduced(assumption)).
% 1.08/1.32 tff(133,assumption,(~(tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19)))), introduced(assumption)).
% 1.08/1.32 tff(134,assumption,(~in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))), introduced(assumption)).
% 1.08/1.32 tff(135,assumption,(~in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19)))), introduced(assumption)).
% 1.08/1.32 tff(136,assumption,(ordinal(tptp_fun_B_2(union(A!19)))), introduced(assumption)).
% 1.08/1.32 tff(137,plain,
% 1.08/1.32 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))) | (in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) | (~ordinal(tptp_fun_B_2(union(A!19)))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) | (~ordinal(tptp_fun_B_2(union(A!19)))))),
% 1.08/1.32 inference(rewrite,[status(thm)],[])).
% 1.08/1.32 tff(138,plain,
% 1.08/1.32 (((~ordinal(tptp_fun_B_2(union(A!19)))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19)))) <=> (in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) | (~ordinal(tptp_fun_B_2(union(A!19)))))),
% 1.08/1.32 inference(rewrite,[status(thm)],[])).
% 1.08/1.32 tff(139,plain,
% 1.08/1.32 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))) | ((~ordinal(tptp_fun_B_2(union(A!19)))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))) | (in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) | (~ordinal(tptp_fun_B_2(union(A!19))))))),
% 1.08/1.32 inference(monotonicity,[status(thm)],[138])).
% 1.08/1.32 tff(140,plain,
% 1.08/1.32 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))) | ((~ordinal(tptp_fun_B_2(union(A!19)))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) | (~ordinal(tptp_fun_B_2(union(A!19)))))),
% 1.08/1.32 inference(transitivity,[status(thm)],[139, 137])).
% 1.08/1.32 tff(141,plain,
% 1.08/1.32 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))) | ((~ordinal(tptp_fun_B_2(union(A!19)))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))))),
% 1.08/1.32 inference(quant_inst,[status(thm)],[])).
% 1.08/1.32 tff(142,plain,
% 1.08/1.32 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19))) | (~ordinal(tptp_fun_B_2(union(A!19))))),
% 1.08/1.32 inference(modus_ponens,[status(thm)],[141, 140])).
% 1.08/1.32 tff(143,plain,
% 1.08/1.32 ($false),
% 1.08/1.32 inference(unit_resolution,[status(thm)],[142, 136, 135, 134, 133, 132])).
% 1.08/1.32 tff(144,plain,((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))) | (~ordinal(tptp_fun_B_2(union(A!19)))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))) | (tptp_fun_C_1(union(A!19)) = tptp_fun_B_2(union(A!19)))), inference(lemma,lemma(discharge,[]))).
% 1.08/1.32 tff(145,plain,
% 1.08/1.32 (~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))),
% 1.08/1.32 inference(unit_resolution,[status(thm)],[144, 131, 58, 56, 54])).
% 1.08/1.32 tff(146,plain,
% 1.08/1.32 (((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))) | in(tptp_fun_C_1(union(A!19)), union(A!19))),
% 1.08/1.32 inference(tautology,[status(thm)],[])).
% 1.08/1.32 tff(147,plain,
% 1.08/1.32 (in(tptp_fun_C_1(union(A!19)), union(A!19))),
% 1.08/1.32 inference(unit_resolution,[status(thm)],[146, 51])).
% 1.08/1.32 tff(148,assumption,((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set))))), introduced(assumption)).
% 1.08/1.32 tff(149,plain,
% 1.08/1.32 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))))))),
% 1.08/1.32 inference(rewrite,[status(thm)],[])).
% 1.08/1.32 tff(150,plain,
% 1.08/1.32 ((~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_C_1(union(A!19)), empty_set)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(empty_set, A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set)))))))))) <=> (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set))))))),
% 1.08/1.32 inference(rewrite,[status(thm)],[])).
% 1.08/1.32 tff(151,plain,
% 1.08/1.32 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_C_1(union(A!19)), empty_set)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(empty_set, A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))))))),
% 1.17/1.32 inference(monotonicity,[status(thm)],[150])).
% 1.17/1.32 tff(152,plain,
% 1.17/1.32 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_C_1(union(A!19)), empty_set)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(empty_set, A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))))))),
% 1.17/1.32 inference(transitivity,[status(thm)],[151, 149])).
% 1.17/1.32 tff(153,plain,
% 1.17/1.32 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_C_1(union(A!19)), empty_set)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(empty_set, A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(empty_set, A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), empty_set))))))))))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(154,plain,
% 1.17/1.33 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set))))))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[153, 152])).
% 1.17/1.33 tff(155,plain,
% 1.17/1.33 ($false),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[154, 81, 148])).
% 1.17/1.33 tff(156,plain,(~((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set)))))), inference(lemma,lemma(discharge,[]))).
% 1.17/1.33 tff(157,plain,
% 1.17/1.33 (((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~((~in(empty_set, A!19)) | in(tptp_fun_C_1(union(A!19)), union(A!19)) | (~in(tptp_fun_C_1(union(A!19)), empty_set))))) | ((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))),
% 1.17/1.33 inference(tautology,[status(thm)],[])).
% 1.17/1.33 tff(158,plain,
% 1.17/1.33 ((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[157, 156])).
% 1.17/1.33 tff(159,plain,
% 1.17/1.33 ((~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))))) | (~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))))),
% 1.17/1.33 inference(tautology,[status(thm)],[])).
% 1.17/1.33 tff(160,plain,
% 1.17/1.33 ((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[159, 158])).
% 1.17/1.33 tff(161,plain,
% 1.17/1.33 (~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[160, 147])).
% 1.17/1.33 tff(162,assumption,(~((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)))), introduced(assumption)).
% 1.17/1.33 tff(163,plain,
% 1.17/1.33 (((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))) | in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)),
% 1.17/1.33 inference(tautology,[status(thm)],[])).
% 1.17/1.33 tff(164,plain,
% 1.17/1.33 (in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[163, 162])).
% 1.17/1.33 tff(165,plain,
% 1.17/1.33 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(166,plain,
% 1.17/1.33 ((ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~ordinal(A!19))) <=> ((~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(167,plain,
% 1.17/1.33 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~ordinal(A!19)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ((~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[166])).
% 1.17/1.33 tff(168,plain,
% 1.17/1.33 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~ordinal(A!19)))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[167, 165])).
% 1.17/1.33 tff(169,plain,
% 1.17/1.33 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | (~ordinal(A!19)))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(170,plain,
% 1.17/1.33 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (~ordinal(A!19)) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19)) | ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[169, 168])).
% 1.17/1.33 tff(171,plain,
% 1.17/1.33 (ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[170, 115, 105, 164])).
% 1.17/1.33 tff(172,plain,
% 1.17/1.33 (((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))),
% 1.17/1.33 inference(tautology,[status(thm)],[])).
% 1.17/1.33 tff(173,plain,
% 1.17/1.33 (in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[172, 162])).
% 1.17/1.33 tff(174,assumption,(~ordinal(tptp_fun_C_1(union(A!19)))), introduced(assumption)).
% 1.17/1.33 tff(175,plain,
% 1.17/1.33 (((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_1(union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))) <=> ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ordinal(tptp_fun_C_1(union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(176,plain,
% 1.17/1.33 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | (ordinal(tptp_fun_C_1(union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(177,plain,
% 1.17/1.33 ((~![A: $i, B: $i] : (ordinal(A) | (~in(A, B)) | (~ordinal(B)))) | ordinal(tptp_fun_C_1(union(A!19))) | (~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~ordinal(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19)))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.17/1.33 tff(178,plain,
% 1.17/1.33 ($false),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[177, 115, 174, 173, 171])).
% 1.17/1.33 tff(179,plain,(((~in(tptp_fun_C_1(union(A!19)), tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_C_1(union(A!19)), A!19), A!19))) | ordinal(tptp_fun_C_1(union(A!19)))), inference(lemma,lemma(discharge,[]))).
% 1.17/1.33 tff(180,plain,
% 1.17/1.33 (ordinal(tptp_fun_C_1(union(A!19)))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[179, 161])).
% 1.17/1.33 tff(181,plain,
% 1.17/1.33 (^[A: $i] : refl(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 1.17/1.33 inference(bind,[status(th)],[])).
% 1.17/1.33 tff(182,plain,
% 1.17/1.33 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 1.17/1.33 inference(quant_intro,[status(thm)],[181])).
% 1.17/1.33 tff(183,plain,
% 1.17/1.33 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 1.17/1.33 inference(bind,[status(th)],[])).
% 1.17/1.33 tff(184,plain,
% 1.17/1.33 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 1.17/1.33 inference(quant_intro,[status(thm)],[183])).
% 1.17/1.33 tff(185,plain,
% 1.17/1.33 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 1.17/1.33 inference(transitivity,[status(thm)],[184, 182])).
% 1.17/1.33 tff(186,plain,
% 1.17/1.33 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 1.17/1.33 inference(bind,[status(th)],[])).
% 1.17/1.33 tff(187,plain,
% 1.17/1.33 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 1.17/1.33 inference(quant_intro,[status(thm)],[186])).
% 1.17/1.33 tff(188,plain,
% 1.17/1.33 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(189,plain,
% 1.17/1.33 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))) <=> (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> (ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), rewrite((ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), (![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> (ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), rewrite((ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))))),
% 1.17/1.33 inference(bind,[status(th)],[])).
% 1.17/1.33 tff(190,plain,
% 1.17/1.33 (![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 1.17/1.33 inference(quant_intro,[status(thm)],[189])).
% 1.17/1.33 tff(191,axiom,(![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_ordinal1')).
% 1.17/1.33 tff(192,plain,
% 1.17/1.33 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[191, 190])).
% 1.17/1.33 tff(193,plain,
% 1.17/1.33 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[192, 188])).
% 1.17/1.33 tff(194,plain,(
% 1.17/1.33 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 1.17/1.33 inference(skolemize,[status(sab)],[193])).
% 1.17/1.33 tff(195,plain,
% 1.17/1.33 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[194, 187])).
% 1.17/1.33 tff(196,plain,
% 1.17/1.33 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[195, 185])).
% 1.17/1.33 tff(197,plain,
% 1.17/1.33 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(198,plain,
% 1.17/1.33 (((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : (in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(199,plain,
% 1.17/1.33 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : (in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[198])).
% 1.17/1.33 tff(200,plain,
% 1.17/1.33 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : (in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B)))),
% 1.17/1.33 inference(transitivity,[status(thm)],[199, 197])).
% 1.17/1.33 tff(201,plain,
% 1.17/1.33 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : (in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B) | (~ordinal(B))))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(202,plain,
% 1.17/1.33 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(union(A!19)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!19))) | in(tptp_fun_C_1(union(A!19)), B) | (tptp_fun_C_1(union(A!19)) = B))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[201, 200])).
% 1.17/1.33 tff(203,plain,
% 1.17/1.33 ($false),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[202, 196, 180, 145])).
% 1.17/1.33 tff(204,plain,((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))), inference(lemma,lemma(discharge,[]))).
% 1.17/1.33 tff(205,plain,
% 1.17/1.33 ((~(epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))))))) | epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19)))))),
% 1.17/1.33 inference(tautology,[status(thm)],[])).
% 1.17/1.33 tff(206,plain,
% 1.17/1.33 ((~(epsilon_connected(union(A!19)) | (~((~in(tptp_fun_C_1(union(A!19)), union(A!19))) | (~in(tptp_fun_B_2(union(A!19)), union(A!19))) | in(tptp_fun_C_1(union(A!19)), tptp_fun_B_2(union(A!19))) | (tptp_fun_B_2(union(A!19)) = tptp_fun_C_1(union(A!19))) | in(tptp_fun_B_2(union(A!19)), tptp_fun_C_1(union(A!19))))))) | epsilon_connected(union(A!19))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[205, 204])).
% 1.17/1.33 tff(207,plain,
% 1.17/1.33 (epsilon_connected(union(A!19))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[206, 47])).
% 1.17/1.33 tff(208,plain,
% 1.17/1.33 (^[A: $i] : refl((~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))))),
% 1.17/1.33 inference(bind,[status(th)],[])).
% 1.17/1.33 tff(209,plain,
% 1.17/1.33 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 1.17/1.33 inference(quant_intro,[status(thm)],[208])).
% 1.17/1.33 tff(210,plain,
% 1.17/1.33 (^[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)))))),
% 1.17/1.33 inference(bind,[status(th)],[])).
% 1.17/1.33 tff(211,plain,
% 1.17/1.33 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 1.17/1.33 inference(quant_intro,[status(thm)],[210])).
% 1.17/1.33 tff(212,plain,
% 1.17/1.33 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(213,axiom,(![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_ordinal1')).
% 1.17/1.33 tff(214,plain,
% 1.17/1.33 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[213, 212])).
% 1.17/1.33 tff(215,plain,(
% 1.17/1.33 ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 1.17/1.33 inference(skolemize,[status(sab)],[214])).
% 1.17/1.33 tff(216,plain,
% 1.17/1.33 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[215, 211])).
% 1.17/1.33 tff(217,plain,
% 1.17/1.33 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 1.17/1.33 inference(modus_ponens,[status(thm)],[216, 209])).
% 1.17/1.33 tff(218,plain,
% 1.17/1.33 ((~![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))) | (~(((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19)))) <=> ordinal(union(A!19))))),
% 1.17/1.33 inference(quant_inst,[status(thm)],[])).
% 1.17/1.33 tff(219,plain,
% 1.17/1.33 (~(((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19)))) <=> ordinal(union(A!19)))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[218, 217])).
% 1.17/1.33 tff(220,plain,
% 1.17/1.33 (~ordinal(union(A!19))),
% 1.17/1.33 inference(or_elim,[status(thm)],[104])).
% 1.17/1.33 tff(221,plain,
% 1.17/1.33 ((((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19)))) <=> ordinal(union(A!19))) | ((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19)))) | ordinal(union(A!19))),
% 1.17/1.33 inference(tautology,[status(thm)],[])).
% 1.17/1.33 tff(222,plain,
% 1.17/1.33 ((((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19)))) <=> ordinal(union(A!19))) | ((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19))))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[221, 220])).
% 1.17/1.33 tff(223,plain,
% 1.17/1.33 ((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19)))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[222, 219])).
% 1.17/1.33 tff(224,plain,
% 1.17/1.33 ((~((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19))))) | (~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19)))),
% 1.17/1.33 inference(tautology,[status(thm)],[])).
% 1.17/1.33 tff(225,plain,
% 1.17/1.33 ((~epsilon_transitive(union(A!19))) | (~epsilon_connected(union(A!19)))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[224, 223])).
% 1.17/1.33 tff(226,plain,
% 1.17/1.33 (~epsilon_transitive(union(A!19))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[225, 207])).
% 1.17/1.33 tff(227,plain,
% 1.17/1.33 ((~(epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))))) | epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))))),
% 1.17/1.33 inference(tautology,[status(thm)],[])).
% 1.17/1.33 tff(228,plain,
% 1.17/1.33 ((~(epsilon_transitive(union(A!19)) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[227, 226])).
% 1.17/1.33 tff(229,plain,
% 1.17/1.33 (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[228, 20])).
% 1.17/1.33 tff(230,plain,
% 1.17/1.33 (((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19))),
% 1.17/1.33 inference(tautology,[status(thm)],[])).
% 1.17/1.33 tff(231,plain,
% 1.17/1.33 (in(tptp_fun_B_0(union(A!19)), union(A!19))),
% 1.17/1.33 inference(unit_resolution,[status(thm)],[230, 229])).
% 1.17/1.33 tff(232,plain,
% 1.17/1.33 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | ((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(233,plain,
% 1.17/1.33 ((~(~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))))))) <=> ((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(234,plain,
% 1.17/1.33 (((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | $false) <=> (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))))))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(235,plain,
% 1.17/1.33 ((~$true) <=> $false),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(236,plain,
% 1.17/1.33 (($true | (~((~((~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))) | (~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19))))))))) <=> $true),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(237,plain,
% 1.17/1.33 ((~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))))) <=> (~((~((~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))) | (~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19))))))))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(238,plain,
% 1.17/1.33 ((union(A!19) = union(A!19)) <=> $true),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(239,plain,
% 1.17/1.33 (((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))) <=> ($true | (~((~((~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))) | (~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[238, 237])).
% 1.17/1.33 tff(240,plain,
% 1.17/1.33 (((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))) <=> $true),
% 1.17/1.33 inference(transitivity,[status(thm)],[239, 236])).
% 1.17/1.33 tff(241,plain,
% 1.17/1.33 ((~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))))))) <=> (~$true)),
% 1.17/1.33 inference(monotonicity,[status(thm)],[240])).
% 1.17/1.33 tff(242,plain,
% 1.17/1.33 ((~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))))))) <=> $false),
% 1.17/1.33 inference(transitivity,[status(thm)],[241, 235])).
% 1.17/1.33 tff(243,plain,
% 1.17/1.33 ((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) <=> (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))))))),
% 1.17/1.33 inference(rewrite,[status(thm)],[])).
% 1.17/1.33 tff(244,plain,
% 1.17/1.33 (((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))))) <=> ((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | $false)),
% 1.17/1.33 inference(monotonicity,[status(thm)],[243, 242])).
% 1.17/1.33 tff(245,plain,
% 1.17/1.33 (((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))))) <=> (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))))))),
% 1.17/1.33 inference(transitivity,[status(thm)],[244, 234])).
% 1.17/1.33 tff(246,plain,
% 1.17/1.33 ((~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))))))))) <=> (~(~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[245])).
% 1.17/1.33 tff(247,plain,
% 1.17/1.33 ((~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))))))))))) <=> ((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))),
% 1.17/1.33 inference(transitivity,[status(thm)],[246, 233])).
% 1.17/1.33 tff(248,plain,
% 1.17/1.33 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | ((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))))))),
% 1.17/1.33 inference(monotonicity,[status(thm)],[247])).
% 1.17/1.33 tff(249,plain,
% 1.17/1.33 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))),
% 1.17/1.34 inference(transitivity,[status(thm)],[248, 232])).
% 1.17/1.34 tff(250,plain,
% 1.17/1.34 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(A!19))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))))) | (~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(union(A!19), A!19)))))))) | (~((union(A!19) = union(A!19)) | (~((~(in(tptp_fun_C_4(union(A!19), A!19), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), A!19), tptp_fun_D_5(union(A!19), A!19))) | (~in(tptp_fun_D_5(union(A!19), A!19), A!19)))))) | (~((~in(tptp_fun_C_4(union(A!19), A!19), union(A!19))) | (~in(union(A!19), A!19)) | (~in(tptp_fun_C_4(union(A!19), A!19), union(A!19)))))))))))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(251,plain,
% 1.17/1.34 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[250, 249])).
% 1.17/1.34 tff(252,plain,
% 1.17/1.34 (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[251, 81, 231])).
% 1.17/1.34 tff(253,plain,
% 1.17/1.34 (((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))) | in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))),
% 1.17/1.34 inference(tautology,[status(thm)],[])).
% 1.17/1.34 tff(254,plain,
% 1.17/1.34 (in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[253, 252])).
% 1.17/1.34 tff(255,assumption,(A!19 = empty_set), introduced(assumption)).
% 1.17/1.34 tff(256,plain,
% 1.17/1.34 (union(A!19) = union(empty_set)),
% 1.17/1.34 inference(monotonicity,[status(thm)],[255])).
% 1.17/1.34 tff(257,plain,
% 1.17/1.34 (tptp_fun_B_0(union(A!19)) = tptp_fun_B_0(union(empty_set))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[256])).
% 1.17/1.34 tff(258,plain,
% 1.17/1.34 (tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set) = tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set)),
% 1.17/1.34 inference(monotonicity,[status(thm)],[257])).
% 1.17/1.34 tff(259,plain,
% 1.17/1.34 (in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set) <=> in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set)),
% 1.17/1.34 inference(monotonicity,[status(thm)],[258])).
% 1.17/1.34 tff(260,plain,
% 1.17/1.34 (in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set) <=> in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)),
% 1.17/1.34 inference(symmetry,[status(thm)],[259])).
% 1.17/1.34 tff(261,plain,
% 1.17/1.34 ((~in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set)) <=> (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[260])).
% 1.17/1.34 tff(262,assumption,(in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set)), introduced(assumption)).
% 1.17/1.34 tff(263,plain,
% 1.17/1.34 (^[A: $i, B: $i] : refl(((~in(A, B)) | (~empty(B))) <=> ((~in(A, B)) | (~empty(B))))),
% 1.17/1.34 inference(bind,[status(th)],[])).
% 1.17/1.34 tff(264,plain,
% 1.17/1.34 (![A: $i, B: $i] : ((~in(A, B)) | (~empty(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))),
% 1.17/1.34 inference(quant_intro,[status(thm)],[263])).
% 1.17/1.34 tff(265,plain,
% 1.17/1.34 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~in(A, B)) | (~empty(B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~in(A, B)) | (~empty(B))))))), rewrite((~(~((~in(A, B)) | (~empty(B))))) <=> ((~in(A, B)) | (~empty(B)))), ((~(in(A, B) & empty(B))) <=> ((~in(A, B)) | (~empty(B)))))),
% 1.17/1.34 inference(bind,[status(th)],[])).
% 1.17/1.34 tff(266,plain,
% 1.17/1.34 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))),
% 1.17/1.34 inference(quant_intro,[status(thm)],[265])).
% 1.17/1.34 tff(267,plain,
% 1.17/1.34 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(268,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_boole')).
% 1.17/1.34 tff(269,plain,
% 1.17/1.34 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[268, 267])).
% 1.17/1.34 tff(270,plain,(
% 1.17/1.34 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 1.17/1.34 inference(skolemize,[status(sab)],[269])).
% 1.17/1.34 tff(271,plain,
% 1.17/1.34 (![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[270, 266])).
% 1.17/1.34 tff(272,plain,
% 1.17/1.34 (![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[271, 264])).
% 1.17/1.34 tff(273,plain,
% 1.17/1.34 (empty(empty_set) <=> empty(empty_set)),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(274,axiom,((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc12_relat_1')).
% 1.17/1.34 tff(275,plain,
% 1.17/1.34 (empty(empty_set) & relation(empty_set)),
% 1.17/1.34 inference(and_elim,[status(thm)],[274])).
% 1.17/1.34 tff(276,plain,
% 1.17/1.34 (empty(empty_set)),
% 1.17/1.34 inference(and_elim,[status(thm)],[275])).
% 1.17/1.34 tff(277,plain,
% 1.17/1.34 (empty(empty_set)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[276, 273])).
% 1.17/1.34 tff(278,plain,
% 1.17/1.34 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(279,plain,
% 1.17/1.34 (((~in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set)) | (~empty(empty_set))) <=> ((~empty(empty_set)) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(280,plain,
% 1.17/1.34 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set)) | (~empty(empty_set)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[279])).
% 1.17/1.34 tff(281,plain,
% 1.17/1.34 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set)) | (~empty(empty_set)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set)))),
% 1.17/1.34 inference(transitivity,[status(thm)],[280, 278])).
% 1.17/1.34 tff(282,plain,
% 1.17/1.34 ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set)) | (~empty(empty_set)))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(283,plain,
% 1.17/1.34 ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[282, 281])).
% 1.17/1.34 tff(284,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[283, 277, 272, 262])).
% 1.17/1.34 tff(285,plain,(~in(tptp_fun_D_3(tptp_fun_B_0(union(empty_set)), empty_set), empty_set)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(286,plain,
% 1.17/1.34 (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[285, 261])).
% 1.17/1.34 tff(287,plain,
% 1.17/1.34 (((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))) | in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)),
% 1.17/1.34 inference(tautology,[status(thm)],[])).
% 1.17/1.34 tff(288,plain,
% 1.17/1.34 ((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[287, 286])).
% 1.17/1.34 tff(289,plain,
% 1.17/1.34 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))))))) | (~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))))))) | (~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set)))))))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(290,plain,
% 1.17/1.34 ((~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(A!19, empty_set)))))))) | (~((union(A!19) = union(empty_set)) | (~((~(in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))))) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)))))))))) <=> (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))))))) | (~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set))))))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(291,plain,
% 1.17/1.34 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(A!19, empty_set)))))))) | (~((union(A!19) = union(empty_set)) | (~((~(in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))))) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))))))) | (~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set)))))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[290])).
% 1.17/1.34 tff(292,plain,
% 1.17/1.34 (((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(A!19, empty_set)))))))) | (~((union(A!19) = union(empty_set)) | (~((~(in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))))) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19))))))))))) <=> ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))))))) | (~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set)))))))),
% 1.17/1.34 inference(transitivity,[status(thm)],[291, 289])).
% 1.17/1.34 tff(293,plain,
% 1.17/1.34 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(A!19, empty_set)))))))) | (~((union(A!19) = union(empty_set)) | (~((~(in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))))) | (~((~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19))))))))))),
% 1.17/1.34 inference(quant_inst,[status(thm)],[])).
% 1.17/1.34 tff(294,plain,
% 1.17/1.34 ((~![A: $i, B: $i, D_20: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_3(C, A))) | (~in(tptp_fun_D_3(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_4(B, A), B) | (~((~in(tptp_fun_C_4(B, A), tptp_fun_D_5(B, A))) | (~in(tptp_fun_D_5(B, A), A)))))) | (~((~in(tptp_fun_C_4(B, A), B)) | (~in(D_20, A)) | (~in(tptp_fun_C_4(B, A), D_20))))))))))) | (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))))))) | (~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set))))))),
% 1.17/1.34 inference(modus_ponens,[status(thm)],[293, 292])).
% 1.17/1.34 tff(295,plain,
% 1.17/1.34 (~((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))))))) | (~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set)))))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[294, 81])).
% 1.17/1.34 tff(296,plain,
% 1.17/1.34 (((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))))))) | (~((~((~((~in(A!19, empty_set)) | (~in(tptp_fun_C_4(union(A!19), empty_set), union(A!19))) | (~in(tptp_fun_C_4(union(A!19), empty_set), A!19)))) | (~((~((~in(tptp_fun_C_4(union(A!19), empty_set), tptp_fun_D_5(union(A!19), empty_set))) | (~in(tptp_fun_D_5(union(A!19), empty_set), empty_set)))) | in(tptp_fun_C_4(union(A!19), empty_set), union(A!19)))))) | (union(A!19) = union(empty_set))))) | ((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))))))),
% 1.17/1.34 inference(tautology,[status(thm)],[])).
% 1.17/1.34 tff(297,plain,
% 1.17/1.34 ((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19))))))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[296, 295])).
% 1.17/1.34 tff(298,plain,
% 1.17/1.34 ((~((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))))))) | (~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19))))))),
% 1.17/1.34 inference(tautology,[status(thm)],[])).
% 1.17/1.34 tff(299,plain,
% 1.17/1.34 ((~(union(A!19) = union(empty_set))) | (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19))))))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[298, 297])).
% 1.17/1.34 tff(300,plain,
% 1.17/1.34 (~((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19)))))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[299, 256])).
% 1.17/1.34 tff(301,plain,
% 1.17/1.34 (((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(A!19, empty_set)) | in(tptp_fun_B_0(union(A!19)), union(A!19)) | (~in(tptp_fun_B_0(union(A!19)), A!19))))) | ((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))),
% 1.17/1.34 inference(tautology,[status(thm)],[])).
% 1.17/1.34 tff(302,plain,
% 1.17/1.34 ((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[301, 300])).
% 1.17/1.34 tff(303,plain,
% 1.17/1.34 ((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))),
% 1.17/1.34 inference(tautology,[status(thm)],[])).
% 1.17/1.34 tff(304,plain,
% 1.17/1.34 ((~((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set)))))) | (~((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), empty_set), empty_set))))),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[303, 231])).
% 1.17/1.34 tff(305,plain,
% 1.17/1.34 ($false),
% 1.17/1.34 inference(unit_resolution,[status(thm)],[304, 302, 288])).
% 1.17/1.34 tff(306,plain,(~(A!19 = empty_set)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.34 tff(307,assumption,(in(A!19, empty_set)), introduced(assumption)).
% 1.17/1.34 tff(308,plain,
% 1.17/1.34 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~empty(empty_set)) | (~in(A!19, empty_set)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(empty_set)) | (~in(A!19, empty_set)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(309,plain,
% 1.17/1.34 (((~in(A!19, empty_set)) | (~empty(empty_set))) <=> ((~empty(empty_set)) | (~in(A!19, empty_set)))),
% 1.17/1.34 inference(rewrite,[status(thm)],[])).
% 1.17/1.34 tff(310,plain,
% 1.17/1.34 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(A!19, empty_set)) | (~empty(empty_set)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~empty(empty_set)) | (~in(A!19, empty_set))))),
% 1.17/1.34 inference(monotonicity,[status(thm)],[309])).
% 1.17/1.34 tff(311,plain,
% 1.17/1.34 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(A!19, empty_set)) | (~empty(empty_set)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(empty_set)) | (~in(A!19, empty_set)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[310, 308])).
% 1.17/1.35 tff(312,plain,
% 1.17/1.35 ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(A!19, empty_set)) | (~empty(empty_set)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(313,plain,
% 1.17/1.35 ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(empty_set)) | (~in(A!19, empty_set))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[312, 311])).
% 1.17/1.35 tff(314,plain,
% 1.17/1.35 ($false),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[313, 277, 272, 307])).
% 1.17/1.35 tff(315,plain,(~in(A!19, empty_set)), inference(lemma,lemma(discharge,[]))).
% 1.17/1.35 tff(316,plain,
% 1.17/1.35 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!19)) | ![B: $i] : ((~ordinal(B)) | in(B, A!19) | in(A!19, B) | (A!19 = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(A!19)) | ![B: $i] : ((~ordinal(B)) | in(B, A!19) | in(A!19, B) | (A!19 = B)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(317,plain,
% 1.17/1.35 (((~ordinal(A!19)) | ![B: $i] : (in(B, A!19) | in(A!19, B) | (A!19 = B) | (~ordinal(B)))) <=> ((~ordinal(A!19)) | ![B: $i] : ((~ordinal(B)) | in(B, A!19) | in(A!19, B) | (A!19 = B)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(318,plain,
% 1.17/1.35 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!19)) | ![B: $i] : (in(B, A!19) | in(A!19, B) | (A!19 = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!19)) | ![B: $i] : ((~ordinal(B)) | in(B, A!19) | in(A!19, B) | (A!19 = B))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[317])).
% 1.17/1.35 tff(319,plain,
% 1.17/1.35 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!19)) | ![B: $i] : (in(B, A!19) | in(A!19, B) | (A!19 = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(A!19)) | ![B: $i] : ((~ordinal(B)) | in(B, A!19) | in(A!19, B) | (A!19 = B)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[318, 316])).
% 1.17/1.35 tff(320,plain,
% 1.17/1.35 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!19)) | ![B: $i] : (in(B, A!19) | in(A!19, B) | (A!19 = B) | (~ordinal(B))))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(321,plain,
% 1.17/1.35 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(A!19)) | ![B: $i] : ((~ordinal(B)) | in(B, A!19) | in(A!19, B) | (A!19 = B))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[320, 319])).
% 1.17/1.35 tff(322,plain,
% 1.17/1.35 (![B: $i] : ((~ordinal(B)) | in(B, A!19) | in(A!19, B) | (A!19 = B))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[321, 196, 105])).
% 1.17/1.35 tff(323,plain,
% 1.17/1.35 (ordinal(empty_set) <=> ordinal(empty_set)),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(324,axiom,(((((((relation(empty_set) & relation_empty_yielding(empty_set)) & function(empty_set)) & one_to_one(empty_set)) & empty(empty_set)) & epsilon_transitive(empty_set)) & epsilon_connected(empty_set)) & ordinal(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_ordinal1')).
% 1.17/1.35 tff(325,plain,
% 1.17/1.35 (ordinal(empty_set)),
% 1.17/1.35 inference(and_elim,[status(thm)],[324])).
% 1.17/1.35 tff(326,plain,
% 1.17/1.35 (ordinal(empty_set)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[325, 323])).
% 1.17/1.35 tff(327,plain,
% 1.17/1.35 (((~![B: $i] : ((~ordinal(B)) | in(B, A!19) | in(A!19, B) | (A!19 = B))) | ((~ordinal(empty_set)) | in(empty_set, A!19) | in(A!19, empty_set) | (A!19 = empty_set))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, A!19) | in(A!19, B) | (A!19 = B))) | (~ordinal(empty_set)) | in(empty_set, A!19) | in(A!19, empty_set) | (A!19 = empty_set))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(328,plain,
% 1.17/1.35 ((~![B: $i] : ((~ordinal(B)) | in(B, A!19) | in(A!19, B) | (A!19 = B))) | ((~ordinal(empty_set)) | in(empty_set, A!19) | in(A!19, empty_set) | (A!19 = empty_set))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(329,plain,
% 1.17/1.35 ((~![B: $i] : ((~ordinal(B)) | in(B, A!19) | in(A!19, B) | (A!19 = B))) | (~ordinal(empty_set)) | in(empty_set, A!19) | in(A!19, empty_set) | (A!19 = empty_set)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[328, 327])).
% 1.17/1.35 tff(330,plain,
% 1.17/1.35 (in(empty_set, A!19) | in(A!19, empty_set) | (A!19 = empty_set)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[329, 326, 322])).
% 1.17/1.35 tff(331,plain,
% 1.17/1.35 (in(empty_set, A!19) | (A!19 = empty_set)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[330, 315])).
% 1.17/1.35 tff(332,plain,
% 1.17/1.35 (in(empty_set, A!19)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[331, 306])).
% 1.17/1.35 tff(333,plain,
% 1.17/1.35 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~empty(A!19)) | (~in(empty_set, A!19)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(A!19)) | (~in(empty_set, A!19)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(334,plain,
% 1.17/1.35 (((~in(empty_set, A!19)) | (~empty(A!19))) <=> ((~empty(A!19)) | (~in(empty_set, A!19)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(335,plain,
% 1.17/1.35 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(empty_set, A!19)) | (~empty(A!19)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~empty(A!19)) | (~in(empty_set, A!19))))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[334])).
% 1.17/1.35 tff(336,plain,
% 1.17/1.35 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(empty_set, A!19)) | (~empty(A!19)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(A!19)) | (~in(empty_set, A!19)))),
% 1.17/1.35 inference(transitivity,[status(thm)],[335, 333])).
% 1.17/1.35 tff(337,plain,
% 1.17/1.35 ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(empty_set, A!19)) | (~empty(A!19)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(338,plain,
% 1.17/1.35 ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(A!19)) | (~in(empty_set, A!19))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[337, 336])).
% 1.17/1.35 tff(339,plain,
% 1.17/1.35 (~empty(A!19)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[338, 272, 332])).
% 1.17/1.35 tff(340,plain,
% 1.17/1.35 (((~in(tptp_fun_B_0(union(A!19)), union(A!19))) | subset(tptp_fun_B_0(union(A!19)), union(A!19))) | (~subset(tptp_fun_B_0(union(A!19)), union(A!19)))),
% 1.17/1.35 inference(tautology,[status(thm)],[])).
% 1.17/1.35 tff(341,plain,
% 1.17/1.35 (~subset(tptp_fun_B_0(union(A!19)), union(A!19))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[340, 229])).
% 1.17/1.35 tff(342,plain,
% 1.17/1.35 (^[A: $i, B: $i] : refl(((~in(A, B)) | subset(A, union(B))) <=> ((~in(A, B)) | subset(A, union(B))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(343,plain,
% 1.17/1.35 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[342])).
% 1.17/1.35 tff(344,plain,
% 1.17/1.35 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(345,plain,
% 1.17/1.35 (^[A: $i, B: $i] : rewrite((in(A, B) => subset(A, union(B))) <=> ((~in(A, B)) | subset(A, union(B))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(346,plain,
% 1.17/1.35 (![A: $i, B: $i] : (in(A, B) => subset(A, union(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[345])).
% 1.17/1.35 tff(347,axiom,(![A: $i, B: $i] : (in(A, B) => subset(A, union(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t92_zfmisc_1')).
% 1.17/1.35 tff(348,plain,
% 1.17/1.35 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[347, 346])).
% 1.17/1.35 tff(349,plain,
% 1.17/1.35 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[348, 344])).
% 1.17/1.35 tff(350,plain,(
% 1.17/1.35 ![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 1.17/1.35 inference(skolemize,[status(sab)],[349])).
% 1.17/1.35 tff(351,plain,
% 1.17/1.35 (![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[350, 343])).
% 1.17/1.35 tff(352,plain,
% 1.17/1.35 (((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) | ((~in(tptp_fun_B_0(union(A!19)), A!19)) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) | (~in(tptp_fun_B_0(union(A!19)), A!19)) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(353,plain,
% 1.17/1.35 ((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) | ((~in(tptp_fun_B_0(union(A!19)), A!19)) | subset(tptp_fun_B_0(union(A!19)), union(A!19)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(354,plain,
% 1.17/1.35 ((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) | (~in(tptp_fun_B_0(union(A!19)), A!19)) | subset(tptp_fun_B_0(union(A!19)), union(A!19))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[353, 352])).
% 1.17/1.35 tff(355,plain,
% 1.17/1.35 (~in(tptp_fun_B_0(union(A!19)), A!19)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[354, 351, 341])).
% 1.17/1.35 tff(356,plain,
% 1.17/1.35 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(357,plain,
% 1.17/1.35 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[356])).
% 1.17/1.35 tff(358,plain,
% 1.17/1.35 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(359,plain,
% 1.17/1.35 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(360,plain,
% 1.17/1.35 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[359])).
% 1.17/1.35 tff(361,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_subset')).
% 1.17/1.35 tff(362,plain,
% 1.17/1.35 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[361, 360])).
% 1.17/1.35 tff(363,plain,
% 1.17/1.35 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[362, 358])).
% 1.17/1.35 tff(364,plain,(
% 1.17/1.35 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.17/1.35 inference(skolemize,[status(sab)],[363])).
% 1.17/1.35 tff(365,plain,
% 1.17/1.35 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[364, 357])).
% 1.17/1.35 tff(366,plain,
% 1.17/1.35 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), A!19))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), A!19))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(367,plain,
% 1.17/1.35 ((empty(A!19) | in(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19))) <=> (empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), A!19))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(368,plain,
% 1.17/1.35 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!19) | in(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), A!19)))),
% 1.17/1.35 inference(monotonicity,[status(thm)],[367])).
% 1.17/1.35 tff(369,plain,
% 1.17/1.35 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!19) | in(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), A!19))),
% 1.17/1.35 inference(transitivity,[status(thm)],[368, 366])).
% 1.17/1.35 tff(370,plain,
% 1.17/1.35 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(A!19) | in(tptp_fun_B_0(union(A!19)), A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(371,plain,
% 1.17/1.35 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19)) | in(tptp_fun_B_0(union(A!19)), A!19)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[370, 369])).
% 1.17/1.35 tff(372,plain,
% 1.17/1.35 (empty(A!19) | (~element(tptp_fun_B_0(union(A!19)), A!19))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[371, 365, 355])).
% 1.17/1.35 tff(373,plain,
% 1.17/1.35 (~element(tptp_fun_B_0(union(A!19)), A!19)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[372, 339])).
% 1.17/1.35 tff(374,plain,
% 1.17/1.35 (^[A: $i, B: $i, C: $i] : refl((element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(375,plain,
% 1.17/1.35 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C)))) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[374])).
% 1.17/1.35 tff(376,plain,
% 1.17/1.35 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(A, B) & element(B, powerset(C))) <=> (~((~in(A, B)) | (~element(B, powerset(C)))))), ((~(in(A, B) & element(B, powerset(C)))) <=> (~(~((~in(A, B)) | (~element(B, powerset(C)))))))), rewrite((~(~((~in(A, B)) | (~element(B, powerset(C)))))) <=> ((~in(A, B)) | (~element(B, powerset(C))))), ((~(in(A, B) & element(B, powerset(C)))) <=> ((~in(A, B)) | (~element(B, powerset(C)))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)))), rewrite((((~in(A, B)) | (~element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))), (((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(377,plain,
% 1.17/1.35 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[376])).
% 1.17/1.35 tff(378,plain,
% 1.17/1.35 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(379,plain,
% 1.17/1.35 (^[A: $i, B: $i, C: $i] : rewrite(((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ((~(in(A, B) & element(B, powerset(C)))) | element(A, C)))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(380,plain,
% 1.17/1.35 (![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[379])).
% 1.17/1.35 tff(381,axiom,(![A: $i, B: $i, C: $i] : ((in(A, B) & element(B, powerset(C))) => element(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t4_subset')).
% 1.17/1.35 tff(382,plain,
% 1.17/1.35 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[381, 380])).
% 1.17/1.35 tff(383,plain,
% 1.17/1.35 (![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[382, 378])).
% 1.17/1.35 tff(384,plain,(
% 1.17/1.35 ![A: $i, B: $i, C: $i] : ((~(in(A, B) & element(B, powerset(C)))) | element(A, C))),
% 1.17/1.35 inference(skolemize,[status(sab)],[383])).
% 1.17/1.35 tff(385,plain,
% 1.17/1.35 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[384, 377])).
% 1.17/1.35 tff(386,plain,
% 1.17/1.35 (![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[385, 375])).
% 1.17/1.35 tff(387,plain,
% 1.17/1.35 (((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_0(union(A!19)), A!19) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))))) <=> ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_B_0(union(A!19)), A!19) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(388,plain,
% 1.17/1.35 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | (element(tptp_fun_B_0(union(A!19)), A!19) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(389,plain,
% 1.17/1.35 ((~![A: $i, B: $i, C: $i] : (element(A, C) | (~in(A, B)) | (~element(B, powerset(C))))) | element(tptp_fun_B_0(union(A!19)), A!19) | (~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.17/1.35 tff(390,plain,
% 1.17/1.35 (~element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[389, 386, 373, 254])).
% 1.17/1.35 tff(391,plain,
% 1.17/1.35 (((~in(tptp_fun_B_0(union(A!19)), tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))) | in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)),
% 1.17/1.35 inference(tautology,[status(thm)],[])).
% 1.17/1.35 tff(392,plain,
% 1.17/1.35 (in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[391, 252])).
% 1.17/1.35 tff(393,plain,
% 1.17/1.35 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_0(A), A)) | subset(tptp_fun_B_0(A), A)))))))) | (~((~((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19)))) | (~(epsilon_transitive(A!19) | (~((~in(tptp_fun_B_0(A!19), A!19)) | subset(tptp_fun_B_0(A!19), A!19)))))))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(394,plain,
% 1.17/1.35 (~((~((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19)))) | (~(epsilon_transitive(A!19) | (~((~in(tptp_fun_B_0(A!19), A!19)) | subset(tptp_fun_B_0(A!19), A!19))))))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[393, 16])).
% 1.17/1.35 tff(395,plain,
% 1.17/1.35 (((~((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19)))) | (~(epsilon_transitive(A!19) | (~((~in(tptp_fun_B_0(A!19), A!19)) | subset(tptp_fun_B_0(A!19), A!19)))))) | ((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19)))),
% 1.17/1.35 inference(tautology,[status(thm)],[])).
% 1.17/1.35 tff(396,plain,
% 1.17/1.35 ((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[395, 394])).
% 1.17/1.35 tff(397,plain,
% 1.17/1.35 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(398,plain,
% 1.17/1.35 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[397])).
% 1.17/1.35 tff(399,plain,
% 1.17/1.35 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(400,plain,
% 1.17/1.35 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[399])).
% 1.17/1.35 tff(401,plain,
% 1.17/1.35 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(402,plain,
% 1.17/1.35 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(403,plain,
% 1.17/1.35 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[402])).
% 1.17/1.35 tff(404,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_ordinal1')).
% 1.17/1.35 tff(405,plain,
% 1.17/1.35 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[404, 403])).
% 1.17/1.35 tff(406,plain,
% 1.17/1.35 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[405, 401])).
% 1.17/1.35 tff(407,plain,(
% 1.17/1.35 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 1.17/1.35 inference(skolemize,[status(sab)],[406])).
% 1.17/1.35 tff(408,plain,
% 1.17/1.35 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[407, 400])).
% 1.17/1.35 tff(409,plain,
% 1.17/1.35 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[408, 398])).
% 1.17/1.35 tff(410,plain,
% 1.17/1.35 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(A!19)) | (~((~epsilon_transitive(A!19)) | (~epsilon_connected(A!19)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(A!19)) | (~((~epsilon_transitive(A!19)) | (~epsilon_connected(A!19)))))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(411,plain,
% 1.17/1.35 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(A!19)) | (~((~epsilon_transitive(A!19)) | (~epsilon_connected(A!19)))))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(412,plain,
% 1.17/1.35 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(A!19)) | (~((~epsilon_transitive(A!19)) | (~epsilon_connected(A!19))))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[411, 410])).
% 1.17/1.35 tff(413,plain,
% 1.17/1.35 (~((~epsilon_transitive(A!19)) | (~epsilon_connected(A!19)))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[412, 409, 105])).
% 1.17/1.35 tff(414,plain,
% 1.17/1.35 (((~epsilon_transitive(A!19)) | (~epsilon_connected(A!19))) | epsilon_transitive(A!19)),
% 1.17/1.35 inference(tautology,[status(thm)],[])).
% 1.17/1.35 tff(415,plain,
% 1.17/1.35 (epsilon_transitive(A!19)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[414, 413])).
% 1.17/1.35 tff(416,plain,
% 1.17/1.35 ((~((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19)))) | (~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19))),
% 1.17/1.35 inference(tautology,[status(thm)],[])).
% 1.17/1.35 tff(417,plain,
% 1.17/1.35 ((~((~epsilon_transitive(A!19)) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19)))) | ![B: $i] : ((~in(B, A!19)) | subset(B, A!19))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[416, 415])).
% 1.17/1.35 tff(418,plain,
% 1.17/1.35 (![B: $i] : ((~in(B, A!19)) | subset(B, A!19))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[417, 396])).
% 1.17/1.35 tff(419,plain,
% 1.17/1.35 (((~![B: $i] : ((~in(B, A!19)) | subset(B, A!19))) | ((~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)) | subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))) <=> ((~![B: $i] : ((~in(B, A!19)) | subset(B, A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)) | subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(420,plain,
% 1.17/1.35 ((~![B: $i] : ((~in(B, A!19)) | subset(B, A!19))) | ((~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)) | subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(421,plain,
% 1.17/1.35 ((~![B: $i] : ((~in(B, A!19)) | subset(B, A!19))) | (~in(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)) | subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[420, 419])).
% 1.17/1.35 tff(422,plain,
% 1.17/1.35 (subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19)),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[421, 418, 392])).
% 1.17/1.35 tff(423,plain,
% 1.17/1.35 ((~(element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19)) <=> subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))) | element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19)) | (~subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))),
% 1.17/1.35 inference(tautology,[status(thm)],[])).
% 1.17/1.35 tff(424,plain,
% 1.17/1.35 (~(element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19)) <=> subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[423, 422, 390])).
% 1.17/1.35 tff(425,plain,
% 1.17/1.35 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 1.17/1.35 inference(bind,[status(th)],[])).
% 1.17/1.35 tff(426,plain,
% 1.17/1.35 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.17/1.35 inference(quant_intro,[status(thm)],[425])).
% 1.17/1.35 tff(427,plain,
% 1.17/1.35 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.17/1.35 inference(rewrite,[status(thm)],[])).
% 1.17/1.35 tff(428,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 1.17/1.35 tff(429,plain,
% 1.17/1.35 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[428, 427])).
% 1.17/1.35 tff(430,plain,(
% 1.17/1.35 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.17/1.35 inference(skolemize,[status(sab)],[429])).
% 1.17/1.35 tff(431,plain,
% 1.17/1.35 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 1.17/1.35 inference(modus_ponens,[status(thm)],[430, 426])).
% 1.17/1.35 tff(432,plain,
% 1.17/1.35 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), powerset(A!19)) <=> subset(tptp_fun_D_3(tptp_fun_B_0(union(A!19)), A!19), A!19))),
% 1.17/1.35 inference(quant_inst,[status(thm)],[])).
% 1.17/1.35 tff(433,plain,
% 1.17/1.35 ($false),
% 1.17/1.35 inference(unit_resolution,[status(thm)],[432, 431, 424])).
% 1.17/1.35 % SZS output end Proof
% 1.17/1.36 % E exiting
%------------------------------------------------------------------------------