%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM402+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:20:53 AM UTC 2025
% Result : Theorem 0.49s 0.69s
% Output : Proof 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM402+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 01:02:42 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.49/0.69 % SZS status Theorem
% 0.49/0.69 % SZS output start Proof
% 0.49/0.69 tff(in_type, type, (
% 0.49/0.69 in: ( $i * $i ) > $o)).
% 0.49/0.69 tff(tptp_fun_D_4_type, type, (
% 0.49/0.69 tptp_fun_D_4: ( $i * $i ) > $i)).
% 0.49/0.69 tff(tptp_fun_A_21_type, type, (
% 0.49/0.69 tptp_fun_A_21: $i)).
% 0.49/0.69 tff(tptp_fun_B_0_type, type, (
% 0.49/0.69 tptp_fun_B_0: $i > $i)).
% 0.49/0.69 tff(union_type, type, (
% 0.49/0.69 union: $i > $i)).
% 0.49/0.69 tff(tptp_fun_C_3_type, type, (
% 0.49/0.69 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.49/0.69 tff(subset_type, type, (
% 0.49/0.69 subset: ( $i * $i ) > $o)).
% 0.49/0.69 tff(epsilon_transitive_type, type, (
% 0.49/0.69 epsilon_transitive: $i > $o)).
% 0.49/0.69 tff(epsilon_connected_type, type, (
% 0.49/0.69 epsilon_connected: $i > $o)).
% 0.49/0.69 tff(ordinal_type, type, (
% 0.49/0.69 ordinal: $i > $o)).
% 0.49/0.69 tff(tptp_fun_C_1_type, type, (
% 0.49/0.69 tptp_fun_C_1: $i > $i)).
% 0.49/0.69 tff(tptp_fun_B_2_type, type, (
% 0.49/0.69 tptp_fun_B_2: $i > $i)).
% 0.49/0.69 tff(tptp_fun_C_5_type, type, (
% 0.49/0.69 tptp_fun_C_5: ( $i * $i ) > $i)).
% 0.49/0.69 tff(tptp_fun_D_6_type, type, (
% 0.49/0.69 tptp_fun_D_6: ( $i * $i ) > $i)).
% 0.49/0.69 tff(1,plain,
% 0.49/0.69 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(2,plain,
% 0.49/0.69 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[1])).
% 0.49/0.69 tff(3,plain,
% 0.49/0.69 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))))),
% 0.49/0.69 inference(bind,[status(th)],[])).
% 0.49/0.69 tff(4,plain,
% 0.49/0.69 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 0.49/0.69 inference(quant_intro,[status(thm)],[3])).
% 0.49/0.69 tff(5,plain,
% 0.49/0.69 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 0.49/0.69 inference(transitivity,[status(thm)],[4, 2])).
% 0.49/0.69 tff(6,plain,
% 0.49/0.69 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(7,plain,
% 0.49/0.70 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[6])).
% 0.49/0.70 tff(8,plain,
% 0.49/0.70 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(9,plain,
% 0.49/0.70 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(10,plain,
% 0.49/0.70 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[9])).
% 0.49/0.70 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.49/0.70 tff(12,plain,
% 0.49/0.70 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.49/0.70 tff(13,plain,
% 0.49/0.70 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.49/0.70 tff(14,plain,(
% 0.49/0.70 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))),
% 0.49/0.70 inference(skolemize,[status(sab)],[13])).
% 0.49/0.70 tff(15,plain,
% 0.49/0.70 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.49/0.70 tff(16,plain,
% 0.49/0.70 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.49/0.70 tff(17,plain,
% 0.49/0.70 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))) | (~((~((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~(subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~((~in(tptp_fun_C_3(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(18,plain,
% 0.49/0.70 (~((~((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~(subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~((~in(tptp_fun_C_3(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.49/0.70 tff(19,plain,
% 0.49/0.70 (((~((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~(subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~((~in(tptp_fun_C_3(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))) | ((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))),
% 0.49/0.70 inference(tautology,[status(thm)],[])).
% 0.49/0.70 tff(20,plain,
% 0.49/0.70 ((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.49/0.70 tff(21,plain,
% 0.49/0.70 (^[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))))))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(22,plain,
% 0.49/0.70 (![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)))))))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[21])).
% 0.49/0.70 tff(23,plain,
% 0.49/0.70 (^[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))))))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(24,plain,
% 0.49/0.70 (![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)))))))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[23])).
% 0.49/0.70 tff(25,plain,
% 0.49/0.70 (![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)))))))),
% 0.49/0.70 inference(transitivity,[status(thm)],[24, 22])).
% 0.49/0.70 tff(26,plain,
% 0.49/0.70 (^[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)))))))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(27,plain,
% 0.49/0.70 (![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)))))))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[26])).
% 0.49/0.70 tff(28,plain,
% 0.49/0.70 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(29,plain,
% 0.49/0.70 (^[A: $i] : rewrite((epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(30,plain,
% 0.49/0.70 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[29])).
% 0.49/0.70 tff(31,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.49/0.70 tff(32,plain,
% 0.49/0.70 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.49/0.70 tff(33,plain,
% 0.49/0.70 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.49/0.70 tff(34,plain,(
% 0.49/0.70 ![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)))))),
% 0.49/0.70 inference(skolemize,[status(sab)],[33])).
% 0.49/0.70 tff(35,plain,
% 0.49/0.70 (![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)))))))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.49/0.70 tff(36,plain,
% 0.49/0.70 (![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)))))))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.49/0.70 tff(37,plain,
% 0.49/0.70 ((~![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(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~(epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~((~in(tptp_fun_B_0(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(38,plain,
% 0.49/0.70 (~((~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~(epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~((~in(tptp_fun_B_0(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.49/0.70 tff(39,plain,
% 0.49/0.70 (((~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~(epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~((~in(tptp_fun_B_0(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))) | ((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))),
% 0.49/0.70 inference(tautology,[status(thm)],[])).
% 0.49/0.70 tff(40,plain,
% 0.49/0.70 ((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.49/0.70 tff(41,plain,
% 0.49/0.70 ((~![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!21))) | ![B: $i] : ((~in(B, union(A!21))) | subset(B, union(A!21))))) | (~(epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))))))))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(42,plain,
% 0.49/0.70 (~((~((~epsilon_transitive(union(A!21))) | ![B: $i] : ((~in(B, union(A!21))) | subset(B, union(A!21))))) | (~(epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21)))))))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[41, 36])).
% 0.49/0.70 tff(43,plain,
% 0.49/0.70 (((~((~epsilon_transitive(union(A!21))) | ![B: $i] : ((~in(B, union(A!21))) | subset(B, union(A!21))))) | (~(epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))))))) | (epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21)))))),
% 0.49/0.70 inference(tautology,[status(thm)],[])).
% 0.49/0.70 tff(44,plain,
% 0.49/0.70 (epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))))),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.49/0.70 tff(45,assumption,((~((~epsilon_connected(union(A!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))))))), introduced(assumption)).
% 0.49/0.70 tff(46,plain,
% 0.49/0.70 (^[A: $i] : refl((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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(C, A)) | (~in(B, 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)))))))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(47,plain,
% 0.49/0.70 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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(C, A)) | (~in(B, 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))))))))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[46])).
% 0.49/0.70 tff(48,plain,
% 0.49/0.70 (^[A: $i] : rewrite((~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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(C, A)) | (~in(B, 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)))))))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(49,plain,
% 0.49/0.70 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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(C, A)) | (~in(B, 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))))))))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[48])).
% 0.49/0.70 tff(50,plain,
% 0.49/0.70 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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(C, A)) | (~in(B, 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))))))))),
% 0.49/0.70 inference(transitivity,[status(thm)],[49, 47])).
% 0.49/0.70 tff(51,plain,
% 0.49/0.70 (^[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(C, A)) | (~in(B, 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(C, A)) | (~in(B, 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(C, A)) | (~in(B, 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(C, A)) | (~in(B, 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(C, A)) | (~in(B, 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))))))))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(52,plain,
% 0.49/0.70 (![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(C, A)) | (~in(B, 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))))))))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[51])).
% 0.49/0.70 tff(53,plain,
% 0.49/0.70 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))) <=> ![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(54,plain,
% 0.49/0.70 (^[A: $i] : rewrite((epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B))))) <=> (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B))))))),
% 0.49/0.70 inference(bind,[status(th)],[])).
% 0.49/0.70 tff(55,plain,
% 0.49/0.70 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B))))) <=> ![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.49/0.70 inference(quant_intro,[status(thm)],[54])).
% 0.49/0.70 tff(56,axiom,(![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~((((in(B, A) & in(C, A)) & (~in(B, C))) & (~(B = C))) & (~in(C, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_ordinal1')).
% 0.49/0.70 tff(57,plain,
% 0.49/0.70 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.49/0.70 tff(58,plain,
% 0.49/0.70 (![A: $i] : (epsilon_connected(A) <=> ![B: $i, C: $i] : (~(in(B, A) & in(C, A) & (~in(B, C)) & (~(B = C)) & (~in(C, B)))))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.49/0.70 tff(59,plain,(
% 0.49/0.70 ![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))))))),
% 0.49/0.70 inference(skolemize,[status(sab)],[58])).
% 0.49/0.70 tff(60,plain,
% 0.49/0.70 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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))))))))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.49/0.70 tff(61,plain,
% 0.49/0.70 (![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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))))))))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.49/0.70 tff(62,plain,
% 0.49/0.70 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))))))))))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(63,plain,
% 0.49/0.70 ((~((~((~epsilon_connected(union(A!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21))))))))) <=> (~((~((~epsilon_connected(union(A!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))))))))),
% 0.49/0.70 inference(rewrite,[status(thm)],[])).
% 0.49/0.70 tff(64,plain,
% 0.49/0.70 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))))))))))),
% 0.49/0.70 inference(monotonicity,[status(thm)],[63])).
% 0.49/0.70 tff(65,plain,
% 0.49/0.70 (((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))))))))) <=> ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))))))))))),
% 0.49/0.70 inference(transitivity,[status(thm)],[64, 62])).
% 0.49/0.70 tff(66,plain,
% 0.49/0.70 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~(in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21)))))))))),
% 0.49/0.70 inference(quant_inst,[status(thm)],[])).
% 0.49/0.70 tff(67,plain,
% 0.49/0.70 ((~![A: $i] : (~((~((~epsilon_connected(A)) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, A)) | (~in(B, 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!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))))))))),
% 0.49/0.70 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.49/0.70 tff(68,plain,
% 0.49/0.70 ($false),
% 0.49/0.70 inference(unit_resolution,[status(thm)],[67, 61, 45])).
% 0.49/0.70 tff(69,plain,(~((~((~epsilon_connected(union(A!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))))))))), inference(lemma,lemma(discharge,[]))).
% 0.49/0.71 tff(70,plain,
% 0.49/0.71 (((~((~epsilon_connected(union(A!21))) | ![B: $i, C: $i] : (in(C, B) | in(B, C) | (B = C) | (~in(C, union(A!21))) | (~in(B, union(A!21)))))) | (~(epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))))))) | (epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))))))),
% 0.49/0.71 inference(tautology,[status(thm)],[])).
% 0.49/0.71 tff(71,plain,
% 0.49/0.71 (epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))))),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.49/0.71 tff(72,assumption,(~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))))), introduced(assumption)).
% 0.49/0.71 tff(73,plain,
% 0.49/0.71 (((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))) | in(tptp_fun_C_1(union(A!21)), union(A!21))),
% 0.49/0.71 inference(tautology,[status(thm)],[])).
% 0.49/0.71 tff(74,plain,
% 0.49/0.71 (in(tptp_fun_C_1(union(A!21)), union(A!21))),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.49/0.71 tff(75,plain,
% 0.49/0.71 (^[A: $i, B: $i, D_22: $i, C: $i, D: $i] : rewrite((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(76,plain,
% 0.49/0.71 (![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) <=> ![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[75])).
% 0.49/0.71 tff(77,plain,
% 0.49/0.71 (^[A: $i, B: $i, D_22: $i, C: $i, D: $i] : refl((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(78,plain,
% 0.49/0.71 (![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) <=> ![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[77])).
% 0.49/0.71 tff(79,plain,
% 0.49/0.71 (![A: $i, B: $i] : ![D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) <=> ![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.49/0.71 inference(pull_quant,[status(thm)],[])).
% 0.49/0.71 tff(80,plain,
% 0.49/0.71 (^[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_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), pull_quant(((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> (~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant((~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))) <=> ![D: $i] : ((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))), ((~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))) <=> (~![D: $i] : ((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))), pull_quant((~![D: $i] : ((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))), ((~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))), (((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))) <=> ((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))), pull_quant(((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))), (((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))), ((~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))) <=> (~?[D: $i] : ((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))), pull_quant((~?[D: $i] : ((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))), ((~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))) <=> ((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))), pull_quant(((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))) <=> (~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))), pull_quant((~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))) <=> (?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))))), pull_quant((?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))) <=> ?[D_22: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))) <=> ?[D_22: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> (~?[D_22: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))))), pull_quant((~?[D_22: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) <=> ![D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> ![D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(81,plain,
% 0.49/0.71 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> ![A: $i, B: $i] : ![D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[80])).
% 0.49/0.71 tff(82,plain,
% 0.49/0.71 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> ![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.49/0.71 inference(transitivity,[status(thm)],[81, 79])).
% 0.49/0.71 tff(83,plain,
% 0.49/0.71 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> ![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.49/0.71 inference(transitivity,[status(thm)],[82, 78])).
% 0.49/0.71 tff(84,plain,
% 0.49/0.71 (^[A: $i, B: $i] : rewrite((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(85,plain,
% 0.49/0.71 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[84])).
% 0.49/0.71 tff(86,plain,
% 0.49/0.71 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))) <=> ![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.49/0.71 inference(transitivity,[status(thm)],[85, 83])).
% 0.49/0.71 tff(87,plain,
% 0.49/0.71 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_4(C, A)) & in(tptp_fun_D_4(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_4(C, A))) | (~in(tptp_fun_D_4(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_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A)) <=> (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A))))), ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) <=> (in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A))))))), rewrite((in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A))))) <=> (in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))), ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) <=> (in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A))))))), rewrite(((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A)))) <=> ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))), (((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A))))) <=> ((in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A))))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))), rewrite(((in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A))))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))) <=> (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))), (((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A))))) <=> (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))), rewrite(((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_4(C, A)) & in(tptp_fun_D_4(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A))))))) <=> (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))))), rewrite((((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_4(C, A)) & in(tptp_fun_D_4(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(88,plain,
% 0.49/0.71 (![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_4(C, A)) & in(tptp_fun_D_4(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))))),
% 0.56/0.71 inference(quant_intro,[status(thm)],[87])).
% 0.56/0.71 tff(89,plain,
% 0.56/0.71 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A)))) <=> ![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.56/0.71 inference(rewrite,[status(thm)],[])).
% 0.56/0.71 tff(90,axiom,(![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_tarski')).
% 0.56/0.71 tff(91,plain,
% 0.56/0.71 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.56/0.71 tff(92,plain,(
% 0.56/0.71 ![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_4(C, A)) & in(tptp_fun_D_4(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_5(B, A), B) | (in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A)) & in(tptp_fun_D_6(B, A), A))) & ((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_5(B, A), D) & in(D, A)))))))),
% 0.56/0.71 inference(skolemize,[status(sab)],[91])).
% 0.56/0.71 tff(93,plain,
% 0.56/0.71 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_5(B, A), D)))))))))))),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.56/0.71 tff(94,plain,
% 0.56/0.71 (![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | ((~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22)))))))))))),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.56/0.71 tff(95,plain,
% 0.56/0.71 (![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))),
% 0.56/0.71 inference(modus_ponens,[status(thm)],[94, 76])).
% 0.56/0.71 tff(96,plain,
% 0.56/0.71 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | ((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(97,plain,
% 0.56/0.72 ((~(~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))))))) <=> ((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(98,plain,
% 0.56/0.72 (((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | $false) <=> (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(99,plain,
% 0.56/0.72 ((~$true) <=> $false),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(100,plain,
% 0.56/0.72 (($true | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))) <=> $true),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(101,plain,
% 0.56/0.72 ((~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))) <=> (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(102,plain,
% 0.56/0.72 ((union(A!21) = union(A!21)) <=> $true),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(103,plain,
% 0.56/0.72 (((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))) <=> ($true | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[102, 101])).
% 0.56/0.72 tff(104,plain,
% 0.56/0.72 (((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))) <=> $true),
% 0.56/0.72 inference(transitivity,[status(thm)],[103, 100])).
% 0.56/0.72 tff(105,plain,
% 0.56/0.72 ((~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))) <=> (~$true)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[104])).
% 0.56/0.72 tff(106,plain,
% 0.56/0.72 ((~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))) <=> $false),
% 0.56/0.72 inference(transitivity,[status(thm)],[105, 99])).
% 0.56/0.72 tff(107,plain,
% 0.56/0.72 ((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) <=> (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(108,plain,
% 0.56/0.72 (((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))) <=> ((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | $false)),
% 0.56/0.72 inference(monotonicity,[status(thm)],[107, 106])).
% 0.56/0.72 tff(109,plain,
% 0.56/0.72 (((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))) <=> (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))))))),
% 0.56/0.72 inference(transitivity,[status(thm)],[108, 98])).
% 0.56/0.72 tff(110,plain,
% 0.56/0.72 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> (~(~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[109])).
% 0.56/0.72 tff(111,plain,
% 0.56/0.72 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> ((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))),
% 0.56/0.72 inference(transitivity,[status(thm)],[110, 97])).
% 0.56/0.72 tff(112,plain,
% 0.56/0.72 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | ((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))))))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[111])).
% 0.56/0.72 tff(113,plain,
% 0.56/0.72 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))),
% 0.56/0.72 inference(transitivity,[status(thm)],[112, 96])).
% 0.56/0.72 tff(114,plain,
% 0.56/0.72 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(115,plain,
% 0.56/0.72 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.56/0.72 tff(116,plain,
% 0.56/0.72 (~((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[115, 95, 74])).
% 0.56/0.72 tff(117,plain,
% 0.56/0.72 (((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))) | in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)),
% 0.56/0.72 inference(tautology,[status(thm)],[])).
% 0.56/0.72 tff(118,plain,
% 0.56/0.72 (in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.56/0.72 tff(119,plain,
% 0.56/0.72 (^[B: $i] : refl((ordinal(B) | (~in(B, A!21))) <=> (ordinal(B) | (~in(B, A!21))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(120,plain,
% 0.56/0.72 (![B: $i] : (ordinal(B) | (~in(B, A!21))) <=> ![B: $i] : (ordinal(B) | (~in(B, A!21)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[119])).
% 0.56/0.72 tff(121,plain,
% 0.56/0.72 (((~ordinal(union(A!21))) & ![B: $i] : ((~in(B, A!21)) | ordinal(B))) <=> ((~ordinal(union(A!21))) & ![B: $i] : (ordinal(B) | (~in(B, A!21))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(122,plain,
% 0.56/0.72 ((~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))) <=> (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B)))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(123,plain,
% 0.56/0.72 ((~![A: $i] : (![B: $i] : (in(B, A) => ordinal(B)) => ordinal(union(A)))) <=> (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B)))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(124,axiom,(~![A: $i] : (![B: $i] : (in(B, A) => ordinal(B)) => ordinal(union(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t35_ordinal1')).
% 0.56/0.72 tff(125,plain,
% 0.56/0.72 (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.56/0.72 tff(126,plain,
% 0.56/0.72 (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[125, 122])).
% 0.56/0.72 tff(127,plain,
% 0.56/0.72 (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.56/0.72 tff(128,plain,
% 0.56/0.72 (~![A: $i] : (ordinal(union(A)) | (~![B: $i] : ((~in(B, A)) | ordinal(B))))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[127, 122])).
% 0.56/0.72 tff(129,plain,
% 0.56/0.72 ((~ordinal(union(A!21))) & ![B: $i] : (ordinal(B) | (~in(B, A!21)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.56/0.72 tff(130,plain,
% 0.56/0.72 (![B: $i] : (ordinal(B) | (~in(B, A!21)))),
% 0.56/0.72 inference(and_elim,[status(thm)],[129])).
% 0.56/0.72 tff(131,plain,
% 0.56/0.72 (![B: $i] : (ordinal(B) | (~in(B, A!21)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[130, 120])).
% 0.56/0.72 tff(132,plain,
% 0.56/0.72 (((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | (ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))) <=> ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(133,plain,
% 0.56/0.72 ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | (ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(134,plain,
% 0.56/0.72 ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.56/0.72 tff(135,plain,
% 0.56/0.72 (ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[134, 131, 118])).
% 0.56/0.72 tff(136,plain,
% 0.56/0.72 (((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21), A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))),
% 0.56/0.72 inference(tautology,[status(thm)],[])).
% 0.56/0.72 tff(137,plain,
% 0.56/0.72 (in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[136, 116])).
% 0.56/0.72 tff(138,plain,
% 0.56/0.72 (^[A: $i, B: $i] : refl(((~in(A, B)) | ordinal(A) | (~ordinal(B))) <=> ((~in(A, B)) | ordinal(A) | (~ordinal(B))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(139,plain,
% 0.56/0.72 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[138])).
% 0.56/0.72 tff(140,plain,
% 0.56/0.72 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(141,plain,
% 0.56/0.72 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) => ordinal(A)) <=> ((~in(A, B)) | ordinal(A))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> (ordinal(B) => ((~in(A, B)) | ordinal(A))))), rewrite((ordinal(B) => ((~in(A, B)) | ordinal(A))) <=> ((~in(A, B)) | ordinal(A) | (~ordinal(B)))), ((ordinal(B) => (in(A, B) => ordinal(A))) <=> ((~in(A, B)) | ordinal(A) | (~ordinal(B)))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(142,plain,
% 0.56/0.72 (![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A))) <=> ![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[141])).
% 0.56/0.72 tff(143,axiom,(![A: $i, B: $i] : (ordinal(B) => (in(A, B) => ordinal(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_ordinal1')).
% 0.56/0.72 tff(144,plain,
% 0.56/0.72 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.56/0.72 tff(145,plain,
% 0.56/0.72 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.56/0.72 tff(146,plain,(
% 0.56/0.72 ![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.56/0.72 inference(skolemize,[status(sab)],[145])).
% 0.56/0.72 tff(147,plain,
% 0.56/0.72 (![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.56/0.72 tff(148,plain,
% 0.56/0.72 (((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | ordinal(tptp_fun_C_1(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | (~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | ordinal(tptp_fun_C_1(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(149,plain,
% 0.56/0.72 ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | ordinal(tptp_fun_C_1(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(150,plain,
% 0.56/0.72 ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | (~in(tptp_fun_C_1(union(A!21)), tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21))) | ordinal(tptp_fun_C_1(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_C_1(union(A!21)), A!21)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.56/0.72 tff(151,plain,
% 0.56/0.72 (ordinal(tptp_fun_C_1(union(A!21)))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[150, 147, 137, 135])).
% 0.56/0.72 tff(152,plain,
% 0.56/0.72 (^[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)))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(153,plain,
% 0.56/0.72 (![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))))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[152])).
% 0.56/0.72 tff(154,plain,
% 0.56/0.72 (^[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)))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(155,plain,
% 0.56/0.72 (![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))))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[154])).
% 0.56/0.72 tff(156,plain,
% 0.56/0.72 (![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))))),
% 0.56/0.72 inference(transitivity,[status(thm)],[155, 153])).
% 0.56/0.72 tff(157,plain,
% 0.56/0.72 (^[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)))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(158,plain,
% 0.56/0.72 (![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))))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[157])).
% 0.56/0.72 tff(159,plain,
% 0.56/0.72 (![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))))))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(160,plain,
% 0.56/0.72 (^[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))))))))),
% 0.56/0.73 inference(bind,[status(th)],[])).
% 0.56/0.73 tff(161,plain,
% 0.56/0.73 (![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))))))),
% 0.56/0.73 inference(quant_intro,[status(thm)],[160])).
% 0.56/0.73 tff(162,axiom,(![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t24_ordinal1')).
% 0.56/0.73 tff(163,plain,
% 0.56/0.73 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.56/0.73 tff(164,plain,
% 0.56/0.73 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.56/0.73 tff(165,plain,(
% 0.56/0.73 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.56/0.73 inference(skolemize,[status(sab)],[164])).
% 0.56/0.73 tff(166,plain,
% 0.56/0.73 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.56/0.73 tff(167,plain,
% 0.56/0.73 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[166, 156])).
% 0.56/0.73 tff(168,plain,
% 0.56/0.73 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!21)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(union(A!21)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(169,plain,
% 0.56/0.73 (((~ordinal(tptp_fun_C_1(union(A!21)))) | ![B: $i] : (in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B) | (~ordinal(B)))) <=> ((~ordinal(tptp_fun_C_1(union(A!21)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(170,plain,
% 0.56/0.73 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!21)))) | ![B: $i] : (in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = 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!21)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[169])).
% 0.56/0.73 tff(171,plain,
% 0.56/0.73 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!21)))) | ![B: $i] : (in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = 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!21)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B)))),
% 0.56/0.73 inference(transitivity,[status(thm)],[170, 168])).
% 0.56/0.73 tff(172,plain,
% 0.56/0.73 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(tptp_fun_C_1(union(A!21)))) | ![B: $i] : (in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B) | (~ordinal(B))))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(173,plain,
% 0.56/0.73 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(tptp_fun_C_1(union(A!21)))) | ![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.56/0.73 tff(174,plain,
% 0.56/0.73 (![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[173, 167, 151])).
% 0.56/0.73 tff(175,plain,
% 0.56/0.73 (((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))) | in(tptp_fun_B_2(union(A!21)), union(A!21))),
% 0.56/0.73 inference(tautology,[status(thm)],[])).
% 0.56/0.73 tff(176,plain,
% 0.56/0.73 (in(tptp_fun_B_2(union(A!21)), union(A!21))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[175, 72])).
% 0.56/0.73 tff(177,plain,
% 0.56/0.73 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | ((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(178,plain,
% 0.56/0.73 ((~(~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))))))) <=> ((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(179,plain,
% 0.56/0.73 (((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | $false) <=> (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(180,plain,
% 0.56/0.73 ((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) <=> (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(181,plain,
% 0.56/0.73 (((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))) <=> ((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | $false)),
% 0.56/0.73 inference(monotonicity,[status(thm)],[180, 106])).
% 0.56/0.73 tff(182,plain,
% 0.56/0.73 (((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))) <=> (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))))))),
% 0.56/0.73 inference(transitivity,[status(thm)],[181, 179])).
% 0.56/0.73 tff(183,plain,
% 0.56/0.73 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> (~(~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[182])).
% 0.56/0.73 tff(184,plain,
% 0.56/0.73 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> ((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))),
% 0.56/0.73 inference(transitivity,[status(thm)],[183, 178])).
% 0.56/0.73 tff(185,plain,
% 0.56/0.73 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | ((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[184])).
% 0.56/0.73 tff(186,plain,
% 0.56/0.73 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))),
% 0.56/0.73 inference(transitivity,[status(thm)],[185, 177])).
% 0.56/0.73 tff(187,plain,
% 0.56/0.73 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_B_2(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(188,plain,
% 0.56/0.73 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.56/0.73 tff(189,plain,
% 0.56/0.73 (~((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[188, 95, 176])).
% 0.56/0.73 tff(190,plain,
% 0.56/0.73 (((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))) | in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)),
% 0.56/0.73 inference(tautology,[status(thm)],[])).
% 0.56/0.73 tff(191,plain,
% 0.56/0.73 (in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.56/0.73 tff(192,plain,
% 0.56/0.73 (((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | (ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))) <=> ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(193,plain,
% 0.56/0.73 ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | (ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(194,plain,
% 0.56/0.73 ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.56/0.73 tff(195,plain,
% 0.56/0.73 (ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[194, 131, 191])).
% 0.56/0.73 tff(196,plain,
% 0.56/0.73 (((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21), A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))),
% 0.56/0.73 inference(tautology,[status(thm)],[])).
% 0.56/0.73 tff(197,plain,
% 0.56/0.73 (in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[196, 189])).
% 0.56/0.73 tff(198,plain,
% 0.56/0.73 (((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | ordinal(tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | (~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | ordinal(tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(199,plain,
% 0.56/0.73 ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | ((~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | ordinal(tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(200,plain,
% 0.56/0.73 ((~![A: $i, B: $i] : ((~in(A, B)) | ordinal(A) | (~ordinal(B)))) | (~in(tptp_fun_B_2(union(A!21)), tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21))) | ordinal(tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_D_4(tptp_fun_B_2(union(A!21)), A!21)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.56/0.73 tff(201,plain,
% 0.56/0.73 (ordinal(tptp_fun_B_2(union(A!21)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[200, 147, 197, 195])).
% 0.56/0.73 tff(202,plain,
% 0.56/0.73 ((tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21))) <=> (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21)))),
% 0.56/0.73 inference(commutativity,[status(thm)],[])).
% 0.56/0.73 tff(203,plain,
% 0.56/0.73 ((tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) <=> (tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21)))),
% 0.56/0.73 inference(symmetry,[status(thm)],[202])).
% 0.56/0.73 tff(204,plain,
% 0.56/0.73 ((~(tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21)))) <=> (~(tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[203])).
% 0.56/0.73 tff(205,plain,
% 0.56/0.73 (((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))) | (~(tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))))),
% 0.56/0.73 inference(tautology,[status(thm)],[])).
% 0.56/0.73 tff(206,plain,
% 0.56/0.73 (~(tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[205, 72])).
% 0.56/0.73 tff(207,plain,
% 0.56/0.73 (~(tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[206, 204])).
% 0.56/0.73 tff(208,plain,
% 0.56/0.73 (((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))) | (~in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))))),
% 0.56/0.73 inference(tautology,[status(thm)],[])).
% 0.56/0.73 tff(209,plain,
% 0.56/0.73 (~in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[208, 72])).
% 0.56/0.73 tff(210,plain,
% 0.56/0.73 (((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))) | (~in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))))),
% 0.56/0.73 inference(tautology,[status(thm)],[])).
% 0.56/0.73 tff(211,plain,
% 0.56/0.73 (~in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21)))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[210, 72])).
% 0.56/0.74 tff(212,plain,
% 0.56/0.74 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B))) | (in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_B_2(union(A!21)))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_B_2(union(A!21)))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(213,plain,
% 0.56/0.74 (((~ordinal(tptp_fun_B_2(union(A!21)))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21)))) <=> (in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_B_2(union(A!21)))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(214,plain,
% 0.56/0.74 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B))) | ((~ordinal(tptp_fun_B_2(union(A!21)))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B))) | (in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_B_2(union(A!21))))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[213])).
% 0.56/0.74 tff(215,plain,
% 0.56/0.74 (((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B))) | ((~ordinal(tptp_fun_B_2(union(A!21)))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21))))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_B_2(union(A!21)))))),
% 0.56/0.74 inference(transitivity,[status(thm)],[214, 212])).
% 0.56/0.74 tff(216,plain,
% 0.56/0.74 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B))) | ((~ordinal(tptp_fun_B_2(union(A!21)))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21))))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(217,plain,
% 0.56/0.74 ((~![B: $i] : ((~ordinal(B)) | in(B, tptp_fun_C_1(union(A!21))) | in(tptp_fun_C_1(union(A!21)), B) | (tptp_fun_C_1(union(A!21)) = B))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))) | (tptp_fun_C_1(union(A!21)) = tptp_fun_B_2(union(A!21))) | (~ordinal(tptp_fun_B_2(union(A!21))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.56/0.74 tff(218,plain,
% 0.56/0.74 ($false),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[217, 211, 209, 207, 201, 174])).
% 0.56/0.74 tff(219,plain,((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))), inference(lemma,lemma(discharge,[]))).
% 0.56/0.74 tff(220,plain,
% 0.56/0.74 ((~(epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))))))) | epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21)))))),
% 0.56/0.74 inference(tautology,[status(thm)],[])).
% 0.56/0.74 tff(221,plain,
% 0.56/0.74 ((~(epsilon_connected(union(A!21)) | (~((~in(tptp_fun_C_1(union(A!21)), union(A!21))) | (~in(tptp_fun_B_2(union(A!21)), union(A!21))) | in(tptp_fun_C_1(union(A!21)), tptp_fun_B_2(union(A!21))) | (tptp_fun_B_2(union(A!21)) = tptp_fun_C_1(union(A!21))) | in(tptp_fun_B_2(union(A!21)), tptp_fun_C_1(union(A!21))))))) | epsilon_connected(union(A!21))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.56/0.74 tff(222,plain,
% 0.56/0.74 (epsilon_connected(union(A!21))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[221, 71])).
% 0.56/0.74 tff(223,plain,
% 0.56/0.74 (^[A: $i] : refl((~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(224,plain,
% 0.56/0.74 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[223])).
% 0.56/0.74 tff(225,plain,
% 0.56/0.74 (^[A: $i] : trans(trans(monotonicity(rewrite((epsilon_transitive(A) & epsilon_connected(A)) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))), ((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))), rewrite((ordinal(A) <=> (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))), ((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))))), rewrite((~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))), ((ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(226,plain,
% 0.56/0.74 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[225])).
% 0.56/0.74 tff(227,plain,
% 0.56/0.74 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(228,axiom,(![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_ordinal1')).
% 0.56/0.74 tff(229,plain,
% 0.56/0.74 (![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.56/0.74 tff(230,plain,(
% 0.56/0.74 ![A: $i] : (ordinal(A) <=> (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.56/0.74 inference(skolemize,[status(sab)],[229])).
% 0.56/0.74 tff(231,plain,
% 0.56/0.74 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[230, 226])).
% 0.56/0.74 tff(232,plain,
% 0.56/0.74 (![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[231, 224])).
% 0.56/0.74 tff(233,plain,
% 0.56/0.74 ((~![A: $i] : (~(((~epsilon_transitive(A)) | (~epsilon_connected(A))) <=> ordinal(A)))) | (~(((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21)))) <=> ordinal(union(A!21))))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(234,plain,
% 0.56/0.74 (~(((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21)))) <=> ordinal(union(A!21)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.56/0.74 tff(235,plain,
% 0.56/0.74 (~ordinal(union(A!21))),
% 0.56/0.74 inference(and_elim,[status(thm)],[129])).
% 0.56/0.74 tff(236,plain,
% 0.56/0.74 ((((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21)))) <=> ordinal(union(A!21))) | ((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21)))) | ordinal(union(A!21))),
% 0.56/0.74 inference(tautology,[status(thm)],[])).
% 0.56/0.74 tff(237,plain,
% 0.56/0.74 ((((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21)))) <=> ordinal(union(A!21))) | ((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21))))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.56/0.74 tff(238,plain,
% 0.56/0.74 ((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[237, 234])).
% 0.56/0.74 tff(239,plain,
% 0.56/0.74 ((~((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21))))) | (~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21)))),
% 0.56/0.74 inference(tautology,[status(thm)],[])).
% 0.56/0.74 tff(240,plain,
% 0.56/0.74 ((~epsilon_transitive(union(A!21))) | (~epsilon_connected(union(A!21)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[239, 238])).
% 0.56/0.74 tff(241,plain,
% 0.56/0.74 (~epsilon_transitive(union(A!21))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[240, 222])).
% 0.56/0.74 tff(242,plain,
% 0.56/0.74 ((~(epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21)))))) | epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))))),
% 0.56/0.74 inference(tautology,[status(thm)],[])).
% 0.56/0.74 tff(243,plain,
% 0.56/0.74 ((~(epsilon_transitive(union(A!21)) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[242, 241])).
% 0.56/0.74 tff(244,plain,
% 0.56/0.74 (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[243, 44])).
% 0.56/0.74 tff(245,plain,
% 0.56/0.74 (((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21))),
% 0.56/0.74 inference(tautology,[status(thm)],[])).
% 0.56/0.74 tff(246,plain,
% 0.56/0.74 (in(tptp_fun_B_0(union(A!21)), union(A!21))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.56/0.74 tff(247,plain,
% 0.56/0.74 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | ((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(248,plain,
% 0.56/0.74 ((~(~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))))))) <=> ((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(249,plain,
% 0.56/0.74 (((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | $false) <=> (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(250,plain,
% 0.56/0.74 ((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) <=> (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(251,plain,
% 0.56/0.74 (((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))) <=> ((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | $false)),
% 0.56/0.74 inference(monotonicity,[status(thm)],[250, 106])).
% 0.56/0.74 tff(252,plain,
% 0.56/0.74 (((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))) <=> (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))))))),
% 0.56/0.74 inference(transitivity,[status(thm)],[251, 249])).
% 0.56/0.74 tff(253,plain,
% 0.56/0.74 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> (~(~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[252])).
% 0.56/0.74 tff(254,plain,
% 0.56/0.74 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> ((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))),
% 0.56/0.74 inference(transitivity,[status(thm)],[253, 248])).
% 0.56/0.74 tff(255,plain,
% 0.56/0.74 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | ((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[254])).
% 0.56/0.74 tff(256,plain,
% 0.56/0.74 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))),
% 0.56/0.74 inference(transitivity,[status(thm)],[255, 247])).
% 0.56/0.74 tff(257,plain,
% 0.56/0.74 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))) | (~((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | in(tptp_fun_B_0(union(A!21)), union(A!21)) | (~in(union(A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(258,plain,
% 0.56/0.74 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~in(tptp_fun_B_0(union(A!21)), union(A!21))) | (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.56/0.74 tff(259,plain,
% 0.56/0.74 (~((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[258, 95, 246])).
% 0.56/0.74 tff(260,plain,
% 0.56/0.74 (((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))) | in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)),
% 0.56/0.74 inference(tautology,[status(thm)],[])).
% 0.56/0.74 tff(261,plain,
% 0.56/0.74 (in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.56/0.74 tff(262,plain,
% 0.56/0.74 (((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | (ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))) <=> ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(263,plain,
% 0.56/0.74 ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | (ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(264,plain,
% 0.56/0.74 ((~![B: $i] : (ordinal(B) | (~in(B, A!21)))) | ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.56/0.74 tff(265,plain,
% 0.56/0.74 (ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[264, 131, 261])).
% 0.56/0.74 tff(266,plain,
% 0.56/0.74 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(267,plain,
% 0.56/0.74 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[266])).
% 0.56/0.74 tff(268,plain,
% 0.56/0.74 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(269,plain,
% 0.56/0.74 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[268])).
% 0.56/0.74 tff(270,plain,
% 0.56/0.74 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(271,plain,
% 0.56/0.74 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(272,plain,
% 0.56/0.74 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[271])).
% 0.56/0.74 tff(273,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_ordinal1')).
% 0.56/0.74 tff(274,plain,
% 0.56/0.74 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.56/0.74 tff(275,plain,
% 0.56/0.74 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[274, 270])).
% 0.56/0.74 tff(276,plain,(
% 0.56/0.74 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.56/0.74 inference(skolemize,[status(sab)],[275])).
% 0.56/0.74 tff(277,plain,
% 0.56/0.74 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[276, 269])).
% 0.56/0.74 tff(278,plain,
% 0.56/0.74 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[277, 267])).
% 0.56/0.74 tff(279,plain,
% 0.56/0.74 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~epsilon_connected(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~epsilon_connected(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(280,plain,
% 0.56/0.74 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~epsilon_connected(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(281,plain,
% 0.56/0.75 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~epsilon_connected(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.56/0.75 tff(282,plain,
% 0.56/0.75 (~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~epsilon_connected(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[281, 278, 265])).
% 0.56/0.75 tff(283,plain,
% 0.56/0.75 (((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~epsilon_connected(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(284,plain,
% 0.56/0.75 (epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.56/0.75 tff(285,plain,
% 0.56/0.75 ((~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(286,plain,
% 0.56/0.75 ((~((~epsilon_transitive(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | ![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[285, 284])).
% 0.56/0.75 tff(287,plain,
% 0.56/0.75 (![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[286, 40])).
% 0.56/0.75 tff(288,plain,
% 0.56/0.75 (((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21))) | in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(289,plain,
% 0.56/0.75 (in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[288, 259])).
% 0.56/0.75 tff(290,plain,
% 0.56/0.75 (((~![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | ((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) <=> ((~![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | (~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(291,plain,
% 0.56/0.75 ((~![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | ((~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(292,plain,
% 0.56/0.75 ((~![B: $i] : ((~in(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(B, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | (~in(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.56/0.75 tff(293,plain,
% 0.56/0.75 (subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[292, 289, 287])).
% 0.56/0.75 tff(294,plain,
% 0.56/0.75 ((~((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | (~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(295,plain,
% 0.56/0.75 ((~((~subset(tptp_fun_B_0(union(A!21)), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[294, 293])).
% 0.56/0.75 tff(296,plain,
% 0.56/0.75 (![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[295, 20])).
% 0.56/0.75 tff(297,plain,
% 0.56/0.75 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_3(B, A), A)) | in(tptp_fun_C_3(B, A), B)))))))) | (~((~((~subset(tptp_fun_B_0(union(A!21)), union(A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, union(A!21))))) | (~(subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))))))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(298,plain,
% 0.56/0.75 (~((~((~subset(tptp_fun_B_0(union(A!21)), union(A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, union(A!21))))) | (~(subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)))))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[297, 16])).
% 0.56/0.75 tff(299,plain,
% 0.56/0.75 (((~((~subset(tptp_fun_B_0(union(A!21)), union(A!21))) | ![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, union(A!21))))) | (~(subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))))))) | (subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)))))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(300,plain,
% 0.56/0.75 (subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[299, 298])).
% 0.56/0.75 tff(301,plain,
% 0.56/0.75 (((~in(tptp_fun_B_0(union(A!21)), union(A!21))) | subset(tptp_fun_B_0(union(A!21)), union(A!21))) | (~subset(tptp_fun_B_0(union(A!21)), union(A!21)))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(302,plain,
% 0.56/0.75 (~subset(tptp_fun_B_0(union(A!21)), union(A!21))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[301, 244])).
% 0.56/0.75 tff(303,plain,
% 0.56/0.75 ((~(subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)))))) | subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(304,plain,
% 0.56/0.75 ((~(subset(tptp_fun_B_0(union(A!21)), union(A!21)) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)))))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[303, 302])).
% 0.56/0.75 tff(305,plain,
% 0.56/0.75 (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[304, 300])).
% 0.56/0.75 tff(306,plain,
% 0.56/0.75 (((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(307,plain,
% 0.56/0.75 (in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[306, 305])).
% 0.56/0.75 tff(308,plain,
% 0.56/0.75 (((~![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | ((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) <=> ((~![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(309,plain,
% 0.56/0.75 ((~![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | ((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(310,plain,
% 0.56/0.75 ((~![C: $i] : ((~in(C, tptp_fun_B_0(union(A!21)))) | in(C, tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.56/0.75 tff(311,plain,
% 0.56/0.75 (in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[310, 307, 296])).
% 0.56/0.75 tff(312,plain,
% 0.56/0.75 (((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_B_0(union(A!21)))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(313,plain,
% 0.56/0.75 (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[312, 305])).
% 0.56/0.75 tff(314,plain,
% 0.56/0.75 ((~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(315,plain,
% 0.56/0.75 (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[314, 313, 261, 311])).
% 0.56/0.75 tff(316,plain,
% 0.56/0.75 (((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))) | (in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))),
% 0.56/0.75 inference(tautology,[status(thm)],[])).
% 0.56/0.75 tff(317,plain,
% 0.56/0.75 ((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[316, 315])).
% 0.56/0.75 tff(318,plain,
% 0.56/0.75 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(319,plain,
% 0.56/0.75 ((~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))))))))))) <=> (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(320,plain,
% 0.56/0.75 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[319])).
% 0.56/0.75 tff(321,plain,
% 0.56/0.75 (((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))) <=> ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))))))))),
% 0.56/0.75 inference(transitivity,[status(thm)],[320, 318])).
% 0.56/0.75 tff(322,plain,
% 0.56/0.75 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~(union(A!21) = union(A!21))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21))) | in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)))))))) | (~((union(A!21) = union(A!21)) | (~((~(in(tptp_fun_C_5(union(A!21), A!21), union(A!21)) | (~((~in(tptp_fun_C_5(union(A!21), A!21), tptp_fun_D_6(union(A!21), A!21))) | (~in(tptp_fun_D_6(union(A!21), A!21), A!21)))))) | (~((~in(tptp_fun_C_5(union(A!21), A!21), union(A!21))) | (~in(union(A!21), A!21)) | (~in(tptp_fun_C_5(union(A!21), A!21), union(A!21)))))))))))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(323,plain,
% 0.56/0.75 ((~![A: $i, B: $i, D_22: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_4(C, A))) | (~in(tptp_fun_D_4(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_5(B, A), B) | (~((~in(tptp_fun_C_5(B, A), tptp_fun_D_6(B, A))) | (~in(tptp_fun_D_6(B, A), A)))))) | (~((~in(tptp_fun_C_5(B, A), B)) | (~in(D_22, A)) | (~in(tptp_fun_C_5(B, A), D_22))))))))))) | (~((~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21))) | (~((~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21))) | (~in(tptp_fun_D_4(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), A!21), A!21)))))) | (~(in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), union(A!21)) | (~in(tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21), A!21)) | (~in(tptp_fun_C_3(union(A!21), tptp_fun_B_0(union(A!21))), tptp_fun_D_4(tptp_fun_B_0(union(A!21)), A!21)))))))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.56/0.76 tff(324,plain,
% 0.56/0.76 ($false),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[323, 95, 317])).
% 0.56/0.76 % SZS output end Proof
% 0.56/0.76 % E exiting
%------------------------------------------------------------------------------