%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU155+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:03 AM UTC 2025
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU155+2 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:07:48 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(in_type, type, (
% 0.19/0.39 in: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_A_12_type, type, (
% 0.19/0.39 tptp_fun_A_12: $i)).
% 0.19/0.39 tff(tptp_fun_C_5_type, type, (
% 0.19/0.39 tptp_fun_C_5: ( $i * $i ) > $i)).
% 0.19/0.39 tff(union_type, type, (
% 0.19/0.39 union: $i > $i)).
% 0.19/0.39 tff(tptp_fun_B_11_type, type, (
% 0.19/0.39 tptp_fun_B_11: $i)).
% 0.19/0.39 tff(tptp_fun_D_7_type, type, (
% 0.19/0.39 tptp_fun_D_7: ( $i * $i ) > $i)).
% 0.19/0.39 tff(subset_type, type, (
% 0.19/0.39 subset: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_C_8_type, type, (
% 0.19/0.39 tptp_fun_C_8: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_D_9_type, type, (
% 0.19/0.39 tptp_fun_D_9: ( $i * $i ) > $i)).
% 0.19/0.39 tff(tptp_fun_B_1_type, type, (
% 0.19/0.39 tptp_fun_B_1: $i > $i)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(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_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(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_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(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_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (^[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_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(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_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.19/0.39 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.19/0.39 tff(14,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[13])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_5(B, A), A)) | in(tptp_fun_C_5(B, A), B)))))))) | (~((~((~subset(A!12, union(B!11))) | ![C: $i] : ((~in(C, A!12)) | in(C, union(B!11))))) | (~(subset(A!12, union(B!11)) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11))))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (~((~((~subset(A!12, union(B!11))) | ![C: $i] : ((~in(C, A!12)) | in(C, union(B!11))))) | (~(subset(A!12, union(B!11)) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (((~((~subset(A!12, union(B!11))) | ![C: $i] : ((~in(C, A!12)) | in(C, union(B!11))))) | (~(subset(A!12, union(B!11)) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11))))))) | (subset(A!12, union(B!11)) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (subset(A!12, union(B!11)) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) <=> (~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (in(A, B) => subset(A, union(B)))) <=> (~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(23,axiom,(~![A: $i, B: $i] : (in(A, B) => subset(A, union(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l50_zfmisc_1')).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.19/0.40 tff(28,plain,(
% 0.19/0.40 ~((~in(A!12, B!11)) | subset(A!12, union(B!11)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[27])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (~subset(A!12, union(B!11))),
% 0.19/0.40 inference(or_elim,[status(thm)],[28])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 ((~(subset(A!12, union(B!11)) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)))))) | subset(A!12, union(B!11)) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11))))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 ((~(subset(A!12, union(B!11)) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)))))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[31, 20])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~in(tptp_fun_C_5(union(B!11), A!12), union(B!11)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | in(tptp_fun_C_5(union(B!11), A!12), A!12)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (in(tptp_fun_C_5(union(B!11), A!12), A!12)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (in(A!12, B!11)),
% 0.19/0.40 inference(or_elim,[status(thm)],[28])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 ((~((~in(A!12, B!11)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(tptp_fun_C_5(union(B!11), A!12), A!12)))) | (~in(A!12, B!11)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(tptp_fun_C_5(union(B!11), A!12), A!12))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (~((~in(A!12, B!11)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(tptp_fun_C_5(union(B!11), A!12), A!12)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[38, 37, 36, 34])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (((~((~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11))) | (~in(tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11), B!11)))))) | (~((~in(A!12, B!11)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(tptp_fun_C_5(union(B!11), A!12), A!12))))) | ((~in(A!12, B!11)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(tptp_fun_C_5(union(B!11), A!12), A!12)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 ((~((~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11))) | (~in(tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11), B!11)))))) | (~((~in(A!12, B!11)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(tptp_fun_C_5(union(B!11), A!12), A!12))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (^[A: $i, B: $i, D_18: $i, C: $i, D: $i] : rewrite((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | (~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18)))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) <=> ![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | (~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (^[A: $i, B: $i, D_18: $i, C: $i, D: $i] : refl((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) <=> ![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18)))))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (![A: $i, B: $i] : ![D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) <=> ![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18)))))))))))),
% 0.19/0.40 inference(pull_quant,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (^[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_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), pull_quant(((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> (~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant((~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))) <=> ![D: $i] : ((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))), ((~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))) <=> (~![D: $i] : ((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))), pull_quant((~![D: $i] : ((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))), ((~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))), (((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))) <=> ((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))), pull_quant(((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))), (((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))), ((~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))) <=> (~?[D: $i] : ((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))), pull_quant((~?[D: $i] : ((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))), ((~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))) <=> ((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))), pull_quant(((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))) <=> (~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))))), pull_quant((~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))) <=> (?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))))), pull_quant((?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))) <=> ?[D_18: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))) <=> ?[D_18: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))))) <=> (~?[D_18: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))))), pull_quant((~?[D_18: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) <=> ![D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))))) <=> ![D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18)))))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))))) <=> ![A: $i, B: $i] : ![D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18)))))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))))) <=> ![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18)))))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))))) <=> ![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18)))))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[49, 45])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (^[A: $i, B: $i] : rewrite((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))))) <=> ![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18)))))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[52, 50])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_7(C, A)) & in(tptp_fun_D_7(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_7(C, A))) | (~in(tptp_fun_D_7(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_8(B, A), tptp_fun_D_9(B, A)) & in(tptp_fun_D_9(B, A), A)) <=> (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A))))), ((in(tptp_fun_C_8(B, A), B) | (in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)) & in(tptp_fun_D_9(B, A), A))) <=> (in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A))))))), rewrite((in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A))))) <=> (in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))), ((in(tptp_fun_C_8(B, A), B) | (in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)) & in(tptp_fun_D_9(B, A), A))) <=> (in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A))))))), rewrite(((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_8(B, A), D) & in(D, A)))) <=> ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))), (((in(tptp_fun_C_8(B, A), B) | (in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)) & in(tptp_fun_D_9(B, A), A))) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_8(B, A), D) & in(D, A))))) <=> ((in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A))))) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))), rewrite(((in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A))))) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))) <=> (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))), (((in(tptp_fun_C_8(B, A), B) | (in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)) & in(tptp_fun_D_9(B, A), A))) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_8(B, A), D) & in(D, A))))) <=> (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_8(B, A), B) | (in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)) & in(tptp_fun_D_9(B, A), A))) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_8(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))), rewrite(((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_8(B, A), B) | (in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)) & in(tptp_fun_D_9(B, A), A))) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_8(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_7(C, A)) & in(tptp_fun_D_7(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_8(B, A), B) | (in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)) & in(tptp_fun_D_9(B, A), A))) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_8(B, A), D) & in(D, A))))))) <=> (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))))), rewrite((((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_7(C, A)) & in(tptp_fun_D_7(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_8(B, A), B) | (in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)) & in(tptp_fun_D_9(B, A), A))) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_8(B, A), D) & in(D, A))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_7(C, A)) & in(tptp_fun_D_7(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_8(B, A), B) | (in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)) & in(tptp_fun_D_9(B, A), A))) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_8(B, A), D) & in(D, A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A)))) <=> ![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(57,axiom,(![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_tarski')).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.41 tff(59,plain,(
% 0.19/0.41 ![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_7(C, A)) & in(tptp_fun_D_7(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_8(B, A), B) | (in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A)) & in(tptp_fun_D_9(B, A), A))) & ((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_8(B, A), D) & in(D, A)))))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[58])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_8(B, A), D)))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | ((~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18)))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | (~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[61, 43])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (((~![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | (~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) | (~((~((~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11))) | (~in(tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11), B!11)))))) | (~((~in(A!12, B!11)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(tptp_fun_C_5(union(B!11), A!12), A!12))))))) <=> ((~![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | (~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) | (~((~((~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11))) | (~in(tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11), B!11)))))) | (~((~in(A!12, B!11)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(tptp_fun_C_5(union(B!11), A!12), A!12)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ((~((~((~(union(B!11) = union(B!11))) | (~((~((~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11))) | (~in(tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11), B!11)))))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(A!12, B!11)))))))) | (~((union(B!11) = union(B!11)) | (~((~(in(tptp_fun_C_8(union(B!11), B!11), union(B!11)) | (~((~in(tptp_fun_C_8(union(B!11), B!11), tptp_fun_D_9(union(B!11), B!11))) | (~in(tptp_fun_D_9(union(B!11), B!11), B!11)))))) | (~((~in(tptp_fun_C_8(union(B!11), B!11), union(B!11))) | (~in(tptp_fun_B_1(B!11), B!11)) | (~in(tptp_fun_C_8(union(B!11), B!11), tptp_fun_B_1(B!11))))))))))) <=> (~((~((~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11))) | (~in(tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11), B!11)))))) | (~((~in(A!12, B!11)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(tptp_fun_C_5(union(B!11), A!12), A!12))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (((~![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | (~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) | (~((~((~(union(B!11) = union(B!11))) | (~((~((~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11))) | (~in(tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11), B!11)))))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(A!12, B!11)))))))) | (~((union(B!11) = union(B!11)) | (~((~(in(tptp_fun_C_8(union(B!11), B!11), union(B!11)) | (~((~in(tptp_fun_C_8(union(B!11), B!11), tptp_fun_D_9(union(B!11), B!11))) | (~in(tptp_fun_D_9(union(B!11), B!11), B!11)))))) | (~((~in(tptp_fun_C_8(union(B!11), B!11), union(B!11))) | (~in(tptp_fun_B_1(B!11), B!11)) | (~in(tptp_fun_C_8(union(B!11), B!11), tptp_fun_B_1(B!11)))))))))))) <=> ((~![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | (~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) | (~((~((~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11))) | (~in(tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11), B!11)))))) | (~((~in(A!12, B!11)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(tptp_fun_C_5(union(B!11), A!12), A!12)))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[64])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (((~![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | (~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) | (~((~((~(union(B!11) = union(B!11))) | (~((~((~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11))) | (~in(tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11), B!11)))))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(A!12, B!11)))))))) | (~((union(B!11) = union(B!11)) | (~((~(in(tptp_fun_C_8(union(B!11), B!11), union(B!11)) | (~((~in(tptp_fun_C_8(union(B!11), B!11), tptp_fun_D_9(union(B!11), B!11))) | (~in(tptp_fun_D_9(union(B!11), B!11), B!11)))))) | (~((~in(tptp_fun_C_8(union(B!11), B!11), union(B!11))) | (~in(tptp_fun_B_1(B!11), B!11)) | (~in(tptp_fun_C_8(union(B!11), B!11), tptp_fun_B_1(B!11)))))))))))) <=> ((~![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | (~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) | (~((~((~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11))) | (~in(tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11), B!11)))))) | (~((~in(A!12, B!11)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(tptp_fun_C_5(union(B!11), A!12), A!12)))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[65, 63])).
% 0.19/0.42 tff(67,plain,
% 0.19/0.42 ((~![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | (~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) | (~((~((~(union(B!11) = union(B!11))) | (~((~((~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11))) | (~in(tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11), B!11)))))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), A!12)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(A!12, B!11)))))))) | (~((union(B!11) = union(B!11)) | (~((~(in(tptp_fun_C_8(union(B!11), B!11), union(B!11)) | (~((~in(tptp_fun_C_8(union(B!11), B!11), tptp_fun_D_9(union(B!11), B!11))) | (~in(tptp_fun_D_9(union(B!11), B!11), B!11)))))) | (~((~in(tptp_fun_C_8(union(B!11), B!11), union(B!11))) | (~in(tptp_fun_B_1(B!11), B!11)) | (~in(tptp_fun_C_8(union(B!11), B!11), tptp_fun_B_1(B!11)))))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 ((~![A: $i, B: $i, D_18: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_7(C, A))) | (~in(tptp_fun_D_7(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_8(B, A), B) | (~((~in(tptp_fun_C_8(B, A), tptp_fun_D_9(B, A))) | (~in(tptp_fun_D_9(B, A), A)))))) | (~((~in(tptp_fun_C_8(B, A), B)) | (~in(D_18, A)) | (~in(tptp_fun_C_8(B, A), D_18))))))))))) | (~((~((~in(tptp_fun_C_5(union(B!11), A!12), union(B!11))) | (~((~in(tptp_fun_C_5(union(B!11), A!12), tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11))) | (~in(tptp_fun_D_7(tptp_fun_C_5(union(B!11), A!12), B!11), B!11)))))) | (~((~in(A!12, B!11)) | in(tptp_fun_C_5(union(B!11), A!12), union(B!11)) | (~in(tptp_fun_C_5(union(B!11), A!12), A!12))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[68, 62, 41])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------