%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU155+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:03 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU155+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:07:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(in_type, type, (
% 0.12/0.38 in: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_A_5_type, type, (
% 0.12/0.38 tptp_fun_A_5: $i)).
% 0.12/0.38 tff(tptp_fun_C_0_type, type, (
% 0.12/0.38 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.38 tff(union_type, type, (
% 0.12/0.38 union: $i > $i)).
% 0.12/0.38 tff(tptp_fun_B_4_type, type, (
% 0.12/0.38 tptp_fun_B_4: $i)).
% 0.12/0.38 tff(tptp_fun_D_1_type, type, (
% 0.12/0.38 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.12/0.38 tff(subset_type, type, (
% 0.12/0.38 subset: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_C_2_type, type, (
% 0.12/0.38 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_D_3_type, type, (
% 0.12/0.38 tptp_fun_D_3: ( $i * $i ) > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (^[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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.38 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')).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.38 tff(14,plain,(
% 0.12/0.38 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(A!5, union(B!4))) | ![C: $i] : ((~in(C, A!5)) | in(C, union(B!4))))) | (~(subset(A!5, union(B!4)) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4))))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (~((~((~subset(A!5, union(B!4))) | ![C: $i] : ((~in(C, A!5)) | in(C, union(B!4))))) | (~(subset(A!5, union(B!4)) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (((~((~subset(A!5, union(B!4))) | ![C: $i] : ((~in(C, A!5)) | in(C, union(B!4))))) | (~(subset(A!5, union(B!4)) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4))))))) | (subset(A!5, union(B!4)) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (subset(A!5, union(B!4)) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))) <=> (~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![A: $i, B: $i] : (in(A, B) => subset(A, union(B)))) <=> (~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(23,axiom,(~![A: $i, B: $i] : (in(A, B) => subset(A, union(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l50_zfmisc_1')).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~![A: $i, B: $i] : ((~in(A, B)) | subset(A, union(B)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.12/0.38 tff(28,plain,(
% 0.12/0.38 ~((~in(A!5, B!4)) | subset(A!5, union(B!4)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (~subset(A!5, union(B!4))),
% 0.12/0.38 inference(or_elim,[status(thm)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~(subset(A!5, union(B!4)) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)))))) | subset(A!5, union(B!4)) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~(subset(A!5, union(B!4)) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)))))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[31, 20])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~in(tptp_fun_C_0(union(B!4), A!5), union(B!4)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | in(tptp_fun_C_0(union(B!4), A!5), A!5)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (in(tptp_fun_C_0(union(B!4), A!5), A!5)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (in(A!5, B!4)),
% 0.12/0.38 inference(or_elim,[status(thm)],[28])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 ((~((~in(A!5, B!4)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(tptp_fun_C_0(union(B!4), A!5), A!5)))) | (~in(A!5, B!4)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(tptp_fun_C_0(union(B!4), A!5), A!5))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (~((~in(A!5, B!4)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(tptp_fun_C_0(union(B!4), A!5), A!5)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[38, 37, 36, 34])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (((~((~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4))) | (~in(tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4), B!4)))))) | (~((~in(A!5, B!4)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(tptp_fun_C_0(union(B!4), A!5), A!5))))) | ((~in(A!5, B!4)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(tptp_fun_C_0(union(B!4), A!5), A!5)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ((~((~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4))) | (~in(tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4), B!4)))))) | (~((~in(A!5, B!4)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(tptp_fun_C_0(union(B!4), A!5), A!5))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (^[A: $i, B: $i, D_6: $i, C: $i, D: $i] : rewrite((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6)))))))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(43,plain,
% 0.21/0.38 (![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) <=> ![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.38 tff(44,plain,
% 0.21/0.38 (^[A: $i, B: $i, D_6: $i, C: $i, D: $i] : refl((~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) <=> (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))))),
% 0.21/0.38 inference(bind,[status(th)],[])).
% 0.21/0.38 tff(45,plain,
% 0.21/0.38 (![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) <=> ![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6)))))))))))),
% 0.21/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.38 tff(46,plain,
% 0.21/0.38 (![A: $i, B: $i] : ![D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) <=> ![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6)))))))))))),
% 0.21/0.38 inference(pull_quant,[status(thm)],[])).
% 0.21/0.38 tff(47,plain,
% 0.21/0.38 (^[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_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), pull_quant(((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | ?[D: $i] : (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))), (((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))) <=> ?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> (~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))), pull_quant((~?[D: $i] : ((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), ((~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))) <=> ![D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))) <=> ![C: $i, D: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A)))))))), (![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))) <=> ![D: $i] : ((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))), ((~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))) <=> (~![D: $i] : ((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))), pull_quant((~![D: $i] : ((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))), ((~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))) <=> ?[D: $i] : (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))), (((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))) <=> ((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))), pull_quant(((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | ?[D: $i] : (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))), (((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))) <=> ?[D: $i] : ((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))), ((~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))) <=> (~?[D: $i] : ((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))), pull_quant((~?[D: $i] : ((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))), ((~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))) <=> ![D: $i] : (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))) <=> ((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))), pull_quant(((B = union(A)) | ![D: $i] : (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))), (((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))) <=> ![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))) <=> (~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))), pull_quant((~![D: $i] : ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))), ((~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))) <=> ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))) <=> (?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))))), pull_quant((?[C: $i, D: $i] : (~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | ?[D: $i] : (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))) <=> ?[D_6: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))), (((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))) <=> ?[D_6: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> (~?[D_6: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))))), pull_quant((~?[D_6: $i, C: $i, D: $i] : ((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) <=> ![D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6)))))))))))), ((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> ![D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6)))))))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> ![A: $i, B: $i] : ![D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6)))))))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> ![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6)))))))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[48, 46])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> ![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6)))))))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[49, 45])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 (^[A: $i, B: $i] : rewrite((~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[51])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))) <=> ![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6)))))))))))),
% 0.21/0.39 inference(transitivity,[status(thm)],[52, 50])).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_1(C, A)) & in(tptp_fun_D_1(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_1(C, A))) | (~in(tptp_fun_D_1(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_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A)) <=> (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A))))), ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) <=> (in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A))))))), rewrite((in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A))))) <=> (in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))), ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) <=> (in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A))))))), rewrite(((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A)))) <=> ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))), (((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A))))) <=> ((in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))), rewrite(((in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A))))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))) <=> (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))), (((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A))))) <=> (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))), rewrite(((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))), (((B = union(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A)))))) <=> ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_1(C, A)) & in(tptp_fun_D_1(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A))))))) <=> (((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))))), rewrite((((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A)))))))) & ((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D))))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))))), ((((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_1(C, A)) & in(tptp_fun_D_1(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A))))))) <=> (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(55,plain,
% 0.21/0.40 (![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_1(C, A)) & in(tptp_fun_D_1(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (![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))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 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/sandbox/benchmark/theBenchmark.p','d4_tarski')).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.40 tff(59,plain,(
% 0.21/0.40 ![A: $i, B: $i] : (((~(B = union(A))) | ![C: $i] : (((~in(C, B)) | (in(C, tptp_fun_D_1(C, A)) & in(tptp_fun_D_1(C, A), A))) & (in(C, B) | ![D: $i] : (~(in(C, D) & in(D, A)))))) & ((B = union(A)) | ((in(tptp_fun_C_2(B, A), B) | (in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) & in(tptp_fun_D_3(B, A), A))) & ((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : (~(in(tptp_fun_C_2(B, A), D) & in(D, A)))))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[58])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (![A: $i, B: $i] : (~((~((~(B = union(A))) | ![C: $i] : (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ![D: $i] : ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ![D: $i] : ((~in(D, A)) | (~in(tptp_fun_C_2(B, A), D)))))))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~(in(C, B) | ((~in(C, D)) | (~in(D, A))))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | ((~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6)))))))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[61, 43])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (((~![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) | (~((~((~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4))) | (~in(tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4), B!4)))))) | (~((~in(A!5, B!4)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(tptp_fun_C_0(union(B!4), A!5), A!5))))))) <=> ((~![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) | (~((~((~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4))) | (~in(tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4), B!4)))))) | (~((~in(A!5, B!4)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(tptp_fun_C_0(union(B!4), A!5), A!5)))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 ((~((~((~(union(B!4) = union(B!4))) | (~((~((~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4))) | (~in(tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4), B!4)))))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(A!5, B!4)))))))) | (~((union(B!4) = union(B!4)) | (~((~(in(tptp_fun_C_2(union(B!4), B!4), union(B!4)) | (~((~in(tptp_fun_C_2(union(B!4), B!4), tptp_fun_D_3(union(B!4), B!4))) | (~in(tptp_fun_D_3(union(B!4), B!4), B!4)))))) | (~((~in(tptp_fun_C_2(union(B!4), B!4), union(B!4))) | (~in(A!5, B!4)) | (~in(tptp_fun_C_2(union(B!4), B!4), A!5)))))))))) <=> (~((~((~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4))) | (~in(tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4), B!4)))))) | (~((~in(A!5, B!4)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(tptp_fun_C_0(union(B!4), A!5), A!5))))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (((~![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) | (~((~((~(union(B!4) = union(B!4))) | (~((~((~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4))) | (~in(tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4), B!4)))))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(A!5, B!4)))))))) | (~((union(B!4) = union(B!4)) | (~((~(in(tptp_fun_C_2(union(B!4), B!4), union(B!4)) | (~((~in(tptp_fun_C_2(union(B!4), B!4), tptp_fun_D_3(union(B!4), B!4))) | (~in(tptp_fun_D_3(union(B!4), B!4), B!4)))))) | (~((~in(tptp_fun_C_2(union(B!4), B!4), union(B!4))) | (~in(A!5, B!4)) | (~in(tptp_fun_C_2(union(B!4), B!4), A!5))))))))))) <=> ((~![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) | (~((~((~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4))) | (~in(tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4), B!4)))))) | (~((~in(A!5, B!4)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(tptp_fun_C_0(union(B!4), A!5), A!5)))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[64])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (((~![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) | (~((~((~(union(B!4) = union(B!4))) | (~((~((~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4))) | (~in(tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4), B!4)))))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(A!5, B!4)))))))) | (~((union(B!4) = union(B!4)) | (~((~(in(tptp_fun_C_2(union(B!4), B!4), union(B!4)) | (~((~in(tptp_fun_C_2(union(B!4), B!4), tptp_fun_D_3(union(B!4), B!4))) | (~in(tptp_fun_D_3(union(B!4), B!4), B!4)))))) | (~((~in(tptp_fun_C_2(union(B!4), B!4), union(B!4))) | (~in(A!5, B!4)) | (~in(tptp_fun_C_2(union(B!4), B!4), A!5))))))))))) <=> ((~![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) | (~((~((~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4))) | (~in(tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4), B!4)))))) | (~((~in(A!5, B!4)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(tptp_fun_C_0(union(B!4), A!5), A!5)))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[65, 63])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 ((~![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) | (~((~((~(union(B!4) = union(B!4))) | (~((~((~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4))) | (~in(tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4), B!4)))))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), A!5)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(A!5, B!4)))))))) | (~((union(B!4) = union(B!4)) | (~((~(in(tptp_fun_C_2(union(B!4), B!4), union(B!4)) | (~((~in(tptp_fun_C_2(union(B!4), B!4), tptp_fun_D_3(union(B!4), B!4))) | (~in(tptp_fun_D_3(union(B!4), B!4), B!4)))))) | (~((~in(tptp_fun_C_2(union(B!4), B!4), union(B!4))) | (~in(A!5, B!4)) | (~in(tptp_fun_C_2(union(B!4), B!4), A!5))))))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 ((~![A: $i, B: $i, D_6: $i, C: $i, D: $i] : (~((~((~(B = union(A))) | (~((~((~in(C, B)) | (~((~in(C, tptp_fun_D_1(C, A))) | (~in(tptp_fun_D_1(C, A), A)))))) | (~((~in(C, D)) | in(C, B) | (~in(D, A)))))))) | (~((B = union(A)) | (~((~(in(tptp_fun_C_2(B, A), B) | (~((~in(tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) | (~in(tptp_fun_D_3(B, A), A)))))) | (~((~in(tptp_fun_C_2(B, A), B)) | (~in(D_6, A)) | (~in(tptp_fun_C_2(B, A), D_6))))))))))) | (~((~((~in(tptp_fun_C_0(union(B!4), A!5), union(B!4))) | (~((~in(tptp_fun_C_0(union(B!4), A!5), tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4))) | (~in(tptp_fun_D_1(tptp_fun_C_0(union(B!4), A!5), B!4), B!4)))))) | (~((~in(A!5, B!4)) | in(tptp_fun_C_0(union(B!4), A!5), union(B!4)) | (~in(tptp_fun_C_0(union(B!4), A!5), A!5))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[68, 62, 41])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------