%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET941+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:26:42 AM UTC 2025
% Result : Theorem 0.24s 0.41s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SET941+1 : TPTP v9.0.0. Released v3.2.0.
% 0.09/0.15 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n012.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Jun 20 05:50:40 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.24/0.41 % SZS status Theorem
% 0.24/0.41 % SZS output start Proof
% 0.24/0.41 tff(in_type, type, (
% 0.24/0.41 in: ( $i * $i ) > $o)).
% 0.24/0.41 tff(tptp_fun_B_6_type, type, (
% 0.24/0.41 tptp_fun_B_6: $i)).
% 0.24/0.41 tff(tptp_fun_D_1_type, type, (
% 0.24/0.41 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.24/0.41 tff(tptp_fun_A_7_type, type, (
% 0.24/0.41 tptp_fun_A_7: $i)).
% 0.24/0.41 tff(tptp_fun_C_0_type, type, (
% 0.24/0.41 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.24/0.41 tff(union_type, type, (
% 0.24/0.41 union: $i > $i)).
% 0.24/0.41 tff(subset_type, type, (
% 0.24/0.41 subset: ( $i * $i ) > $o)).
% 0.24/0.41 tff(tptp_fun_C_2_type, type, (
% 0.24/0.41 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.24/0.41 tff(tptp_fun_D_3_type, type, (
% 0.24/0.41 tptp_fun_D_3: ( $i * $i ) > $i)).
% 0.24/0.41 tff(1,plain,
% 0.24/0.41 (^[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))))))))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(2,plain,
% 0.24/0.41 (![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)))))))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.24/0.41 tff(3,plain,
% 0.24/0.41 (^[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))))))))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(4,plain,
% 0.24/0.41 (![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)))))))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.24/0.41 tff(5,plain,
% 0.24/0.41 (![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)))))))),
% 0.24/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.24/0.41 tff(6,plain,
% 0.24/0.41 (^[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)))))))))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(7,plain,
% 0.24/0.41 (![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)))))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.24/0.42 tff(8,plain,
% 0.24/0.42 (![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)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(9,plain,
% 0.24/0.42 (^[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))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(10,plain,
% 0.24/0.42 (![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)))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[9])).
% 0.24/0.42 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')).
% 0.24/0.42 tff(12,plain,
% 0.24/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.24/0.42 tff(13,plain,
% 0.24/0.42 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.24/0.42 tff(14,plain,(
% 0.24/0.42 ![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)))))),
% 0.24/0.42 inference(skolemize,[status(sab)],[13])).
% 0.24/0.42 tff(15,plain,
% 0.24/0.42 (![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)))))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.24/0.42 tff(16,plain,
% 0.24/0.42 (![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)))))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.24/0.42 tff(17,plain,
% 0.24/0.42 ((~![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(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6)))) | (~(subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7)), B!6)))))))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(18,plain,
% 0.24/0.42 (~((~((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6)))) | (~(subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7)), B!6))))))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.24/0.42 tff(19,plain,
% 0.24/0.42 (((~((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6)))) | (~(subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7)), B!6)))))) | ((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6)))),
% 0.24/0.42 inference(tautology,[status(thm)],[])).
% 0.24/0.42 tff(20,plain,
% 0.24/0.42 ((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.24/0.42 tff(21,plain,
% 0.24/0.42 ((~![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(union(A!7), B!6)) | ![C: $i] : ((~in(C, union(A!7))) | in(C, B!6)))) | (~(subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)))))))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(22,plain,
% 0.24/0.42 (~((~((~subset(union(A!7), B!6)) | ![C: $i] : ((~in(C, union(A!7))) | in(C, B!6)))) | (~(subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))))))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[21, 16])).
% 0.24/0.42 tff(23,plain,
% 0.24/0.42 (((~((~subset(union(A!7), B!6)) | ![C: $i] : ((~in(C, union(A!7))) | in(C, B!6)))) | (~(subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)))))) | (subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))))),
% 0.24/0.42 inference(tautology,[status(thm)],[])).
% 0.24/0.42 tff(24,plain,
% 0.24/0.42 (subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.24/0.42 tff(25,plain,
% 0.24/0.42 ((![C: $i] : ((~in(C, A!7)) | subset(C, B!6)) & (~subset(union(A!7), B!6))) <=> (![C: $i] : ((~in(C, A!7)) | subset(C, B!6)) & (~subset(union(A!7), B!6)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(26,plain,
% 0.24/0.42 ((~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))) <=> (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(27,plain,
% 0.24/0.42 ((~![A: $i, B: $i] : (![C: $i] : (in(C, A) => subset(C, B)) => subset(union(A), B))) <=> (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(28,axiom,(~![A: $i, B: $i] : (![C: $i] : (in(C, A) => subset(C, B)) => subset(union(A), B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t94_zfmisc_1')).
% 0.24/0.42 tff(29,plain,
% 0.24/0.42 (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.24/0.42 tff(30,plain,
% 0.24/0.42 (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.24/0.42 tff(31,plain,
% 0.24/0.42 (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.24/0.42 tff(32,plain,
% 0.24/0.42 (~![A: $i, B: $i] : ((~![C: $i] : ((~in(C, A)) | subset(C, B))) | subset(union(A), B))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.24/0.42 tff(33,plain,
% 0.24/0.42 (![C: $i] : ((~in(C, A!7)) | subset(C, B!6)) & (~subset(union(A!7), B!6))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.24/0.42 tff(34,plain,
% 0.24/0.42 (~subset(union(A!7), B!6)),
% 0.24/0.42 inference(and_elim,[status(thm)],[33])).
% 0.24/0.42 tff(35,plain,
% 0.24/0.42 ((~(subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))))) | subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)))),
% 0.24/0.42 inference(tautology,[status(thm)],[])).
% 0.24/0.42 tff(36,plain,
% 0.24/0.42 ((~(subset(union(A!7), B!6) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.24/0.42 tff(37,plain,
% 0.24/0.42 (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[36, 24])).
% 0.24/0.42 tff(38,plain,
% 0.24/0.42 (((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))),
% 0.24/0.42 inference(tautology,[status(thm)],[])).
% 0.24/0.42 tff(39,plain,
% 0.24/0.42 (in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.24/0.42 tff(40,plain,
% 0.24/0.42 (^[A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) <=> (~((~((~(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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(41,plain,
% 0.24/0.42 (![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) <=> ![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[40])).
% 0.24/0.42 tff(42,plain,
% 0.24/0.42 (^[A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) <=> (~((~((~(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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(43,plain,
% 0.24/0.42 (![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) <=> ![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[42])).
% 0.24/0.42 tff(44,plain,
% 0.24/0.42 (![A: $i, B: $i] : ![D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) <=> ![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.24/0.42 inference(pull_quant,[status(thm)],[])).
% 0.24/0.42 tff(45,plain,
% 0.24/0.42 (^[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_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))), (((~((~(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_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))), ((~((~((~(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_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))))), pull_quant((~?[D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) <=> ![D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))), ((~((~((~(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_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))))),
% 0.24/0.43 inference(bind,[status(th)],[])).
% 0.24/0.43 tff(46,plain,
% 0.24/0.43 (![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_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.24/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.24/0.43 tff(47,plain,
% 0.24/0.43 (![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_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.24/0.43 inference(transitivity,[status(thm)],[46, 44])).
% 0.24/0.43 tff(48,plain,
% 0.24/0.43 (![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_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.24/0.43 inference(transitivity,[status(thm)],[47, 43])).
% 0.24/0.43 tff(49,plain,
% 0.24/0.43 (^[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))))))))))))),
% 0.24/0.43 inference(bind,[status(th)],[])).
% 0.24/0.43 tff(50,plain,
% 0.24/0.43 (![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)))))))))))),
% 0.24/0.43 inference(quant_intro,[status(thm)],[49])).
% 0.24/0.43 tff(51,plain,
% 0.24/0.43 (![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_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.24/0.43 inference(transitivity,[status(thm)],[50, 48])).
% 0.24/0.43 tff(52,plain,
% 0.24/0.43 (^[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)))))))))))))),
% 0.24/0.44 inference(bind,[status(th)],[])).
% 0.24/0.44 tff(53,plain,
% 0.24/0.44 (![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)))))))))))),
% 0.24/0.44 inference(quant_intro,[status(thm)],[52])).
% 0.24/0.44 tff(54,plain,
% 0.24/0.44 (![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))))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(55,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')).
% 0.24/0.44 tff(56,plain,
% 0.24/0.44 (![A: $i, B: $i] : ((B = union(A)) <=> ![C: $i] : (in(C, B) <=> ?[D: $i] : (in(C, D) & in(D, A))))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.24/0.44 tff(57,plain,(
% 0.24/0.44 ![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)))))))),
% 0.24/0.44 inference(skolemize,[status(sab)],[56])).
% 0.24/0.44 tff(58,plain,
% 0.24/0.44 (![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)))))))))))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.24/0.44 tff(59,plain,
% 0.24/0.44 (![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8)))))))))))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.24/0.44 tff(60,plain,
% 0.24/0.44 (![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))),
% 0.24/0.44 inference(modus_ponens,[status(thm)],[59, 41])).
% 0.24/0.44 tff(61,plain,
% 0.24/0.44 (((~![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | ((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) <=> ((~![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | (~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(62,plain,
% 0.24/0.44 ((~(~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))))))) <=> ((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(63,plain,
% 0.24/0.44 (((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | $false) <=> (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))))))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(64,plain,
% 0.24/0.44 ((~$true) <=> $false),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(65,plain,
% 0.24/0.44 (($true | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))) <=> $true),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(66,plain,
% 0.24/0.44 ((~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))))))) <=> (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(67,plain,
% 0.24/0.44 ((union(A!7) = union(A!7)) <=> $true),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(68,plain,
% 0.24/0.44 (((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))) <=> ($true | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))))))))),
% 0.24/0.44 inference(monotonicity,[status(thm)],[67, 66])).
% 0.24/0.44 tff(69,plain,
% 0.24/0.44 (((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))) <=> $true),
% 0.24/0.44 inference(transitivity,[status(thm)],[68, 65])).
% 0.24/0.44 tff(70,plain,
% 0.24/0.44 ((~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))))))))) <=> (~$true)),
% 0.24/0.44 inference(monotonicity,[status(thm)],[69])).
% 0.24/0.44 tff(71,plain,
% 0.24/0.44 ((~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))))))))) <=> $false),
% 0.24/0.44 inference(transitivity,[status(thm)],[70, 64])).
% 0.24/0.44 tff(72,plain,
% 0.24/0.44 ((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) <=> (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))))))),
% 0.24/0.44 inference(rewrite,[status(thm)],[])).
% 0.24/0.44 tff(73,plain,
% 0.24/0.44 (((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))))) <=> ((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | $false)),
% 0.24/0.44 inference(monotonicity,[status(thm)],[72, 71])).
% 0.24/0.44 tff(74,plain,
% 0.24/0.44 (((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))))) <=> (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))))))),
% 0.24/0.45 inference(transitivity,[status(thm)],[73, 63])).
% 0.24/0.45 tff(75,plain,
% 0.24/0.45 ((~((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))))))))))) <=> (~(~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))))),
% 0.24/0.45 inference(monotonicity,[status(thm)],[74])).
% 0.24/0.45 tff(76,plain,
% 0.24/0.45 ((~((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))))))))))) <=> ((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))),
% 0.24/0.45 inference(transitivity,[status(thm)],[75, 62])).
% 0.24/0.45 tff(77,plain,
% 0.24/0.45 (((~![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | (~((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))))))) <=> ((~![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | ((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))))))),
% 0.24/0.45 inference(monotonicity,[status(thm)],[76])).
% 0.24/0.45 tff(78,plain,
% 0.24/0.45 (((~![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | (~((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))))))) <=> ((~![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | (~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))),
% 0.24/0.45 inference(transitivity,[status(thm)],[77, 61])).
% 0.24/0.45 tff(79,plain,
% 0.24/0.45 ((~![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | (~((~((~(union(A!7) = union(A!7))) | (~((~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), union(A!7)) | (~in(union(A!7), A!7)))))))) | (~((union(A!7) = union(A!7)) | (~((~(in(tptp_fun_C_2(union(A!7), A!7), union(A!7)) | (~((~in(tptp_fun_C_2(union(A!7), A!7), tptp_fun_D_3(union(A!7), A!7))) | (~in(tptp_fun_D_3(union(A!7), A!7), A!7)))))) | (~((~in(tptp_fun_C_2(union(A!7), A!7), union(A!7))) | (~in(union(A!7), A!7)) | (~in(tptp_fun_C_2(union(A!7), A!7), union(A!7)))))))))))),
% 0.24/0.45 inference(quant_inst,[status(thm)],[])).
% 0.24/0.45 tff(80,plain,
% 0.24/0.45 ((~![A: $i, B: $i, D_8: $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_8, A)) | (~in(tptp_fun_C_2(B, A), D_8))))))))))) | (~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.24/0.45 tff(81,plain,
% 0.24/0.45 (~((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)))),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[80, 60, 39])).
% 0.24/0.45 tff(82,plain,
% 0.24/0.45 (((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))) | in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)),
% 0.24/0.45 inference(tautology,[status(thm)],[])).
% 0.24/0.45 tff(83,plain,
% 0.24/0.45 (in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.24/0.45 tff(84,plain,
% 0.24/0.45 (^[C: $i] : refl(((~in(C, A!7)) | subset(C, B!6)) <=> ((~in(C, A!7)) | subset(C, B!6)))),
% 0.24/0.45 inference(bind,[status(th)],[])).
% 0.24/0.45 tff(85,plain,
% 0.24/0.45 (![C: $i] : ((~in(C, A!7)) | subset(C, B!6)) <=> ![C: $i] : ((~in(C, A!7)) | subset(C, B!6))),
% 0.24/0.45 inference(quant_intro,[status(thm)],[84])).
% 0.24/0.45 tff(86,plain,
% 0.24/0.45 (![C: $i] : ((~in(C, A!7)) | subset(C, B!6))),
% 0.24/0.45 inference(and_elim,[status(thm)],[33])).
% 0.24/0.45 tff(87,plain,
% 0.24/0.45 (![C: $i] : ((~in(C, A!7)) | subset(C, B!6))),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.24/0.45 tff(88,plain,
% 0.24/0.45 (((~![C: $i] : ((~in(C, A!7)) | subset(C, B!6))) | ((~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)) | subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6))) <=> ((~![C: $i] : ((~in(C, A!7)) | subset(C, B!6))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)) | subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6))),
% 0.24/0.45 inference(rewrite,[status(thm)],[])).
% 0.24/0.45 tff(89,plain,
% 0.24/0.45 ((~![C: $i] : ((~in(C, A!7)) | subset(C, B!6))) | ((~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)) | subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6))),
% 0.24/0.45 inference(quant_inst,[status(thm)],[])).
% 0.24/0.45 tff(90,plain,
% 0.24/0.45 ((~![C: $i] : ((~in(C, A!7)) | subset(C, B!6))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7)) | subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)),
% 0.24/0.45 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.24/0.45 tff(91,plain,
% 0.24/0.45 (subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[90, 87, 83])).
% 0.24/0.45 tff(92,plain,
% 0.24/0.45 ((~((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6)))) | (~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))),
% 0.24/0.45 inference(tautology,[status(thm)],[])).
% 0.24/0.45 tff(93,plain,
% 0.24/0.45 ((~((~subset(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), B!6)) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6)))) | ![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.24/0.45 tff(94,plain,
% 0.24/0.45 (![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[93, 20])).
% 0.24/0.45 tff(95,plain,
% 0.24/0.45 (((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | (~in(tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7), A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))),
% 0.24/0.45 inference(tautology,[status(thm)],[])).
% 0.24/0.45 tff(96,plain,
% 0.24/0.45 (in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))),
% 0.24/0.45 inference(unit_resolution,[status(thm)],[95, 81])).
% 0.24/0.45 tff(97,plain,
% 0.24/0.45 (((~in(tptp_fun_C_0(B!6, union(A!7)), union(A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)) | (~in(tptp_fun_C_0(B!6, union(A!7)), B!6))),
% 0.24/0.46 inference(tautology,[status(thm)],[])).
% 0.24/0.46 tff(98,plain,
% 0.24/0.46 (~in(tptp_fun_C_0(B!6, union(A!7)), B!6)),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[97, 37])).
% 0.24/0.46 tff(99,plain,
% 0.24/0.46 (((~![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))) | ((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))) <=> ((~![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))) | (~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))),
% 0.24/0.46 inference(rewrite,[status(thm)],[])).
% 0.24/0.46 tff(100,plain,
% 0.24/0.46 ((~![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))) | ((~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6))),
% 0.24/0.46 inference(quant_inst,[status(thm)],[])).
% 0.24/0.46 tff(101,plain,
% 0.24/0.46 ((~![C: $i] : ((~in(C, tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(C, B!6))) | (~in(tptp_fun_C_0(B!6, union(A!7)), tptp_fun_D_1(tptp_fun_C_0(B!6, union(A!7)), A!7))) | in(tptp_fun_C_0(B!6, union(A!7)), B!6)),
% 0.24/0.46 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.24/0.46 tff(102,plain,
% 0.24/0.46 ($false),
% 0.24/0.46 inference(unit_resolution,[status(thm)],[101, 98, 96, 94])).
% 0.24/0.46 % SZS output end Proof
% 0.24/0.46 % E exiting
%------------------------------------------------------------------------------