%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM401+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:20:53 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM401+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:03:41 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(in_type, type, (
% 0.12/0.39 in: ( $i * $i ) > $o)).
% 0.12/0.39 tff(set_union2_type, type, (
% 0.12/0.39 set_union2: ( $i * $i ) > $i)).
% 0.12/0.39 tff(singleton_type, type, (
% 0.12/0.39 singleton: $i > $i)).
% 0.12/0.39 tff(tptp_fun_B_18_type, type, (
% 0.12/0.39 tptp_fun_B_18: $i)).
% 0.12/0.39 tff(tptp_fun_A_17_type, type, (
% 0.12/0.39 tptp_fun_A_17: $i)).
% 0.12/0.39 tff(succ_type, type, (
% 0.12/0.39 succ: $i > $i)).
% 0.12/0.39 tff(tptp_fun_D_2_type, type, (
% 0.12/0.39 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_C_0_type, type, (
% 0.12/0.39 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.39 tff(ordinal_type, type, (
% 0.12/0.39 ordinal: $i > $o)).
% 0.12/0.39 tff(ordinal_subset_type, type, (
% 0.12/0.39 ordinal_subset: ( $i * $i ) > $o)).
% 0.12/0.39 tff(subset_type, type, (
% 0.12/0.39 subset: ( $i * $i ) > $o)).
% 0.12/0.39 tff(epsilon_transitive_type, type, (
% 0.12/0.39 epsilon_transitive: $i > $o)).
% 0.12/0.39 tff(tptp_fun_B_1_type, type, (
% 0.12/0.39 tptp_fun_B_1: $i > $i)).
% 0.12/0.39 tff(epsilon_connected_type, type, (
% 0.12/0.39 epsilon_connected: $i > $o)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[A: $i] : refl((succ(A) = set_union2(A, singleton(A))) <=> (succ(A) = set_union2(A, singleton(A))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![A: $i] : (succ(A) = set_union2(A, singleton(A))) <=> ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(4,axiom,(![A: $i] : (succ(A) = set_union2(A, singleton(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_ordinal1')).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.39 tff(6,plain,(
% 0.12/0.39 ![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[5])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![A: $i] : (succ(A) = set_union2(A, singleton(A)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 ((~![A: $i] : (succ(A) = set_union2(A, singleton(A)))) | (succ(B!18) = set_union2(B!18, singleton(B!18)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (succ(B!18) = set_union2(B!18, singleton(B!18))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (set_union2(B!18, singleton(B!18)) = succ(B!18)),
% 0.12/0.39 inference(symmetry,[status(thm)],[9])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (in(A!17, set_union2(B!18, singleton(B!18))) <=> in(A!17, succ(B!18))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (in(A!17, succ(B!18)) <=> in(A!17, set_union2(B!18, singleton(B!18)))),
% 0.12/0.39 inference(symmetry,[status(thm)],[11])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 ((~in(A!17, succ(B!18))) <=> (~in(A!17, set_union2(B!18, singleton(B!18))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[12])).
% 0.12/0.39 tff(14,assumption,(~in(A!17, succ(B!18))), introduced(assumption)).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (~in(A!17, set_union2(B!18, singleton(B!18)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.12/0.39 inference(pull_quant,[status(thm)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.40 tff(21,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[20, 18])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[21, 17])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[24, 22])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))) <=> (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (^[A: $i, B: $i, C: $i] : rewrite(((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.12/0.40 tff(31,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.12/0.40 tff(32,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.12/0.40 tff(34,plain,(
% 0.12/0.40 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[33])).
% 0.12/0.40 tff(35,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((~(~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) <=> (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (((~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) | $false) <=> (~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 ((~$true) <=> $false),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (($true | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 ((~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))) <=> (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 ((in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 ((~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))) <=> (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 ((~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))) <=> (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[44, 42])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 ((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) <=> $true),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))) <=> ($true | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[46, 45])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))) <=> $true),
% 0.12/0.40 inference(transitivity,[status(thm)],[47, 41])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 ((~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))))) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[48])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 ((~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))))) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[49, 40])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 ((~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) <=> (~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (($false | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) <=> (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 ((in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))) <=> (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 ((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) <=> (~$true)),
% 0.12/0.40 inference(monotonicity,[status(thm)],[46])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 ((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) <=> $false),
% 0.12/0.40 inference(transitivity,[status(thm)],[54, 40])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) <=> ($false | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[55, 53])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) <=> (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[56, 52])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 ((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) <=> (~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[57])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 ((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) <=> (~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[58, 51])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))))) <=> ((~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) | $false)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[59, 50])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))))) <=> (~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[60, 39])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 ((~((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))))))) <=> (~(~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 ((~((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18)))))))) <=> (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[62, 38])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[63])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[64, 37])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (~((~((~(set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18)))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))))) | (~((set_union2(B!18, singleton(B!18)) = set_union2(B!18, singleton(B!18))) | (~(in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), set_union2(B!18, singleton(B!18))) <=> (in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), singleton(B!18)) | in(tptp_fun_D_2(set_union2(B!18, singleton(B!18)), singleton(B!18), B!18), B!18))))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), B) | in(tptp_fun_D_2(C, B, A), A))))))))) | (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[67, 36])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 ((~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) | in(A!17, set_union2(B!18, singleton(B!18))) | (~(in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (in(A!17, set_union2(B!18, singleton(B!18))) | (~(in(A!17, singleton(B!18)) | in(A!17, B!18)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 (~(in(A!17, singleton(B!18)) | in(A!17, B!18))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[70, 15])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 ((in(A!17, singleton(B!18)) | in(A!17, B!18)) | (~in(A!17, B!18))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (~in(A!17, B!18)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.41 tff(74,assumption,(~(in(A!17, singleton(B!18)) <=> (A!17 = B!18))), introduced(assumption)).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.20/0.41 inference(pull_quant,[status(thm)],[])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[79, 77])).
% 0.20/0.42 tff(81,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[80, 76])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[83, 81])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))) <=> (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite(((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(88,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.42 tff(90,plain,(
% 0.20/0.42 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[89])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 ((~(~(in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) <=> (in(A!17, singleton(B!18)) <=> (A!17 = B!18))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (((~(in(A!17, singleton(B!18)) <=> (A!17 = B!18))) | $false) <=> (~(in(A!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 (($true | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))) <=> $true),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 ((~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))) <=> (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 ((singleton(B!18) = singleton(B!18)) <=> $true),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (((singleton(B!18) = singleton(B!18)) | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[98, 97])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (((singleton(B!18) = singleton(B!18)) | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))) <=> $true),
% 0.20/0.42 inference(transitivity,[status(thm)],[99, 96])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 ((~((singleton(B!18) = singleton(B!18)) | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))))) <=> (~$true)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[100])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 ((~((singleton(B!18) = singleton(B!18)) | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))))) <=> $false),
% 0.20/0.42 inference(transitivity,[status(thm)],[101, 40])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 ((~(in(A!17, singleton(B!18)) <=> (A!17 = B!18))) <=> (~(in(A!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (($false | (in(A!17, singleton(B!18)) <=> (A!17 = B!18))) <=> (in(A!17, singleton(B!18)) <=> (A!17 = B!18))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 ((~(singleton(B!18) = singleton(B!18))) <=> (~$true)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[98])).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 ((~(singleton(B!18) = singleton(B!18))) <=> $false),
% 0.20/0.42 inference(transitivity,[status(thm)],[105, 40])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18))) <=> ($false | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[106])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18))) <=> (in(A!17, singleton(B!18)) <=> (A!17 = B!18))),
% 0.20/0.42 inference(transitivity,[status(thm)],[107, 104])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 ((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) <=> (~(in(A!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[108])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 ((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) <=> (~(in(A!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[109, 103])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 (((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))))) <=> ((~(in(A!17, singleton(B!18)) <=> (A!17 = B!18))) | $false)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[110, 102])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 (((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))))) <=> (~(in(A!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[111, 95])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 ((~((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))))))) <=> (~(~(in(A!17, singleton(B!18)) <=> (A!17 = B!18))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 ((~((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18))))))) <=> (in(A!17, singleton(B!18)) <=> (A!17 = B!18))),
% 0.20/0.42 inference(transitivity,[status(thm)],[113, 94])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[114])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))))))) <=> ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[115, 93])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(singleton(B!18) = singleton(B!18))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18)))) | (~((singleton(B!18) = singleton(B!18)) | (~(in(tptp_fun_C_0(singleton(B!18), B!18), singleton(B!18)) <=> (tptp_fun_C_0(singleton(B!18), B!18) = B!18)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(A!17, singleton(B!18)) <=> (A!17 = B!18))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[118, 92, 74])).
% 0.20/0.42 tff(120,plain,(in(A!17, singleton(B!18)) <=> (A!17 = B!18)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 ((in(A!17, singleton(B!18)) | in(A!17, B!18)) | (~in(A!17, singleton(B!18)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (~in(A!17, singleton(B!18))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[121, 71])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 ((~(in(A!17, singleton(B!18)) <=> (A!17 = B!18))) | in(A!17, singleton(B!18)) | (~(A!17 = B!18))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (~(A!17 = B!18)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[123, 122, 120])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 ((~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (in(A, succ(B)) <=> ordinal_subset(A, B))))) <=> (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(127,axiom,(~![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (in(A, succ(B)) <=> ordinal_subset(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t34_ordinal1')).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[128, 125])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 (~![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (in(A, succ(B)) <=> ordinal_subset(A, B))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[130, 125])).
% 0.20/0.43 tff(132,plain,
% 0.20/0.43 (ordinal(A!17)),
% 0.20/0.43 inference(and_elim,[status(thm)],[131])).
% 0.20/0.43 tff(133,plain,
% 0.20/0.43 (^[A: $i] : refl(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(134,plain,
% 0.20/0.43 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.43 tff(135,plain,
% 0.20/0.43 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[136, 134])).
% 0.20/0.43 tff(138,plain,
% 0.20/0.43 (^[A: $i] : rewrite(((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))) <=> (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> (ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), rewrite((ordinal(B) => (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))), ((ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), (![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))) <=> ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> (ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))))), rewrite((ordinal(A) => ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))), ((ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(142,plain,
% 0.20/0.43 (![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A)))))) <=> ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.43 tff(143,axiom,(![A: $i] : (ordinal(A) => ![B: $i] : (ordinal(B) => (~(((~in(A, B)) & (~(A = B))) & (~in(B, A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_ordinal1')).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 (![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.20/0.43 tff(146,plain,(
% 0.20/0.43 ![A: $i] : ((~ordinal(A)) | ![B: $i] : ((~ordinal(B)) | (~((~in(A, B)) & (~(A = B)) & (~in(B, A))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[145])).
% 0.20/0.43 tff(147,plain,
% 0.20/0.43 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.20/0.43 tff(148,plain,
% 0.20/0.43 (![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[147, 137])).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!17)) | ![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B)))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(A!17)) | ![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(150,plain,
% 0.20/0.43 (((~ordinal(A!17)) | ![B: $i] : (in(B, A!17) | in(A!17, B) | (A!17 = B) | (~ordinal(B)))) <=> ((~ordinal(A!17)) | ![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(151,plain,
% 0.20/0.43 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!17)) | ![B: $i] : (in(B, A!17) | in(A!17, B) | (A!17 = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!17)) | ![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.43 tff(152,plain,
% 0.20/0.43 (((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!17)) | ![B: $i] : (in(B, A!17) | in(A!17, B) | (A!17 = B) | (~ordinal(B))))) <=> ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(A!17)) | ![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[151, 149])).
% 0.20/0.43 tff(153,plain,
% 0.20/0.43 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | ((~ordinal(A!17)) | ![B: $i] : (in(B, A!17) | in(A!17, B) | (A!17 = B) | (~ordinal(B))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(154,plain,
% 0.20/0.43 ((~![A: $i] : ((~ordinal(A)) | ![B: $i] : (in(B, A) | in(A, B) | (A = B) | (~ordinal(B))))) | (~ordinal(A!17)) | ![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.43 tff(155,plain,
% 0.20/0.43 (![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[154, 148, 132])).
% 0.20/0.43 tff(156,plain,
% 0.20/0.43 (~((~ordinal(B!18)) | (in(A!17, succ(B!18)) <=> ordinal_subset(A!17, B!18)))),
% 0.20/0.43 inference(and_elim,[status(thm)],[131])).
% 0.20/0.43 tff(157,plain,
% 0.20/0.43 (ordinal(B!18)),
% 0.20/0.43 inference(or_elim,[status(thm)],[156])).
% 0.20/0.43 tff(158,plain,
% 0.20/0.43 (((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | ((~ordinal(B!18)) | (A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | (~ordinal(B!18)) | (A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(159,plain,
% 0.20/0.43 (((~ordinal(B!18)) | in(B!18, A!17) | in(A!17, B!18) | (A!17 = B!18)) <=> ((~ordinal(B!18)) | (A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(160,plain,
% 0.20/0.43 (((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | ((~ordinal(B!18)) | in(B!18, A!17) | in(A!17, B!18) | (A!17 = B!18))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | ((~ordinal(B!18)) | (A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[159])).
% 0.20/0.43 tff(161,plain,
% 0.20/0.43 (((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | ((~ordinal(B!18)) | in(B!18, A!17) | in(A!17, B!18) | (A!17 = B!18))) <=> ((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | (~ordinal(B!18)) | (A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17))),
% 0.20/0.43 inference(transitivity,[status(thm)],[160, 158])).
% 0.20/0.43 tff(162,plain,
% 0.20/0.43 ((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | ((~ordinal(B!18)) | in(B!18, A!17) | in(A!17, B!18) | (A!17 = B!18))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(163,plain,
% 0.20/0.43 ((~![B: $i] : ((~ordinal(B)) | in(B, A!17) | in(A!17, B) | (A!17 = B))) | (~ordinal(B!18)) | (A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.43 tff(164,plain,
% 0.20/0.43 ((A!17 = B!18) | in(A!17, B!18) | in(B!18, A!17)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[163, 157, 155])).
% 0.20/0.43 tff(165,plain,
% 0.20/0.43 (in(B!18, A!17)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[164, 124, 73])).
% 0.20/0.43 tff(166,plain,
% 0.20/0.43 (~(in(A!17, succ(B!18)) <=> ordinal_subset(A!17, B!18))),
% 0.20/0.43 inference(or_elim,[status(thm)],[156])).
% 0.20/0.43 tff(167,plain,
% 0.20/0.43 ((in(A!17, succ(B!18)) <=> ordinal_subset(A!17, B!18)) | in(A!17, succ(B!18)) | ordinal_subset(A!17, B!18)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(168,plain,
% 0.20/0.43 (in(A!17, succ(B!18)) | ordinal_subset(A!17, B!18)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 (ordinal_subset(A!17, B!18)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[168, 14])).
% 0.20/0.43 tff(170,plain,
% 0.20/0.43 (^[A: $i, B: $i] : refl(((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(171,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((ordinal(A) & ordinal(B)) <=> (~((~ordinal(B)) | (~ordinal(A))))), ((~(ordinal(A) & ordinal(B))) <=> (~(~((~ordinal(B)) | (~ordinal(A))))))), rewrite((~(~((~ordinal(B)) | (~ordinal(A))))) <=> ((~ordinal(B)) | (~ordinal(A)))), ((~(ordinal(A) & ordinal(B))) <=> ((~ordinal(B)) | (~ordinal(A))))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> (((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))))), rewrite((((~ordinal(B)) | (~ordinal(A))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))), (((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(173,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[172])).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(175,plain,
% 0.20/0.43 (^[A: $i, B: $i] : rewrite(((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(176,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B))) <=> ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[175])).
% 0.20/0.43 tff(177,axiom,(![A: $i, B: $i] : ((ordinal(A) & ordinal(B)) => (ordinal_subset(A, B) <=> subset(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_r1_ordinal1')).
% 0.20/0.43 tff(178,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.43 tff(179,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.20/0.43 tff(180,plain,(
% 0.20/0.43 ![A: $i, B: $i] : ((~(ordinal(A) & ordinal(B))) | (ordinal_subset(A, B) <=> subset(A, B)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[179])).
% 0.20/0.43 tff(181,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[180, 173])).
% 0.20/0.43 tff(182,plain,
% 0.20/0.43 (![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[181, 171])).
% 0.20/0.43 tff(183,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!17)) | (~ordinal(B!18)) | (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!17)) | (~ordinal(B!18)) | (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(184,plain,
% 0.20/0.43 (((ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)) | (~ordinal(B!18)) | (~ordinal(A!17))) <=> ((~ordinal(A!17)) | (~ordinal(B!18)) | (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(185,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)) | (~ordinal(B!18)) | (~ordinal(A!17)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((~ordinal(A!17)) | (~ordinal(B!18)) | (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[184])).
% 0.20/0.43 tff(186,plain,
% 0.20/0.43 (((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)) | (~ordinal(B!18)) | (~ordinal(A!17)))) <=> ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!17)) | (~ordinal(B!18)) | (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[185, 183])).
% 0.20/0.43 tff(187,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | ((ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)) | (~ordinal(B!18)) | (~ordinal(A!17)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(188,plain,
% 0.20/0.43 ((~![A: $i, B: $i] : ((ordinal_subset(A, B) <=> subset(A, B)) | (~ordinal(B)) | (~ordinal(A)))) | (~ordinal(A!17)) | (~ordinal(B!18)) | (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.20/0.43 tff(189,plain,
% 0.20/0.43 (ordinal_subset(A!17, B!18) <=> subset(A!17, B!18)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[188, 182, 132, 157])).
% 0.20/0.43 tff(190,plain,
% 0.20/0.43 ((~(ordinal_subset(A!17, B!18) <=> subset(A!17, B!18))) | (~ordinal_subset(A!17, B!18)) | subset(A!17, B!18)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(191,plain,
% 0.20/0.43 ((~ordinal_subset(A!17, B!18)) | subset(A!17, B!18)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.20/0.43 tff(192,plain,
% 0.20/0.43 (subset(A!17, B!18)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[191, 169])).
% 0.20/0.43 tff(193,plain,
% 0.20/0.43 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(194,plain,
% 0.20/0.43 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[193])).
% 0.20/0.44 tff(195,plain,
% 0.20/0.44 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(196,plain,
% 0.20/0.44 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[195])).
% 0.20/0.44 tff(197,plain,
% 0.20/0.44 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(198,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.20/0.44 tff(199,plain,
% 0.20/0.44 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.44 tff(200,plain,(
% 0.20/0.44 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[199])).
% 0.20/0.44 tff(201,plain,
% 0.20/0.44 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.20/0.44 tff(202,plain,
% 0.20/0.44 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[201, 194])).
% 0.20/0.44 tff(203,plain,
% 0.20/0.44 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(A!17, B!18)) | (~subset(B!18, A!17))) <=> (A!17 = B!18)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(204,plain,
% 0.20/0.44 (~(((~subset(A!17, B!18)) | (~subset(B!18, A!17))) <=> (A!17 = B!18))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.20/0.44 tff(205,plain,
% 0.20/0.44 ((((~subset(A!17, B!18)) | (~subset(B!18, A!17))) <=> (A!17 = B!18)) | ((~subset(A!17, B!18)) | (~subset(B!18, A!17))) | (A!17 = B!18)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(206,plain,
% 0.20/0.44 (((~subset(A!17, B!18)) | (~subset(B!18, A!17))) | (A!17 = B!18)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.20/0.44 tff(207,plain,
% 0.20/0.44 ((~subset(A!17, B!18)) | (~subset(B!18, A!17))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[206, 124])).
% 0.20/0.44 tff(208,plain,
% 0.20/0.44 ((~((~subset(A!17, B!18)) | (~subset(B!18, A!17)))) | (~subset(A!17, B!18)) | (~subset(B!18, A!17))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(209,plain,
% 0.20/0.44 (~subset(B!18, A!17)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[208, 207, 192])).
% 0.20/0.44 tff(210,plain,
% 0.20/0.44 (^[A: $i] : refl((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(211,plain,
% 0.20/0.44 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[210])).
% 0.20/0.44 tff(212,plain,
% 0.20/0.44 (^[A: $i] : rewrite((~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(213,plain,
% 0.20/0.44 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[212])).
% 0.20/0.44 tff(214,plain,
% 0.20/0.44 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[213, 211])).
% 0.20/0.44 tff(215,plain,
% 0.20/0.44 (^[A: $i] : trans(monotonicity(rewrite(((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))) <=> (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))))), rewrite((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))), ((((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))) <=> (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(216,plain,
% 0.20/0.44 (![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A))))) <=> ![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[215])).
% 0.20/0.44 tff(217,plain,
% 0.20/0.44 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(218,plain,
% 0.20/0.44 (^[A: $i] : rewrite((epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(219,plain,
% 0.20/0.44 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A))) <=> ![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[218])).
% 0.20/0.44 tff(220,axiom,(![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : (in(B, A) => subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_ordinal1')).
% 0.20/0.44 tff(221,plain,
% 0.20/0.44 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.20/0.44 tff(222,plain,
% 0.20/0.44 (![A: $i] : (epsilon_transitive(A) <=> ![B: $i] : ((~in(B, A)) | subset(B, A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.20/0.44 tff(223,plain,(
% 0.20/0.44 ![A: $i] : (((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A))) & (epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[222])).
% 0.20/0.44 tff(224,plain,
% 0.20/0.44 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[223, 216])).
% 0.20/0.44 tff(225,plain,
% 0.20/0.44 (![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[224, 214])).
% 0.20/0.44 tff(226,plain,
% 0.20/0.44 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))) | (~((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | (~(epsilon_transitive(A!17) | (~((~in(tptp_fun_B_1(A!17), A!17)) | subset(tptp_fun_B_1(A!17), A!17)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(227,plain,
% 0.20/0.44 (~((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | (~(epsilon_transitive(A!17) | (~((~in(tptp_fun_B_1(A!17), A!17)) | subset(tptp_fun_B_1(A!17), A!17))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[226, 225])).
% 0.20/0.44 tff(228,plain,
% 0.20/0.44 (((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | (~(epsilon_transitive(A!17) | (~((~in(tptp_fun_B_1(A!17), A!17)) | subset(tptp_fun_B_1(A!17), A!17)))))) | ((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(229,plain,
% 0.20/0.44 ((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[228, 227])).
% 0.20/0.44 tff(230,plain,
% 0.20/0.44 (^[A: $i] : refl(((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(231,plain,
% 0.20/0.44 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[230])).
% 0.20/0.44 tff(232,plain,
% 0.20/0.44 (^[A: $i] : rewrite(((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(233,plain,
% 0.20/0.44 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[232])).
% 0.20/0.44 tff(234,plain,
% 0.20/0.44 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(235,plain,
% 0.20/0.44 (^[A: $i] : rewrite((ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(236,plain,
% 0.20/0.44 (![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A))) <=> ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[235])).
% 0.20/0.44 tff(237,axiom,(![A: $i] : (ordinal(A) => (epsilon_transitive(A) & epsilon_connected(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_ordinal1')).
% 0.20/0.44 tff(238,plain,
% 0.20/0.44 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.20/0.44 tff(239,plain,
% 0.20/0.44 (![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[238, 234])).
% 0.20/0.44 tff(240,plain,(
% 0.20/0.44 ![A: $i] : ((~ordinal(A)) | (epsilon_transitive(A) & epsilon_connected(A)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[239])).
% 0.20/0.44 tff(241,plain,
% 0.20/0.44 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[240, 233])).
% 0.20/0.44 tff(242,plain,
% 0.20/0.44 (![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[241, 231])).
% 0.20/0.44 tff(243,plain,
% 0.20/0.44 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(A!17)) | (~((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(A!17)) | (~((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(244,plain,
% 0.20/0.44 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(A!17)) | (~((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(245,plain,
% 0.20/0.44 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(A!17)) | (~((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.20/0.44 tff(246,plain,
% 0.20/0.44 (~((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[245, 242, 132])).
% 0.20/0.44 tff(247,plain,
% 0.20/0.44 (((~epsilon_transitive(A!17)) | (~epsilon_connected(A!17))) | epsilon_transitive(A!17)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(248,plain,
% 0.20/0.44 (epsilon_transitive(A!17)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[247, 246])).
% 0.20/0.44 tff(249,plain,
% 0.20/0.44 ((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | (~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(250,plain,
% 0.20/0.44 ((~((~epsilon_transitive(A!17)) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17)))) | ![B: $i] : ((~in(B, A!17)) | subset(B, A!17))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[249, 248])).
% 0.20/0.44 tff(251,plain,
% 0.20/0.44 (![B: $i] : ((~in(B, A!17)) | subset(B, A!17))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[250, 229])).
% 0.20/0.44 tff(252,plain,
% 0.20/0.44 (((~![B: $i] : ((~in(B, A!17)) | subset(B, A!17))) | ((~in(B!18, A!17)) | subset(B!18, A!17))) <=> ((~![B: $i] : ((~in(B, A!17)) | subset(B, A!17))) | (~in(B!18, A!17)) | subset(B!18, A!17))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(253,plain,
% 0.20/0.44 ((~![B: $i] : ((~in(B, A!17)) | subset(B, A!17))) | ((~in(B!18, A!17)) | subset(B!18, A!17))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(254,plain,
% 0.20/0.44 ((~![B: $i] : ((~in(B, A!17)) | subset(B, A!17))) | (~in(B!18, A!17)) | subset(B!18, A!17)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.20/0.44 tff(255,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[254, 251, 209, 165])).
% 0.20/0.44 tff(256,plain,(in(A!17, succ(B!18))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(257,plain,
% 0.20/0.44 (in(A!17, set_union2(B!18, singleton(B!18)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[256, 12])).
% 0.20/0.44 tff(258,plain,
% 0.20/0.44 ((in(A!17, succ(B!18)) <=> ordinal_subset(A!17, B!18)) | (~in(A!17, succ(B!18))) | (~ordinal_subset(A!17, B!18))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(259,plain,
% 0.20/0.44 ((~in(A!17, succ(B!18))) | (~ordinal_subset(A!17, B!18))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[258, 166])).
% 0.20/0.44 tff(260,plain,
% 0.20/0.44 (~ordinal_subset(A!17, B!18)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[259, 256])).
% 0.20/0.44 tff(261,plain,
% 0.20/0.44 ((~(ordinal_subset(A!17, B!18) <=> subset(A!17, B!18))) | ordinal_subset(A!17, B!18) | (~subset(A!17, B!18))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(262,plain,
% 0.20/0.44 (ordinal_subset(A!17, B!18) | (~subset(A!17, B!18))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[261, 189])).
% 0.20/0.44 tff(263,plain,
% 0.20/0.44 (~subset(A!17, B!18)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[262, 260])).
% 0.20/0.44 tff(264,plain,
% 0.20/0.44 ((~![A: $i] : (~((~((~epsilon_transitive(A)) | ![B: $i] : ((~in(B, A)) | subset(B, A)))) | (~(epsilon_transitive(A) | (~((~in(tptp_fun_B_1(A), A)) | subset(tptp_fun_B_1(A), A)))))))) | (~((~((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))) | (~(epsilon_transitive(B!18) | (~((~in(tptp_fun_B_1(B!18), B!18)) | subset(tptp_fun_B_1(B!18), B!18)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(265,plain,
% 0.20/0.44 (~((~((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))) | (~(epsilon_transitive(B!18) | (~((~in(tptp_fun_B_1(B!18), B!18)) | subset(tptp_fun_B_1(B!18), B!18))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[264, 225])).
% 0.20/0.44 tff(266,plain,
% 0.20/0.44 (((~((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))) | (~(epsilon_transitive(B!18) | (~((~in(tptp_fun_B_1(B!18), B!18)) | subset(tptp_fun_B_1(B!18), B!18)))))) | ((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(267,plain,
% 0.20/0.44 ((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[266, 265])).
% 0.20/0.44 tff(268,plain,
% 0.20/0.44 (((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!18)) | (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18)))))) <=> ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!18)) | (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(269,plain,
% 0.20/0.44 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | ((~ordinal(B!18)) | (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(270,plain,
% 0.20/0.44 ((~![A: $i] : ((~ordinal(A)) | (~((~epsilon_transitive(A)) | (~epsilon_connected(A)))))) | (~ordinal(B!18)) | (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.20/0.44 tff(271,plain,
% 0.20/0.44 (~((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[270, 242, 157])).
% 0.20/0.44 tff(272,plain,
% 0.20/0.44 (((~epsilon_transitive(B!18)) | (~epsilon_connected(B!18))) | epsilon_transitive(B!18)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(273,plain,
% 0.20/0.44 (epsilon_transitive(B!18)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[272, 271])).
% 0.20/0.44 tff(274,plain,
% 0.20/0.44 ((~((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))) | (~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(275,plain,
% 0.20/0.44 ((~((~epsilon_transitive(B!18)) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18)))) | ![B: $i] : ((~in(B, B!18)) | subset(B, B!18))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[274, 273])).
% 0.20/0.44 tff(276,plain,
% 0.20/0.44 (![B: $i] : ((~in(B, B!18)) | subset(B, B!18))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[275, 267])).
% 0.20/0.44 tff(277,plain,
% 0.20/0.44 (((~![B: $i] : ((~in(B, B!18)) | subset(B, B!18))) | ((~in(A!17, B!18)) | subset(A!17, B!18))) <=> ((~![B: $i] : ((~in(B, B!18)) | subset(B, B!18))) | (~in(A!17, B!18)) | subset(A!17, B!18))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(278,plain,
% 0.20/0.44 ((~![B: $i] : ((~in(B, B!18)) | subset(B, B!18))) | ((~in(A!17, B!18)) | subset(A!17, B!18))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(279,plain,
% 0.20/0.44 ((~![B: $i] : ((~in(B, B!18)) | subset(B, B!18))) | (~in(A!17, B!18)) | subset(A!17, B!18)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.20/0.44 tff(280,plain,
% 0.20/0.44 ((~in(A!17, B!18)) | subset(A!17, B!18)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[279, 276])).
% 0.20/0.44 tff(281,plain,
% 0.20/0.44 (~in(A!17, B!18)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[280, 263])).
% 0.20/0.44 tff(282,plain,
% 0.20/0.44 (((~subset(A!17, B!18)) | (~subset(B!18, A!17))) | subset(A!17, B!18)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(283,plain,
% 0.20/0.44 ((~subset(A!17, B!18)) | (~subset(B!18, A!17))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[282, 263])).
% 0.20/0.44 tff(284,plain,
% 0.20/0.44 ((((~subset(A!17, B!18)) | (~subset(B!18, A!17))) <=> (A!17 = B!18)) | (~((~subset(A!17, B!18)) | (~subset(B!18, A!17)))) | (~(A!17 = B!18))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(285,plain,
% 0.20/0.44 ((~((~subset(A!17, B!18)) | (~subset(B!18, A!17)))) | (~(A!17 = B!18))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[284, 204])).
% 0.20/0.44 tff(286,plain,
% 0.20/0.45 (~(A!17 = B!18)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[285, 283])).
% 0.20/0.45 tff(287,plain,
% 0.20/0.45 ((~(in(A!17, singleton(B!18)) <=> (A!17 = B!18))) | (~in(A!17, singleton(B!18))) | (A!17 = B!18)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(288,plain,
% 0.20/0.45 (~in(A!17, singleton(B!18))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[287, 286, 120])).
% 0.20/0.45 tff(289,plain,
% 0.20/0.45 ((~(in(A!17, singleton(B!18)) | in(A!17, B!18))) | in(A!17, singleton(B!18)) | in(A!17, B!18)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(290,plain,
% 0.20/0.45 (~(in(A!17, singleton(B!18)) | in(A!17, B!18))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[289, 288, 281])).
% 0.20/0.45 tff(291,plain,
% 0.20/0.45 ((~(in(A!17, set_union2(B!18, singleton(B!18))) <=> (in(A!17, singleton(B!18)) | in(A!17, B!18)))) | (~in(A!17, set_union2(B!18, singleton(B!18)))) | (in(A!17, singleton(B!18)) | in(A!17, B!18))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(292,plain,
% 0.20/0.45 ((~in(A!17, set_union2(B!18, singleton(B!18)))) | (in(A!17, singleton(B!18)) | in(A!17, B!18))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[291, 68])).
% 0.20/0.45 tff(293,plain,
% 0.20/0.45 (~in(A!17, set_union2(B!18, singleton(B!18)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[292, 290])).
% 0.20/0.45 tff(294,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[293, 257])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------