%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU159+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:05 AM UTC 2025
% Result : Theorem 18.06s 18.28s
% Output : Proof 18.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU159+2 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:08:07 EDT 2025
% 0.12/0.33 % CPUTime :
% 18.06/18.28 % SZS status Theorem
% 18.06/18.28 % SZS output start Proof
% 18.06/18.28 tff(in_type, type, (
% 18.06/18.28 in: ( $i * $i ) > $o)).
% 18.06/18.28 tff(set_union2_type, type, (
% 18.06/18.28 set_union2: ( $i * $i ) > $i)).
% 18.06/18.28 tff(unordered_pair_type, type, (
% 18.06/18.28 unordered_pair: ( $i * $i ) > $i)).
% 18.06/18.28 tff(tptp_fun_A_21_type, type, (
% 18.06/18.28 tptp_fun_A_21: $i)).
% 18.06/18.28 tff(tptp_fun_B_20_type, type, (
% 18.06/18.28 tptp_fun_B_20: $i)).
% 18.06/18.28 tff(tptp_fun_C_19_type, type, (
% 18.06/18.28 tptp_fun_C_19: $i)).
% 18.06/18.28 tff(set_difference_type, type, (
% 18.06/18.28 set_difference: ( $i * $i ) > $i)).
% 18.06/18.28 tff(subset_type, type, (
% 18.06/18.28 subset: ( $i * $i ) > $o)).
% 18.06/18.28 tff(tptp_fun_C_10_type, type, (
% 18.06/18.28 tptp_fun_C_10: ( $i * $i ) > $i)).
% 18.06/18.28 tff(tptp_fun_D_3_type, type, (
% 18.06/18.28 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 18.06/18.28 tff(singleton_type, type, (
% 18.06/18.28 singleton: $i > $i)).
% 18.06/18.28 tff(tptp_fun_C_0_type, type, (
% 18.06/18.28 tptp_fun_C_0: ( $i * $i ) > $i)).
% 18.06/18.28 tff(tptp_fun_D_4_type, type, (
% 18.06/18.28 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 18.06/18.28 tff(1,plain,
% 18.06/18.28 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))))),
% 18.06/18.28 inference(bind,[status(th)],[])).
% 18.06/18.28 tff(2,plain,
% 18.06/18.28 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 18.06/18.28 inference(quant_intro,[status(thm)],[1])).
% 18.06/18.28 tff(3,plain,
% 18.06/18.28 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 18.06/18.28 inference(pull_quant,[status(thm)],[])).
% 18.06/18.28 tff(4,plain,
% 18.06/18.28 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))))),
% 18.06/18.28 inference(bind,[status(th)],[])).
% 18.06/18.28 tff(5,plain,
% 18.06/18.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 18.06/18.28 inference(quant_intro,[status(thm)],[4])).
% 18.06/18.28 tff(6,plain,
% 18.06/18.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 18.06/18.28 inference(transitivity,[status(thm)],[5, 3])).
% 18.06/18.28 tff(7,plain,
% 18.06/18.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 18.06/18.28 inference(transitivity,[status(thm)],[6, 2])).
% 18.06/18.28 tff(8,plain,
% 18.06/18.28 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))))),
% 18.06/18.28 inference(bind,[status(th)],[])).
% 18.06/18.28 tff(9,plain,
% 18.06/18.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 18.06/18.28 inference(quant_intro,[status(thm)],[8])).
% 18.06/18.28 tff(10,plain,
% 18.06/18.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 18.06/18.28 inference(transitivity,[status(thm)],[9, 7])).
% 18.06/18.28 tff(11,plain,
% 18.06/18.28 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))) <=> (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))))),
% 18.06/18.28 inference(bind,[status(th)],[])).
% 18.06/18.28 tff(12,plain,
% 18.06/18.28 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 18.12/18.28 inference(quant_intro,[status(thm)],[11])).
% 18.12/18.28 tff(13,plain,
% 18.12/18.28 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 18.12/18.28 inference(rewrite,[status(thm)],[])).
% 18.12/18.28 tff(14,plain,
% 18.12/18.28 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 18.12/18.28 inference(bind,[status(th)],[])).
% 18.12/18.28 tff(15,plain,
% 18.12/18.28 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 18.12/18.28 inference(quant_intro,[status(thm)],[14])).
% 18.12/18.28 tff(16,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_tarski')).
% 18.12/18.28 tff(17,plain,
% 18.12/18.28 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 18.12/18.28 inference(modus_ponens,[status(thm)],[16, 15])).
% 18.12/18.28 tff(18,plain,
% 18.12/18.28 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 18.12/18.28 inference(modus_ponens,[status(thm)],[17, 13])).
% 18.12/18.28 tff(19,plain,(
% 18.12/18.28 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))),
% 18.12/18.28 inference(skolemize,[status(sab)],[18])).
% 18.12/18.28 tff(20,plain,
% 18.12/18.28 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 18.12/18.28 inference(modus_ponens,[status(thm)],[19, 12])).
% 18.12/18.28 tff(21,plain,
% 18.12/18.28 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))),
% 18.12/18.28 inference(modus_ponens,[status(thm)],[20, 10])).
% 18.12/18.28 tff(22,plain,
% 18.12/18.28 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 18.12/18.28 inference(quant_inst,[status(thm)],[])).
% 18.12/18.28 tff(23,plain,
% 18.12/18.28 (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))),
% 18.12/18.28 inference(unit_resolution,[status(thm)],[22, 21])).
% 18.12/18.28 tff(24,plain,
% 18.12/18.28 (((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))) | ((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))),
% 18.12/18.28 inference(tautology,[status(thm)],[])).
% 18.12/18.28 tff(25,plain,
% 18.12/18.28 ((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 18.12/18.28 inference(unit_resolution,[status(thm)],[24, 23])).
% 18.12/18.28 tff(26,plain,
% 18.12/18.28 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 18.12/18.28 inference(bind,[status(th)],[])).
% 18.12/18.28 tff(27,plain,
% 18.12/18.28 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 18.12/18.28 inference(quant_intro,[status(thm)],[26])).
% 18.12/18.28 tff(28,plain,
% 18.12/18.28 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 18.12/18.28 inference(rewrite,[status(thm)],[])).
% 18.12/18.28 tff(29,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 18.12/18.28 tff(30,plain,
% 18.12/18.28 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 18.12/18.28 inference(modus_ponens,[status(thm)],[29, 28])).
% 18.12/18.28 tff(31,plain,(
% 18.12/18.28 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 18.12/18.28 inference(skolemize,[status(sab)],[30])).
% 18.12/18.28 tff(32,plain,
% 18.12/18.28 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 18.12/18.28 inference(modus_ponens,[status(thm)],[31, 27])).
% 18.12/18.28 tff(33,plain,
% 18.12/18.28 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))),
% 18.12/18.28 inference(quant_inst,[status(thm)],[])).
% 18.12/18.28 tff(34,plain,
% 18.12/18.28 (unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)),
% 18.12/18.28 inference(unit_resolution,[status(thm)],[33, 32])).
% 18.12/18.28 tff(35,plain,
% 18.12/18.28 ((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))) | (~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 18.12/18.28 inference(tautology,[status(thm)],[])).
% 18.12/18.28 tff(36,plain,
% 18.12/18.28 ((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 18.12/18.28 inference(unit_resolution,[status(thm)],[35, 34])).
% 18.12/18.28 tff(37,plain,
% 18.12/18.28 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 18.12/18.29 inference(unit_resolution,[status(thm)],[36, 25])).
% 18.12/18.29 tff(38,plain,
% 18.12/18.29 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!21, B!20) = unordered_pair(B!20, A!21))),
% 18.12/18.29 inference(quant_inst,[status(thm)],[])).
% 18.12/18.29 tff(39,plain,
% 18.12/18.29 (unordered_pair(A!21, B!20) = unordered_pair(B!20, A!21)),
% 18.12/18.29 inference(unit_resolution,[status(thm)],[38, 32])).
% 18.12/18.29 tff(40,plain,
% 18.12/18.29 (unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)),
% 18.12/18.29 inference(symmetry,[status(thm)],[39])).
% 18.12/18.29 tff(41,plain,
% 18.12/18.29 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))),
% 18.12/18.29 inference(monotonicity,[status(thm)],[40])).
% 18.12/18.29 tff(42,plain,
% 18.12/18.29 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20)) <=> in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21))),
% 18.12/18.29 inference(symmetry,[status(thm)],[41])).
% 18.12/18.29 tff(43,assumption,(~subset(unordered_pair(A!21, B!20), C!19)), introduced(assumption)).
% 18.12/18.29 tff(44,plain,
% 18.12/18.29 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))))),
% 18.12/18.29 inference(bind,[status(th)],[])).
% 18.12/18.29 tff(45,plain,
% 18.12/18.29 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 18.12/18.29 inference(quant_intro,[status(thm)],[44])).
% 18.12/18.29 tff(46,plain,
% 18.12/18.29 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))))),
% 18.12/18.29 inference(bind,[status(th)],[])).
% 18.12/18.29 tff(47,plain,
% 18.12/18.29 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 18.12/18.29 inference(quant_intro,[status(thm)],[46])).
% 18.12/18.29 tff(48,plain,
% 18.12/18.29 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 18.12/18.29 inference(transitivity,[status(thm)],[47, 45])).
% 18.12/18.29 tff(49,plain,
% 18.12/18.29 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))))),
% 18.12/18.29 inference(bind,[status(th)],[])).
% 18.12/18.29 tff(50,plain,
% 18.12/18.29 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 18.12/18.29 inference(quant_intro,[status(thm)],[49])).
% 18.12/18.29 tff(51,plain,
% 18.12/18.29 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 18.12/18.29 inference(rewrite,[status(thm)],[])).
% 18.12/18.29 tff(52,plain,
% 18.12/18.29 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 18.12/18.29 inference(bind,[status(th)],[])).
% 18.12/18.29 tff(53,plain,
% 18.12/18.29 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 18.12/18.29 inference(quant_intro,[status(thm)],[52])).
% 18.12/18.29 tff(54,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 18.12/18.29 tff(55,plain,
% 18.12/18.29 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 18.12/18.29 inference(modus_ponens,[status(thm)],[54, 53])).
% 18.12/18.29 tff(56,plain,
% 18.12/18.29 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 18.12/18.29 inference(modus_ponens,[status(thm)],[55, 51])).
% 18.12/18.29 tff(57,plain,(
% 18.12/18.29 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))),
% 18.12/18.29 inference(skolemize,[status(sab)],[56])).
% 18.12/18.29 tff(58,plain,
% 18.12/18.29 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 18.12/18.29 inference(modus_ponens,[status(thm)],[57, 50])).
% 18.12/18.29 tff(59,plain,
% 18.12/18.29 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 18.12/18.29 inference(modus_ponens,[status(thm)],[58, 48])).
% 18.12/18.29 tff(60,plain,
% 18.12/18.29 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))) | (~((~((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19)))) | (~(subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)))))))),
% 18.12/18.29 inference(quant_inst,[status(thm)],[])).
% 18.12/18.29 tff(61,plain,
% 18.12/18.29 (~((~((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19)))) | (~(subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))))),
% 18.12/18.29 inference(unit_resolution,[status(thm)],[60, 59])).
% 18.12/18.29 tff(62,plain,
% 18.12/18.29 (((~((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19)))) | (~(subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)))))) | (subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))),
% 18.12/18.29 inference(tautology,[status(thm)],[])).
% 18.12/18.29 tff(63,plain,
% 18.12/18.29 (subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)))),
% 18.12/18.29 inference(unit_resolution,[status(thm)],[62, 61])).
% 18.12/18.29 tff(64,plain,
% 18.12/18.29 ((~(subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)))),
% 18.12/18.29 inference(tautology,[status(thm)],[])).
% 18.12/18.29 tff(65,plain,
% 18.12/18.29 (subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)))),
% 18.12/18.29 inference(unit_resolution,[status(thm)],[64, 63])).
% 18.12/18.29 tff(66,plain,
% 18.12/18.29 (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))),
% 18.12/18.29 inference(unit_resolution,[status(thm)],[65, 43])).
% 18.12/18.29 tff(67,plain,
% 18.12/18.29 (((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))),
% 18.12/18.29 inference(tautology,[status(thm)],[])).
% 18.12/18.29 tff(68,plain,
% 18.12/18.29 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))),
% 18.12/18.29 inference(unit_resolution,[status(thm)],[67, 66])).
% 18.12/18.29 tff(69,plain,
% 18.12/18.29 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21))),
% 18.12/18.29 inference(modus_ponens,[status(thm)],[68, 42])).
% 18.12/18.29 tff(70,plain,
% 18.12/18.29 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21)) <=> ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(B!20, A!21))) | ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 18.12/18.29 inference(tautology,[status(thm)],[])).
% 18.12/18.29 tff(71,plain,
% 18.12/18.29 ((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)),
% 18.12/18.29 inference(unit_resolution,[status(thm)],[70, 69, 37])).
% 18.12/18.29 tff(72,plain,
% 18.12/18.29 (^[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))))))))),
% 18.12/18.29 inference(bind,[status(th)],[])).
% 18.12/18.29 tff(73,plain,
% 18.12/18.29 (![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)))))))),
% 18.12/18.29 inference(quant_intro,[status(thm)],[72])).
% 18.12/18.29 tff(74,plain,
% 18.12/18.29 (![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)))))))),
% 18.12/18.29 inference(pull_quant,[status(thm)],[])).
% 18.12/18.29 tff(75,plain,
% 18.12/18.29 (^[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)))))))))),
% 18.12/18.29 inference(bind,[status(th)],[])).
% 18.12/18.29 tff(76,plain,
% 18.12/18.29 (![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)))))))),
% 18.12/18.29 inference(quant_intro,[status(thm)],[75])).
% 18.12/18.29 tff(77,plain,
% 18.12/18.29 (![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)))))))),
% 18.12/18.29 inference(transitivity,[status(thm)],[76, 74])).
% 18.12/18.29 tff(78,plain,
% 18.12/18.29 (![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)))))))),
% 18.12/18.29 inference(transitivity,[status(thm)],[77, 73])).
% 18.12/18.29 tff(79,plain,
% 18.12/18.29 (^[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))))))))),
% 18.12/18.29 inference(bind,[status(th)],[])).
% 18.12/18.29 tff(80,plain,
% 18.12/18.29 (![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)))))))),
% 18.12/18.29 inference(quant_intro,[status(thm)],[79])).
% 18.12/18.29 tff(81,plain,
% 18.12/18.29 (![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)))))))),
% 18.12/18.29 inference(transitivity,[status(thm)],[80, 78])).
% 18.12/18.29 tff(82,plain,
% 18.12/18.29 (^[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)))))))))),
% 18.12/18.29 inference(bind,[status(th)],[])).
% 18.12/18.29 tff(83,plain,
% 18.12/18.29 (![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)))))))),
% 18.12/18.29 inference(quant_intro,[status(thm)],[82])).
% 18.12/18.29 tff(84,plain,
% 18.12/18.29 (![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)))),
% 18.12/18.29 inference(rewrite,[status(thm)],[])).
% 18.12/18.29 tff(85,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_tarski')).
% 18.12/18.29 tff(86,plain,
% 18.12/18.29 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 18.12/18.29 inference(modus_ponens,[status(thm)],[85, 84])).
% 18.12/18.29 tff(87,plain,(
% 18.12/18.29 ![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)))))),
% 18.12/18.29 inference(skolemize,[status(sab)],[86])).
% 18.12/18.29 tff(88,plain,
% 18.12/18.29 (![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)))))))),
% 18.12/18.29 inference(modus_ponens,[status(thm)],[87, 83])).
% 18.12/18.29 tff(89,plain,
% 18.12/18.29 (![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)))))))),
% 18.12/18.29 inference(modus_ponens,[status(thm)],[88, 81])).
% 18.12/18.29 tff(90,plain,
% 18.12/18.29 (((~![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(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) <=> ((~![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(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 18.12/18.29 inference(rewrite,[status(thm)],[])).
% 18.12/18.29 tff(91,plain,
% 18.12/18.29 ((~(~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 18.12/18.29 inference(rewrite,[status(thm)],[])).
% 18.12/18.29 tff(92,plain,
% 18.12/18.29 (((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) | $false) <=> (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 18.12/18.29 inference(rewrite,[status(thm)],[])).
% 18.12/18.29 tff(93,plain,
% 18.12/18.29 ((~$true) <=> $false),
% 18.12/18.29 inference(rewrite,[status(thm)],[])).
% 18.12/18.29 tff(94,plain,
% 18.12/18.29 (($true | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))) <=> $true),
% 18.12/18.29 inference(rewrite,[status(thm)],[])).
% 18.12/18.29 tff(95,plain,
% 18.12/18.29 ((~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))) <=> (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))),
% 18.12/18.29 inference(rewrite,[status(thm)],[])).
% 18.12/18.29 tff(96,plain,
% 18.12/18.29 ((singleton(B!20) = singleton(B!20)) <=> $true),
% 18.12/18.29 inference(rewrite,[status(thm)],[])).
% 18.12/18.29 tff(97,plain,
% 18.12/18.29 (((singleton(B!20) = singleton(B!20)) | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))))),
% 18.12/18.29 inference(monotonicity,[status(thm)],[96, 95])).
% 18.12/18.29 tff(98,plain,
% 18.12/18.29 (((singleton(B!20) = singleton(B!20)) | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))) <=> $true),
% 18.12/18.29 inference(transitivity,[status(thm)],[97, 94])).
% 18.12/18.29 tff(99,plain,
% 18.12/18.29 ((~((singleton(B!20) = singleton(B!20)) | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))))) <=> (~$true)),
% 18.12/18.29 inference(monotonicity,[status(thm)],[98])).
% 18.12/18.29 tff(100,plain,
% 18.12/18.29 ((~((singleton(B!20) = singleton(B!20)) | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))))) <=> $false),
% 18.12/18.29 inference(transitivity,[status(thm)],[99, 93])).
% 18.12/18.29 tff(101,plain,
% 18.12/18.29 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) <=> (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 18.12/18.29 inference(rewrite,[status(thm)],[])).
% 18.12/18.29 tff(102,plain,
% 18.12/18.29 (($false | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 18.12/18.29 inference(rewrite,[status(thm)],[])).
% 18.12/18.29 tff(103,plain,
% 18.12/18.29 ((~(singleton(B!20) = singleton(B!20))) <=> (~$true)),
% 18.12/18.29 inference(monotonicity,[status(thm)],[96])).
% 18.12/18.29 tff(104,plain,
% 18.12/18.29 ((~(singleton(B!20) = singleton(B!20))) <=> $false),
% 18.12/18.29 inference(transitivity,[status(thm)],[103, 93])).
% 18.12/18.29 tff(105,plain,
% 18.12/18.29 (((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) <=> ($false | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 18.12/18.29 inference(monotonicity,[status(thm)],[104])).
% 18.12/18.29 tff(106,plain,
% 18.12/18.29 (((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 18.12/18.29 inference(transitivity,[status(thm)],[105, 102])).
% 18.12/18.29 tff(107,plain,
% 18.12/18.29 ((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) <=> (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 18.12/18.29 inference(monotonicity,[status(thm)],[106])).
% 18.12/18.29 tff(108,plain,
% 18.12/18.29 ((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) <=> (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 18.12/18.29 inference(transitivity,[status(thm)],[107, 101])).
% 18.12/18.29 tff(109,plain,
% 18.12/18.29 (((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))))) <=> ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) | $false)),
% 18.12/18.29 inference(monotonicity,[status(thm)],[108, 100])).
% 18.12/18.29 tff(110,plain,
% 18.12/18.29 (((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))))) <=> (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 18.12/18.29 inference(transitivity,[status(thm)],[109, 92])).
% 18.12/18.29 tff(111,plain,
% 18.12/18.29 ((~((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))))))) <=> (~(~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))))),
% 18.12/18.29 inference(monotonicity,[status(thm)],[110])).
% 18.12/18.29 tff(112,plain,
% 18.12/18.29 ((~((~((~(singleton(B!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20))))))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 18.12/18.29 inference(transitivity,[status(thm)],[111, 91])).
% 18.12/18.29 tff(113,plain,
% 18.12/18.29 (((~![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!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))))))) <=> ((~![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(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 18.12/18.29 inference(monotonicity,[status(thm)],[112])).
% 18.12/18.29 tff(114,plain,
% 18.12/18.29 (((~![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!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))))))) <=> ((~![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(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))),
% 18.12/18.29 inference(transitivity,[status(thm)],[113, 90])).
% 18.12/18.29 tff(115,plain,
% 18.12/18.29 ((~![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!20) = singleton(B!20))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)))) | (~((singleton(B!20) = singleton(B!20)) | (~(in(tptp_fun_C_0(singleton(B!20), B!20), singleton(B!20)) <=> (tptp_fun_C_0(singleton(B!20), B!20) = B!20)))))))),
% 18.12/18.29 inference(quant_inst,[status(thm)],[])).
% 18.12/18.29 tff(116,plain,
% 18.12/18.29 ((~![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(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 18.12/18.29 inference(modus_ponens,[status(thm)],[115, 114])).
% 18.12/18.29 tff(117,plain,
% 18.12/18.29 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)),
% 18.12/18.29 inference(unit_resolution,[status(thm)],[116, 89])).
% 18.12/18.29 tff(118,plain,
% 18.12/18.29 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))))),
% 18.12/18.29 inference(bind,[status(th)],[])).
% 18.12/18.29 tff(119,plain,
% 18.12/18.29 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 18.12/18.29 inference(quant_intro,[status(thm)],[118])).
% 18.12/18.29 tff(120,plain,
% 18.12/18.29 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 18.12/18.29 inference(pull_quant,[status(thm)],[])).
% 18.12/18.29 tff(121,plain,
% 18.12/18.29 (^[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, A) | in(D, B)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))))),
% 18.12/18.29 inference(bind,[status(th)],[])).
% 18.12/18.29 tff(122,plain,
% 18.12/18.29 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 18.12/18.30 inference(quant_intro,[status(thm)],[121])).
% 18.12/18.30 tff(123,plain,
% 18.12/18.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 18.12/18.30 inference(transitivity,[status(thm)],[122, 120])).
% 18.12/18.30 tff(124,plain,
% 18.12/18.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 18.12/18.30 inference(transitivity,[status(thm)],[123, 119])).
% 18.12/18.30 tff(125,plain,
% 18.12/18.30 (^[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)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))))),
% 18.12/18.30 inference(bind,[status(th)],[])).
% 18.12/18.30 tff(126,plain,
% 18.12/18.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 18.12/18.30 inference(quant_intro,[status(thm)],[125])).
% 18.12/18.30 tff(127,plain,
% 18.12/18.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 18.12/18.30 inference(transitivity,[status(thm)],[126, 124])).
% 18.12/18.30 tff(128,plain,
% 18.12/18.30 (^[A: $i, B: $i, C: $i] : trans(monotonicity(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, A) | in(D, B))))), trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))) <=> (in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))), ((~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))) <=> (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))), rewrite((~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))) <=> (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))), ((~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))) <=> (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))))),
% 18.12/18.30 inference(bind,[status(th)],[])).
% 18.12/18.30 tff(129,plain,
% 18.12/18.30 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 18.12/18.30 inference(quant_intro,[status(thm)],[128])).
% 18.12/18.30 tff(130,plain,
% 18.12/18.30 (![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, A) | in(D, B))))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(131,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/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 18.12/18.30 tff(132,plain,
% 18.12/18.30 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[131, 130])).
% 18.12/18.30 tff(133,plain,(
% 18.12/18.30 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))),
% 18.12/18.30 inference(skolemize,[status(sab)],[132])).
% 18.12/18.30 tff(134,plain,
% 18.12/18.30 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[133, 129])).
% 18.12/18.30 tff(135,plain,
% 18.12/18.30 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[134, 127])).
% 18.12/18.30 tff(136,plain,
% 18.12/18.30 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20))))))))))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(137,plain,
% 18.12/18.30 ((~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19)))))))) <=> (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)))))))))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(138,plain,
% 18.12/18.30 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20))))))))))),
% 18.12/18.30 inference(monotonicity,[status(thm)],[137])).
% 18.12/18.30 tff(139,plain,
% 18.12/18.30 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20))))))))))),
% 18.12/18.30 inference(transitivity,[status(thm)],[138, 136])).
% 18.12/18.30 tff(140,plain,
% 18.12/18.30 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19))))))))),
% 18.12/18.30 inference(quant_inst,[status(thm)],[])).
% 18.12/18.30 tff(141,plain,
% 18.12/18.30 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)))))))))),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[140, 139])).
% 18.12/18.30 tff(142,plain,
% 18.12/18.30 (~((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20))))))))),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[141, 135])).
% 18.12/18.30 tff(143,plain,
% 18.12/18.30 (((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~((C!19 = set_union2(singleton(B!20), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(B!20)), singleton(B!20)))))))) | ((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))),
% 18.12/18.30 inference(tautology,[status(thm)],[])).
% 18.12/18.30 tff(144,plain,
% 18.12/18.30 ((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[143, 142])).
% 18.12/18.30 tff(145,plain,
% 18.12/18.30 ((~(~(((~in(A!21, C!19)) | (~in(B!20, C!19))) <=> subset(unordered_pair(A!21, B!20), C!19)))) <=> (((~in(A!21, C!19)) | (~in(B!20, C!19))) <=> subset(unordered_pair(A!21, B!20), C!19))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(146,plain,
% 18.12/18.30 ((~(((~in(A!21, C!19)) | (~in(B!20, C!19))) <=> subset(unordered_pair(A!21, B!20), C!19))) <=> (~(((~in(A!21, C!19)) | (~in(B!20, C!19))) <=> subset(unordered_pair(A!21, B!20), C!19)))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(147,plain,
% 18.12/18.30 ((subset(unordered_pair(A!21, B!20), C!19) <=> (~((~in(A!21, C!19)) | (~in(B!20, C!19))))) <=> (~(((~in(A!21, C!19)) | (~in(B!20, C!19))) <=> subset(unordered_pair(A!21, B!20), C!19)))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(148,plain,
% 18.12/18.30 ((in(A!21, C!19) & in(B!20, C!19)) <=> (~((~in(A!21, C!19)) | (~in(B!20, C!19))))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(149,plain,
% 18.12/18.30 ((subset(unordered_pair(A!21, B!20), C!19) <=> (in(A!21, C!19) & in(B!20, C!19))) <=> (subset(unordered_pair(A!21, B!20), C!19) <=> (~((~in(A!21, C!19)) | (~in(B!20, C!19)))))),
% 18.12/18.30 inference(monotonicity,[status(thm)],[148])).
% 18.12/18.30 tff(150,plain,
% 18.12/18.30 ((subset(unordered_pair(A!21, B!20), C!19) <=> (in(A!21, C!19) & in(B!20, C!19))) <=> (~(((~in(A!21, C!19)) | (~in(B!20, C!19))) <=> subset(unordered_pair(A!21, B!20), C!19)))),
% 18.12/18.30 inference(transitivity,[status(thm)],[149, 147])).
% 18.12/18.30 tff(151,plain,
% 18.12/18.30 ((subset(unordered_pair(A!21, B!20), C!19) <=> (in(A!21, C!19) & in(B!20, C!19))) <=> (~(((~in(A!21, C!19)) | (~in(B!20, C!19))) <=> subset(unordered_pair(A!21, B!20), C!19)))),
% 18.12/18.30 inference(transitivity,[status(thm)],[150, 146])).
% 18.12/18.30 tff(152,plain,
% 18.12/18.30 ((~(subset(unordered_pair(A!21, B!20), C!19) <=> (in(A!21, C!19) & in(B!20, C!19)))) <=> (~(~(((~in(A!21, C!19)) | (~in(B!20, C!19))) <=> subset(unordered_pair(A!21, B!20), C!19))))),
% 18.12/18.30 inference(monotonicity,[status(thm)],[151])).
% 18.12/18.30 tff(153,plain,
% 18.12/18.30 ((~(subset(unordered_pair(A!21, B!20), C!19) <=> (in(A!21, C!19) & in(B!20, C!19)))) <=> (((~in(A!21, C!19)) | (~in(B!20, C!19))) <=> subset(unordered_pair(A!21, B!20), C!19))),
% 18.12/18.30 inference(transitivity,[status(thm)],[152, 145])).
% 18.12/18.30 tff(154,plain,
% 18.12/18.30 ((~(subset(unordered_pair(A!21, B!20), C!19) <=> (in(A!21, C!19) & in(B!20, C!19)))) <=> (~(subset(unordered_pair(A!21, B!20), C!19) <=> (in(A!21, C!19) & in(B!20, C!19))))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(155,plain,
% 18.12/18.30 ((~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))) <=> (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C))))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(156,axiom,(~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t38_zfmisc_1')).
% 18.12/18.30 tff(157,plain,
% 18.12/18.30 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[156, 155])).
% 18.12/18.30 tff(158,plain,
% 18.12/18.30 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[157, 155])).
% 18.12/18.30 tff(159,plain,
% 18.12/18.30 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[158, 155])).
% 18.12/18.30 tff(160,plain,
% 18.12/18.30 (~![A: $i, B: $i, C: $i] : (subset(unordered_pair(A, B), C) <=> (in(A, C) & in(B, C)))),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[159, 155])).
% 18.12/18.30 tff(161,plain,(
% 18.12/18.30 ~(subset(unordered_pair(A!21, B!20), C!19) <=> (in(A!21, C!19) & in(B!20, C!19)))),
% 18.12/18.30 inference(skolemize,[status(sab)],[160])).
% 18.12/18.30 tff(162,plain,
% 18.12/18.30 (~(subset(unordered_pair(A!21, B!20), C!19) <=> (in(A!21, C!19) & in(B!20, C!19)))),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[161, 154])).
% 18.12/18.30 tff(163,plain,
% 18.12/18.30 (((~in(A!21, C!19)) | (~in(B!20, C!19))) <=> subset(unordered_pair(A!21, B!20), C!19)),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[162, 153])).
% 18.12/18.30 tff(164,plain,
% 18.12/18.30 ((~((~in(A!21, C!19)) | (~in(B!20, C!19)))) | subset(unordered_pair(A!21, B!20), C!19) | (~(((~in(A!21, C!19)) | (~in(B!20, C!19))) <=> subset(unordered_pair(A!21, B!20), C!19)))),
% 18.12/18.30 inference(tautology,[status(thm)],[])).
% 18.12/18.30 tff(165,plain,
% 18.12/18.30 ((~((~in(A!21, C!19)) | (~in(B!20, C!19)))) | subset(unordered_pair(A!21, B!20), C!19)),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[164, 163])).
% 18.12/18.30 tff(166,plain,
% 18.12/18.30 (~((~in(A!21, C!19)) | (~in(B!20, C!19)))),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[165, 43])).
% 18.12/18.30 tff(167,plain,
% 18.12/18.30 (((~in(A!21, C!19)) | (~in(B!20, C!19))) | in(B!20, C!19)),
% 18.12/18.30 inference(tautology,[status(thm)],[])).
% 18.12/18.30 tff(168,plain,
% 18.12/18.30 (in(B!20, C!19)),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[167, 166])).
% 18.12/18.30 tff(169,plain,
% 18.12/18.30 (^[A: $i, B: $i] : refl(((~in(A, B)) | (set_union2(singleton(A), B) = B)) <=> ((~in(A, B)) | (set_union2(singleton(A), B) = B)))),
% 18.12/18.30 inference(bind,[status(th)],[])).
% 18.12/18.30 tff(170,plain,
% 18.12/18.30 (![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 18.12/18.30 inference(quant_intro,[status(thm)],[169])).
% 18.12/18.30 tff(171,plain,
% 18.12/18.30 (![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(172,plain,
% 18.12/18.30 (^[A: $i, B: $i] : rewrite((in(A, B) => (set_union2(singleton(A), B) = B)) <=> ((~in(A, B)) | (set_union2(singleton(A), B) = B)))),
% 18.12/18.30 inference(bind,[status(th)],[])).
% 18.12/18.30 tff(173,plain,
% 18.12/18.30 (![A: $i, B: $i] : (in(A, B) => (set_union2(singleton(A), B) = B)) <=> ![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 18.12/18.30 inference(quant_intro,[status(thm)],[172])).
% 18.12/18.30 tff(174,axiom,(![A: $i, B: $i] : (in(A, B) => (set_union2(singleton(A), B) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l23_zfmisc_1')).
% 18.12/18.30 tff(175,plain,
% 18.12/18.30 (![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[174, 173])).
% 18.12/18.30 tff(176,plain,
% 18.12/18.30 (![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[175, 171])).
% 18.12/18.30 tff(177,plain,(
% 18.12/18.30 ![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 18.12/18.30 inference(skolemize,[status(sab)],[176])).
% 18.12/18.30 tff(178,plain,
% 18.12/18.30 (![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[177, 170])).
% 18.12/18.30 tff(179,plain,
% 18.12/18.30 (((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | ((~in(B!20, C!19)) | (set_union2(singleton(B!20), C!19) = C!19))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | (~in(B!20, C!19)) | (set_union2(singleton(B!20), C!19) = C!19))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(180,plain,
% 18.12/18.30 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | ((~in(B!20, C!19)) | (set_union2(singleton(B!20), C!19) = C!19))),
% 18.12/18.30 inference(quant_inst,[status(thm)],[])).
% 18.12/18.30 tff(181,plain,
% 18.12/18.30 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | (~in(B!20, C!19)) | (set_union2(singleton(B!20), C!19) = C!19)),
% 18.12/18.30 inference(modus_ponens,[status(thm)],[180, 179])).
% 18.12/18.30 tff(182,plain,
% 18.12/18.30 (set_union2(singleton(B!20), C!19) = C!19),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[181, 178, 168])).
% 18.12/18.30 tff(183,plain,
% 18.12/18.30 (C!19 = set_union2(singleton(B!20), C!19)),
% 18.12/18.30 inference(symmetry,[status(thm)],[182])).
% 18.12/18.30 tff(184,plain,
% 18.12/18.30 ((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))),
% 18.12/18.30 inference(tautology,[status(thm)],[])).
% 18.12/18.30 tff(185,plain,
% 18.12/18.30 ((~((~(C!19 = set_union2(singleton(B!20), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[184, 183])).
% 18.12/18.30 tff(186,plain,
% 18.12/18.30 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[185, 144])).
% 18.12/18.30 tff(187,plain,
% 18.12/18.30 (((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)) | (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))),
% 18.12/18.30 inference(tautology,[status(thm)],[])).
% 18.12/18.30 tff(188,plain,
% 18.12/18.30 (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[187, 66])).
% 18.12/18.30 tff(189,plain,
% 18.12/18.30 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))),
% 18.12/18.30 inference(tautology,[status(thm)],[])).
% 18.12/18.30 tff(190,plain,
% 18.12/18.30 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))) | (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))))),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[189, 188])).
% 18.12/18.30 tff(191,plain,
% 18.12/18.30 (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[190, 186])).
% 18.12/18.30 tff(192,plain,
% 18.12/18.30 ((in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))) | (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)))),
% 18.12/18.30 inference(tautology,[status(thm)],[])).
% 18.12/18.30 tff(193,plain,
% 18.12/18.30 (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20))),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[192, 191])).
% 18.12/18.30 tff(194,plain,
% 18.12/18.30 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) | (~(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 18.12/18.30 inference(tautology,[status(thm)],[])).
% 18.12/18.30 tff(195,plain,
% 18.12/18.30 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(B!20)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))) | (~(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20))),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[194, 193])).
% 18.12/18.30 tff(196,plain,
% 18.12/18.30 (~(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20)),
% 18.12/18.30 inference(unit_resolution,[status(thm)],[195, 117])).
% 18.12/18.30 tff(197,plain,
% 18.12/18.30 (((~![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(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) <=> ((~![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(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(198,plain,
% 18.12/18.30 ((~(~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 18.12/18.30 inference(rewrite,[status(thm)],[])).
% 18.12/18.30 tff(199,plain,
% 18.12/18.30 (((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) | $false) <=> (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 18.12/18.31 inference(rewrite,[status(thm)],[])).
% 18.12/18.31 tff(200,plain,
% 18.12/18.31 (($true | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))) <=> $true),
% 18.12/18.31 inference(rewrite,[status(thm)],[])).
% 18.12/18.31 tff(201,plain,
% 18.12/18.31 ((~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))) <=> (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))),
% 18.12/18.31 inference(rewrite,[status(thm)],[])).
% 18.12/18.31 tff(202,plain,
% 18.12/18.31 ((singleton(A!21) = singleton(A!21)) <=> $true),
% 18.12/18.31 inference(rewrite,[status(thm)],[])).
% 18.12/18.31 tff(203,plain,
% 18.12/18.31 (((singleton(A!21) = singleton(A!21)) | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))))),
% 18.12/18.31 inference(monotonicity,[status(thm)],[202, 201])).
% 18.12/18.31 tff(204,plain,
% 18.12/18.31 (((singleton(A!21) = singleton(A!21)) | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))) <=> $true),
% 18.12/18.31 inference(transitivity,[status(thm)],[203, 200])).
% 18.12/18.31 tff(205,plain,
% 18.12/18.31 ((~((singleton(A!21) = singleton(A!21)) | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))))) <=> (~$true)),
% 18.12/18.31 inference(monotonicity,[status(thm)],[204])).
% 18.12/18.31 tff(206,plain,
% 18.12/18.31 ((~((singleton(A!21) = singleton(A!21)) | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))))) <=> $false),
% 18.12/18.31 inference(transitivity,[status(thm)],[205, 93])).
% 18.12/18.31 tff(207,plain,
% 18.12/18.31 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) <=> (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 18.12/18.31 inference(rewrite,[status(thm)],[])).
% 18.12/18.31 tff(208,plain,
% 18.12/18.31 (($false | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 18.12/18.31 inference(rewrite,[status(thm)],[])).
% 18.12/18.31 tff(209,plain,
% 18.12/18.31 ((~(singleton(A!21) = singleton(A!21))) <=> (~$true)),
% 18.12/18.31 inference(monotonicity,[status(thm)],[202])).
% 18.12/18.31 tff(210,plain,
% 18.12/18.31 ((~(singleton(A!21) = singleton(A!21))) <=> $false),
% 18.12/18.31 inference(transitivity,[status(thm)],[209, 93])).
% 18.12/18.31 tff(211,plain,
% 18.12/18.31 (((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) <=> ($false | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 18.12/18.31 inference(monotonicity,[status(thm)],[210])).
% 18.12/18.31 tff(212,plain,
% 18.12/18.31 (((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 18.12/18.31 inference(transitivity,[status(thm)],[211, 208])).
% 18.12/18.31 tff(213,plain,
% 18.12/18.31 ((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) <=> (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 18.12/18.31 inference(monotonicity,[status(thm)],[212])).
% 18.12/18.31 tff(214,plain,
% 18.12/18.31 ((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) <=> (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 18.12/18.31 inference(transitivity,[status(thm)],[213, 207])).
% 18.12/18.31 tff(215,plain,
% 18.12/18.31 (((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))))) <=> ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) | $false)),
% 18.12/18.31 inference(monotonicity,[status(thm)],[214, 206])).
% 18.12/18.31 tff(216,plain,
% 18.12/18.31 (((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))))) <=> (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 18.12/18.31 inference(transitivity,[status(thm)],[215, 199])).
% 18.12/18.31 tff(217,plain,
% 18.12/18.31 ((~((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))))))) <=> (~(~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))))),
% 18.12/18.31 inference(monotonicity,[status(thm)],[216])).
% 18.12/18.31 tff(218,plain,
% 18.12/18.31 ((~((~((~(singleton(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21))))))) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 18.12/18.31 inference(transitivity,[status(thm)],[217, 198])).
% 18.12/18.31 tff(219,plain,
% 18.12/18.31 (((~![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(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))))))) <=> ((~![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(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 18.12/18.31 inference(monotonicity,[status(thm)],[218])).
% 18.12/18.31 tff(220,plain,
% 18.12/18.31 (((~![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(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))))))) <=> ((~![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(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))),
% 18.12/18.31 inference(transitivity,[status(thm)],[219, 197])).
% 18.12/18.31 tff(221,plain,
% 18.12/18.31 ((~![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(A!21) = singleton(A!21))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)))) | (~((singleton(A!21) = singleton(A!21)) | (~(in(tptp_fun_C_0(singleton(A!21), A!21), singleton(A!21)) <=> (tptp_fun_C_0(singleton(A!21), A!21) = A!21)))))))),
% 18.12/18.31 inference(quant_inst,[status(thm)],[])).
% 18.12/18.31 tff(222,plain,
% 18.12/18.31 ((~![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(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 18.12/18.31 inference(modus_ponens,[status(thm)],[221, 220])).
% 18.12/18.31 tff(223,plain,
% 18.12/18.31 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[222, 89])).
% 18.12/18.31 tff(224,plain,
% 18.12/18.31 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((~(in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21))))) | (C!19 = set_union2(singleton(A!21), C!19))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((~(in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21))))) | (C!19 = set_union2(singleton(A!21), C!19)))))))),
% 18.12/18.31 inference(rewrite,[status(thm)],[])).
% 18.12/18.31 tff(225,plain,
% 18.12/18.31 ((~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21)) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19)))))))) <=> (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((~(in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21))))) | (C!19 = set_union2(singleton(A!21), C!19))))))),
% 18.12/18.31 inference(rewrite,[status(thm)],[])).
% 18.12/18.31 tff(226,plain,
% 18.12/18.31 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21)) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((~(in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21))))) | (C!19 = set_union2(singleton(A!21), C!19)))))))),
% 18.12/18.31 inference(monotonicity,[status(thm)],[225])).
% 18.12/18.31 tff(227,plain,
% 18.12/18.31 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21)) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((~(in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21))))) | (C!19 = set_union2(singleton(A!21), C!19)))))))),
% 18.12/18.31 inference(transitivity,[status(thm)],[226, 224])).
% 18.12/18.31 tff(228,plain,
% 18.12/18.31 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19))))) | (~((C!19 = set_union2(singleton(A!21), C!19)) | (~(in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21)) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19))))))))),
% 18.12/18.31 inference(quant_inst,[status(thm)],[])).
% 18.12/18.31 tff(229,plain,
% 18.12/18.31 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) | in(tptp_fun_D_4(C, B, A), B))))))))) | (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((~(in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21))))) | (C!19 = set_union2(singleton(A!21), C!19))))))),
% 18.12/18.31 inference(modus_ponens,[status(thm)],[228, 227])).
% 18.12/18.31 tff(230,plain,
% 18.12/18.31 (~((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((~(in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21))))) | (C!19 = set_union2(singleton(A!21), C!19)))))),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[229, 135])).
% 18.12/18.31 tff(231,plain,
% 18.12/18.31 (((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~((~(in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) <=> (in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), C!19) | in(tptp_fun_D_4(C!19, C!19, singleton(A!21)), singleton(A!21))))) | (C!19 = set_union2(singleton(A!21), C!19))))) | ((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))),
% 18.12/18.31 inference(tautology,[status(thm)],[])).
% 18.12/18.31 tff(232,plain,
% 18.12/18.31 ((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[231, 230])).
% 18.12/18.31 tff(233,plain,
% 18.12/18.31 (((~in(A!21, C!19)) | (~in(B!20, C!19))) | in(A!21, C!19)),
% 18.12/18.31 inference(tautology,[status(thm)],[])).
% 18.12/18.31 tff(234,plain,
% 18.12/18.31 (in(A!21, C!19)),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[233, 166])).
% 18.12/18.31 tff(235,plain,
% 18.12/18.31 (((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | ((~in(A!21, C!19)) | (set_union2(singleton(A!21), C!19) = C!19))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | (~in(A!21, C!19)) | (set_union2(singleton(A!21), C!19) = C!19))),
% 18.12/18.31 inference(rewrite,[status(thm)],[])).
% 18.12/18.31 tff(236,plain,
% 18.12/18.31 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | ((~in(A!21, C!19)) | (set_union2(singleton(A!21), C!19) = C!19))),
% 18.12/18.31 inference(quant_inst,[status(thm)],[])).
% 18.12/18.31 tff(237,plain,
% 18.12/18.31 ((~![A: $i, B: $i] : ((~in(A, B)) | (set_union2(singleton(A), B) = B))) | (~in(A!21, C!19)) | (set_union2(singleton(A!21), C!19) = C!19)),
% 18.12/18.31 inference(modus_ponens,[status(thm)],[236, 235])).
% 18.12/18.31 tff(238,plain,
% 18.12/18.31 (set_union2(singleton(A!21), C!19) = C!19),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[237, 178, 234])).
% 18.12/18.31 tff(239,plain,
% 18.12/18.31 (C!19 = set_union2(singleton(A!21), C!19)),
% 18.12/18.31 inference(symmetry,[status(thm)],[238])).
% 18.12/18.31 tff(240,plain,
% 18.12/18.31 ((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))),
% 18.12/18.31 inference(tautology,[status(thm)],[])).
% 18.12/18.31 tff(241,plain,
% 18.12/18.31 ((~((~(C!19 = set_union2(singleton(A!21), C!19))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))))) | (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[240, 239])).
% 18.12/18.31 tff(242,plain,
% 18.12/18.31 (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[241, 232])).
% 18.12/18.31 tff(243,plain,
% 18.12/18.31 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))),
% 18.12/18.31 inference(tautology,[status(thm)],[])).
% 18.12/18.31 tff(244,plain,
% 18.12/18.31 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) <=> (in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))) | (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))))),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[243, 188])).
% 18.12/18.31 tff(245,plain,
% 18.12/18.31 (~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[244, 242])).
% 18.12/18.31 tff(246,plain,
% 18.12/18.31 ((in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))) | (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)))),
% 18.12/18.31 inference(tautology,[status(thm)],[])).
% 18.12/18.31 tff(247,plain,
% 18.12/18.31 (~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21))),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[246, 245])).
% 18.12/18.31 tff(248,plain,
% 18.12/18.31 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) | (~(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 18.12/18.31 inference(tautology,[status(thm)],[])).
% 18.12/18.31 tff(249,plain,
% 18.12/18.31 ((~(in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), singleton(A!21)) <=> (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) | (~(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[248, 247])).
% 18.12/18.31 tff(250,plain,
% 18.12/18.31 (~(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[249, 223])).
% 18.12/18.31 tff(251,plain,
% 18.12/18.31 ((~((tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21))) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = B!20) | (tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)) = A!21)),
% 18.12/18.31 inference(tautology,[status(thm)],[])).
% 18.12/18.31 tff(252,plain,
% 18.12/18.31 ($false),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[251, 250, 196, 71])).
% 18.12/18.31 tff(253,plain,(subset(unordered_pair(A!21, B!20), C!19)), inference(lemma,lemma(discharge,[]))).
% 18.12/18.31 tff(254,plain,
% 18.12/18.31 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 18.12/18.31 inference(bind,[status(th)],[])).
% 18.12/18.31 tff(255,plain,
% 18.12/18.31 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 18.12/18.31 inference(quant_intro,[status(thm)],[254])).
% 18.12/18.31 tff(256,plain,
% 18.12/18.31 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 18.12/18.31 inference(rewrite,[status(thm)],[])).
% 18.12/18.31 tff(257,plain,
% 18.12/18.31 (^[A: $i, B: $i] : rewrite((subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 18.12/18.31 inference(bind,[status(th)],[])).
% 18.12/18.31 tff(258,plain,
% 18.12/18.31 (![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A)))) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 18.12/18.31 inference(quant_intro,[status(thm)],[257])).
% 18.12/18.31 tff(259,axiom,(![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t45_xboole_1')).
% 18.12/18.31 tff(260,plain,
% 18.12/18.31 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 18.12/18.31 inference(modus_ponens,[status(thm)],[259, 258])).
% 18.12/18.31 tff(261,plain,
% 18.12/18.31 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 18.12/18.31 inference(modus_ponens,[status(thm)],[260, 256])).
% 18.12/18.31 tff(262,plain,(
% 18.12/18.31 ![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 18.12/18.31 inference(skolemize,[status(sab)],[261])).
% 18.12/18.31 tff(263,plain,
% 18.12/18.31 (![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 18.12/18.31 inference(modus_ponens,[status(thm)],[262, 255])).
% 18.12/18.31 tff(264,plain,
% 18.12/18.31 (((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(unordered_pair(A!21, B!20), C!19)) | (C!19 = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20)))))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(unordered_pair(A!21, B!20), C!19)) | (C!19 = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20)))))),
% 18.12/18.31 inference(rewrite,[status(thm)],[])).
% 18.12/18.31 tff(265,plain,
% 18.12/18.31 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | ((~subset(unordered_pair(A!21, B!20), C!19)) | (C!19 = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20)))))),
% 18.12/18.31 inference(quant_inst,[status(thm)],[])).
% 18.12/18.31 tff(266,plain,
% 18.12/18.31 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) | (~subset(unordered_pair(A!21, B!20), C!19)) | (C!19 = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20))))),
% 18.12/18.31 inference(modus_ponens,[status(thm)],[265, 264])).
% 18.12/18.31 tff(267,plain,
% 18.12/18.31 ((~subset(unordered_pair(A!21, B!20), C!19)) | (C!19 = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20))))),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[266, 263])).
% 18.12/18.31 tff(268,plain,
% 18.12/18.31 (C!19 = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20)))),
% 18.12/18.31 inference(unit_resolution,[status(thm)],[267, 253])).
% 18.12/18.31 tff(269,plain,
% 18.12/18.31 (set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20))) = C!19),
% 18.12/18.31 inference(symmetry,[status(thm)],[268])).
% 18.12/18.31 tff(270,plain,
% 18.12/18.31 (set_difference(C!19, unordered_pair(A!21, B!20)) = set_difference(C!19, unordered_pair(B!20, A!21))),
% 18.12/18.31 inference(monotonicity,[status(thm)],[39])).
% 18.12/18.32 tff(271,plain,
% 18.12/18.32 (set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20))) = set_union2(unordered_pair(B!20, A!21), set_difference(C!19, unordered_pair(B!20, A!21)))),
% 18.12/18.32 inference(monotonicity,[status(thm)],[39, 270])).
% 18.12/18.32 tff(272,plain,
% 18.12/18.32 (set_union2(unordered_pair(B!20, A!21), set_difference(C!19, unordered_pair(B!20, A!21))) = set_union2(unordered_pair(A!21, B!20), set_difference(C!19, unordered_pair(A!21, B!20)))),
% 18.12/18.32 inference(symmetry,[status(thm)],[271])).
% 18.12/18.32 tff(273,plain,
% 18.12/18.32 (^[A: $i, B: $i] : refl((set_union2(A, set_difference(B, A)) = set_union2(A, B)) <=> (set_union2(A, set_difference(B, A)) = set_union2(A, B)))),
% 18.12/18.32 inference(bind,[status(th)],[])).
% 18.12/18.32 tff(274,plain,
% 18.12/18.32 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B)) <=> ![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 18.12/18.32 inference(quant_intro,[status(thm)],[273])).
% 18.12/18.32 tff(275,plain,
% 18.12/18.32 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B)) <=> ![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 18.12/18.32 inference(rewrite,[status(thm)],[])).
% 18.12/18.32 tff(276,axiom,(![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t39_xboole_1')).
% 18.12/18.32 tff(277,plain,
% 18.12/18.32 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 18.12/18.32 inference(modus_ponens,[status(thm)],[276, 275])).
% 18.12/18.32 tff(278,plain,(
% 18.12/18.32 ![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 18.12/18.32 inference(skolemize,[status(sab)],[277])).
% 18.12/18.32 tff(279,plain,
% 18.12/18.32 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 18.12/18.32 inference(modus_ponens,[status(thm)],[278, 274])).
% 18.12/18.32 tff(280,plain,
% 18.12/18.32 ((~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))) | (set_union2(unordered_pair(B!20, A!21), set_difference(C!19, unordered_pair(B!20, A!21))) = set_union2(unordered_pair(B!20, A!21), C!19))),
% 18.12/18.32 inference(quant_inst,[status(thm)],[])).
% 18.12/18.32 tff(281,plain,
% 18.12/18.32 (set_union2(unordered_pair(B!20, A!21), set_difference(C!19, unordered_pair(B!20, A!21))) = set_union2(unordered_pair(B!20, A!21), C!19)),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[280, 279])).
% 18.12/18.32 tff(282,plain,
% 18.12/18.32 (set_union2(unordered_pair(B!20, A!21), C!19) = set_union2(unordered_pair(B!20, A!21), set_difference(C!19, unordered_pair(B!20, A!21)))),
% 18.12/18.32 inference(symmetry,[status(thm)],[281])).
% 18.12/18.32 tff(283,plain,
% 18.12/18.32 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 18.12/18.32 inference(bind,[status(th)],[])).
% 18.12/18.32 tff(284,plain,
% 18.12/18.32 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 18.12/18.32 inference(quant_intro,[status(thm)],[283])).
% 18.12/18.32 tff(285,plain,
% 18.12/18.32 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 18.12/18.32 inference(rewrite,[status(thm)],[])).
% 18.12/18.32 tff(286,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 18.12/18.32 tff(287,plain,
% 18.12/18.32 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 18.12/18.32 inference(modus_ponens,[status(thm)],[286, 285])).
% 18.12/18.32 tff(288,plain,(
% 18.12/18.32 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 18.12/18.32 inference(skolemize,[status(sab)],[287])).
% 18.12/18.32 tff(289,plain,
% 18.12/18.32 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 18.12/18.32 inference(modus_ponens,[status(thm)],[288, 284])).
% 18.12/18.32 tff(290,plain,
% 18.12/18.32 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(C!19, unordered_pair(B!20, A!21)) = set_union2(unordered_pair(B!20, A!21), C!19))),
% 18.12/18.32 inference(quant_inst,[status(thm)],[])).
% 18.12/18.32 tff(291,plain,
% 18.12/18.32 (set_union2(C!19, unordered_pair(B!20, A!21)) = set_union2(unordered_pair(B!20, A!21), C!19)),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[290, 289])).
% 18.12/18.32 tff(292,plain,
% 18.12/18.32 (set_union2(C!19, unordered_pair(B!20, A!21)) = C!19),
% 18.12/18.32 inference(transitivity,[status(thm)],[291, 282, 272, 269])).
% 18.12/18.32 tff(293,plain,
% 18.12/18.32 (in(B!20, set_union2(C!19, unordered_pair(B!20, A!21))) <=> in(B!20, C!19)),
% 18.12/18.32 inference(monotonicity,[status(thm)],[292])).
% 18.12/18.32 tff(294,plain,
% 18.12/18.32 (in(B!20, C!19) <=> in(B!20, set_union2(C!19, unordered_pair(B!20, A!21)))),
% 18.12/18.32 inference(symmetry,[status(thm)],[293])).
% 18.12/18.32 tff(295,plain,
% 18.12/18.32 ((~in(B!20, C!19)) <=> (~in(B!20, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 18.12/18.32 inference(monotonicity,[status(thm)],[294])).
% 18.12/18.32 tff(296,plain,
% 18.12/18.32 (in(A!21, unordered_pair(A!21, B!20)) <=> in(A!21, unordered_pair(B!20, A!21))),
% 18.12/18.32 inference(monotonicity,[status(thm)],[39])).
% 18.12/18.32 tff(297,plain,
% 18.12/18.32 (in(A!21, unordered_pair(B!20, A!21)) <=> in(A!21, unordered_pair(A!21, B!20))),
% 18.12/18.32 inference(symmetry,[status(thm)],[296])).
% 18.12/18.32 tff(298,assumption,((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))), introduced(assumption)).
% 18.12/18.32 tff(299,plain,
% 18.12/18.32 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))))),
% 18.12/18.32 inference(rewrite,[status(thm)],[])).
% 18.12/18.32 tff(300,plain,
% 18.12/18.32 ((~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(A!21, unordered_pair(B!20, A!21)) <=> ((A!21 = B!20) | (A!21 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))) <=> (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 18.12/18.32 inference(rewrite,[status(thm)],[])).
% 18.12/18.32 tff(301,plain,
% 18.12/18.32 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(A!21, unordered_pair(B!20, A!21)) <=> ((A!21 = B!20) | (A!21 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))))),
% 18.12/18.32 inference(monotonicity,[status(thm)],[300])).
% 18.12/18.32 tff(302,plain,
% 18.12/18.32 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(A!21, unordered_pair(B!20, A!21)) <=> ((A!21 = B!20) | (A!21 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))))),
% 18.12/18.32 inference(transitivity,[status(thm)],[301, 299])).
% 18.12/18.32 tff(303,plain,
% 18.12/18.32 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(A!21, unordered_pair(B!20, A!21)) <=> ((A!21 = B!20) | (A!21 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 18.12/18.32 inference(quant_inst,[status(thm)],[])).
% 18.12/18.32 tff(304,plain,
% 18.12/18.32 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 18.12/18.32 inference(modus_ponens,[status(thm)],[303, 302])).
% 18.12/18.32 tff(305,plain,
% 18.12/18.32 ($false),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[304, 21, 298])).
% 18.12/18.32 tff(306,plain,(~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))), inference(lemma,lemma(discharge,[]))).
% 18.12/18.32 tff(307,plain,
% 18.12/18.32 (((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))) | ((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))),
% 18.12/18.32 inference(tautology,[status(thm)],[])).
% 18.12/18.32 tff(308,plain,
% 18.12/18.32 ((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21))),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[307, 306])).
% 18.12/18.32 tff(309,plain,
% 18.12/18.32 ((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | (~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21))),
% 18.12/18.32 inference(tautology,[status(thm)],[])).
% 18.12/18.32 tff(310,plain,
% 18.12/18.32 ((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(A!21, unordered_pair(B!20, A!21)))) | in(A!21, unordered_pair(B!20, A!21))),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[309, 34])).
% 18.12/18.32 tff(311,plain,
% 18.12/18.32 (in(A!21, unordered_pair(B!20, A!21))),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[310, 308])).
% 18.12/18.32 tff(312,plain,
% 18.12/18.32 (in(A!21, unordered_pair(A!21, B!20))),
% 18.12/18.32 inference(modus_ponens,[status(thm)],[311, 297])).
% 18.12/18.32 tff(313,assumption,(~in(A!21, unordered_pair(A!21, B!20))), introduced(assumption)).
% 18.12/18.32 tff(314,plain,
% 18.12/18.32 ($false),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[313, 312])).
% 18.12/18.32 tff(315,plain,(in(A!21, unordered_pair(A!21, B!20))), inference(lemma,lemma(discharge,[]))).
% 18.12/18.32 tff(316,plain,
% 18.12/18.32 (((~((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19)))) | (~(subset(unordered_pair(A!21, B!20), C!19) | (~((~in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), unordered_pair(A!21, B!20))) | in(tptp_fun_C_10(C!19, unordered_pair(A!21, B!20)), C!19)))))) | ((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19)))),
% 18.12/18.32 inference(tautology,[status(thm)],[])).
% 18.12/18.32 tff(317,plain,
% 18.12/18.32 ((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[316, 61])).
% 18.12/18.32 tff(318,plain,
% 18.12/18.32 ((~((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19)))) | (~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))),
% 18.12/18.32 inference(tautology,[status(thm)],[])).
% 18.12/18.32 tff(319,plain,
% 18.12/18.32 ((~subset(unordered_pair(A!21, B!20), C!19)) | ![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[318, 317])).
% 18.12/18.32 tff(320,plain,
% 18.12/18.32 (![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[319, 253])).
% 18.12/18.32 tff(321,plain,
% 18.12/18.32 (((~![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))) | ((~in(A!21, unordered_pair(A!21, B!20))) | in(A!21, C!19))) <=> ((~![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))) | (~in(A!21, unordered_pair(A!21, B!20))) | in(A!21, C!19))),
% 18.12/18.32 inference(rewrite,[status(thm)],[])).
% 18.12/18.32 tff(322,plain,
% 18.12/18.32 ((~![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))) | ((~in(A!21, unordered_pair(A!21, B!20))) | in(A!21, C!19))),
% 18.12/18.32 inference(quant_inst,[status(thm)],[])).
% 18.12/18.32 tff(323,plain,
% 18.12/18.32 ((~![C: $i] : ((~in(C, unordered_pair(A!21, B!20))) | in(C, C!19))) | (~in(A!21, unordered_pair(A!21, B!20))) | in(A!21, C!19)),
% 18.12/18.32 inference(modus_ponens,[status(thm)],[322, 321])).
% 18.12/18.32 tff(324,plain,
% 18.12/18.32 (in(A!21, C!19)),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[323, 320, 315])).
% 18.12/18.32 tff(325,plain,
% 18.12/18.32 (((~in(A!21, C!19)) | (~in(B!20, C!19))) | (~subset(unordered_pair(A!21, B!20), C!19)) | (~(((~in(A!21, C!19)) | (~in(B!20, C!19))) <=> subset(unordered_pair(A!21, B!20), C!19)))),
% 18.12/18.32 inference(tautology,[status(thm)],[])).
% 18.12/18.32 tff(326,plain,
% 18.12/18.32 (((~in(A!21, C!19)) | (~in(B!20, C!19))) | (~subset(unordered_pair(A!21, B!20), C!19))),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[325, 163])).
% 18.12/18.32 tff(327,plain,
% 18.12/18.32 ((~in(A!21, C!19)) | (~in(B!20, C!19))),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[326, 253])).
% 18.12/18.32 tff(328,plain,
% 18.12/18.32 ((~((~in(A!21, C!19)) | (~in(B!20, C!19)))) | (~in(A!21, C!19)) | (~in(B!20, C!19))),
% 18.12/18.32 inference(tautology,[status(thm)],[])).
% 18.12/18.32 tff(329,plain,
% 18.12/18.32 ((~in(A!21, C!19)) | (~in(B!20, C!19))),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[328, 327])).
% 18.12/18.32 tff(330,plain,
% 18.12/18.32 (~in(B!20, C!19)),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[329, 324])).
% 18.12/18.32 tff(331,plain,
% 18.12/18.32 (~in(B!20, set_union2(C!19, unordered_pair(B!20, A!21)))),
% 18.12/18.32 inference(modus_ponens,[status(thm)],[330, 295])).
% 18.12/18.32 tff(332,assumption,((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))), introduced(assumption)).
% 18.12/18.32 tff(333,plain,
% 18.12/18.32 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))))),
% 18.12/18.32 inference(rewrite,[status(thm)],[])).
% 18.12/18.32 tff(334,plain,
% 18.12/18.32 ((~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(B!20, unordered_pair(B!20, A!21)) <=> ((B!20 = B!20) | (B!20 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))) <=> (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 18.12/18.32 inference(rewrite,[status(thm)],[])).
% 18.12/18.32 tff(335,plain,
% 18.12/18.32 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(B!20, unordered_pair(B!20, A!21)) <=> ((B!20 = B!20) | (B!20 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))))),
% 18.12/18.32 inference(monotonicity,[status(thm)],[334])).
% 18.12/18.32 tff(336,plain,
% 18.12/18.32 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(B!20, unordered_pair(B!20, A!21)) <=> ((B!20 = B!20) | (B!20 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))))),
% 18.12/18.32 inference(transitivity,[status(thm)],[335, 333])).
% 18.12/18.32 tff(337,plain,
% 18.12/18.32 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | (in(B!20, unordered_pair(B!20, A!21)) <=> ((B!20 = B!20) | (B!20 = A!21))))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 18.12/18.32 inference(quant_inst,[status(thm)],[])).
% 18.12/18.32 tff(338,plain,
% 18.12/18.32 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_3(C, B, A), C) <=> ((tptp_fun_D_3(C, B, A) = B) | (tptp_fun_D_3(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))))),
% 18.12/18.32 inference(modus_ponens,[status(thm)],[337, 336])).
% 18.12/18.32 tff(339,plain,
% 18.12/18.32 ($false),
% 18.12/18.32 inference(unit_resolution,[status(thm)],[338, 21, 332])).
% 18.12/18.32 tff(340,plain,(~((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21)))))))), inference(lemma,lemma(discharge,[]))).
% 18.12/18.33 tff(341,plain,
% 18.12/18.33 (((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~((unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20)) | (~(in(tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21), unordered_pair(B!20, A!21)) <=> ((tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = B!20) | (tptp_fun_D_3(unordered_pair(B!20, A!21), B!20, A!21) = A!21))))))) | ((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))),
% 18.12/18.33 inference(tautology,[status(thm)],[])).
% 18.12/18.33 tff(342,plain,
% 18.12/18.33 ((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21))),
% 18.12/18.33 inference(unit_resolution,[status(thm)],[341, 340])).
% 18.12/18.33 tff(343,plain,
% 18.12/18.33 ((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | (~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21))),
% 18.12/18.33 inference(tautology,[status(thm)],[])).
% 18.12/18.33 tff(344,plain,
% 18.12/18.33 ((~((~(unordered_pair(B!20, A!21) = unordered_pair(A!21, B!20))) | in(B!20, unordered_pair(B!20, A!21)))) | in(B!20, unordered_pair(B!20, A!21))),
% 18.12/18.33 inference(unit_resolution,[status(thm)],[343, 34])).
% 18.12/18.33 tff(345,plain,
% 18.12/18.33 (in(B!20, unordered_pair(B!20, A!21))),
% 18.12/18.33 inference(unit_resolution,[status(thm)],[344, 342])).
% 18.12/18.33 tff(346,plain,
% 18.12/18.33 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))) | (~((~((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21)))))) | (~(subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21))) | (~((~in(tptp_fun_C_10(set_union2(C!19, unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21))) | in(tptp_fun_C_10(set_union2(C!19, unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21)), set_union2(C!19, unordered_pair(B!20, A!21)))))))))),
% 18.12/18.33 inference(quant_inst,[status(thm)],[])).
% 18.12/18.33 tff(347,plain,
% 18.12/18.33 (~((~((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21)))))) | (~(subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21))) | (~((~in(tptp_fun_C_10(set_union2(C!19, unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21))) | in(tptp_fun_C_10(set_union2(C!19, unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21)), set_union2(C!19, unordered_pair(B!20, A!21))))))))),
% 18.12/18.33 inference(unit_resolution,[status(thm)],[346, 59])).
% 18.12/18.33 tff(348,plain,
% 18.12/18.33 (((~((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21)))))) | (~(subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21))) | (~((~in(tptp_fun_C_10(set_union2(C!19, unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21))) | in(tptp_fun_C_10(set_union2(C!19, unordered_pair(B!20, A!21)), unordered_pair(B!20, A!21)), set_union2(C!19, unordered_pair(B!20, A!21)))))))) | ((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21)))))),
% 18.12/18.33 inference(tautology,[status(thm)],[])).
% 18.12/18.33 tff(349,plain,
% 18.12/18.33 ((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 18.12/18.33 inference(unit_resolution,[status(thm)],[348, 347])).
% 18.12/18.33 tff(350,plain,
% 18.12/18.33 (set_union2(unordered_pair(B!20, A!21), C!19) = set_union2(C!19, unordered_pair(B!20, A!21))),
% 18.12/18.33 inference(symmetry,[status(thm)],[291])).
% 18.12/18.33 tff(351,plain,
% 18.12/18.33 (subset(unordered_pair(B!20, A!21), set_union2(unordered_pair(B!20, A!21), C!19)) <=> subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))),
% 18.12/18.33 inference(monotonicity,[status(thm)],[350])).
% 18.12/18.33 tff(352,plain,
% 18.12/18.33 (^[A: $i, B: $i] : refl(subset(A, set_union2(A, B)) <=> subset(A, set_union2(A, B)))),
% 18.12/18.33 inference(bind,[status(th)],[])).
% 18.12/18.33 tff(353,plain,
% 18.12/18.33 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 18.12/18.33 inference(quant_intro,[status(thm)],[352])).
% 18.12/18.33 tff(354,plain,
% 18.12/18.33 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 18.12/18.33 inference(rewrite,[status(thm)],[])).
% 18.12/18.33 tff(355,axiom,(![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_xboole_1')).
% 18.12/18.33 tff(356,plain,
% 18.12/18.33 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 18.12/18.33 inference(modus_ponens,[status(thm)],[355, 354])).
% 18.12/18.33 tff(357,plain,(
% 18.12/18.33 ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 18.12/18.33 inference(skolemize,[status(sab)],[356])).
% 18.12/18.33 tff(358,plain,
% 18.12/18.33 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 18.12/18.33 inference(modus_ponens,[status(thm)],[357, 353])).
% 18.12/18.33 tff(359,plain,
% 18.12/18.33 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(unordered_pair(B!20, A!21), set_union2(unordered_pair(B!20, A!21), C!19))),
% 18.12/18.33 inference(quant_inst,[status(thm)],[])).
% 18.12/18.33 tff(360,plain,
% 18.12/18.33 (subset(unordered_pair(B!20, A!21), set_union2(unordered_pair(B!20, A!21), C!19))),
% 18.12/18.33 inference(unit_resolution,[status(thm)],[359, 358])).
% 18.12/18.33 tff(361,plain,
% 18.12/18.33 (subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))),
% 18.12/18.33 inference(modus_ponens,[status(thm)],[360, 351])).
% 18.12/18.33 tff(362,plain,
% 18.12/18.33 ((~((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21)))))) | (~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 18.12/18.33 inference(tautology,[status(thm)],[])).
% 18.12/18.33 tff(363,plain,
% 18.12/18.33 ((~((~subset(unordered_pair(B!20, A!21), set_union2(C!19, unordered_pair(B!20, A!21)))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21)))))) | ![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 18.12/18.33 inference(unit_resolution,[status(thm)],[362, 361])).
% 18.12/18.33 tff(364,plain,
% 18.12/18.33 (![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 18.12/18.33 inference(unit_resolution,[status(thm)],[363, 349])).
% 18.12/18.33 tff(365,plain,
% 18.12/18.33 (((~![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))) | ((~in(B!20, unordered_pair(B!20, A!21))) | in(B!20, set_union2(C!19, unordered_pair(B!20, A!21))))) <=> ((~![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))) | (~in(B!20, unordered_pair(B!20, A!21))) | in(B!20, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 18.12/18.33 inference(rewrite,[status(thm)],[])).
% 18.12/18.33 tff(366,plain,
% 18.12/18.33 ((~![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))) | ((~in(B!20, unordered_pair(B!20, A!21))) | in(B!20, set_union2(C!19, unordered_pair(B!20, A!21))))),
% 18.12/18.33 inference(quant_inst,[status(thm)],[])).
% 18.12/18.33 tff(367,plain,
% 18.12/18.33 ((~![C: $i] : ((~in(C, unordered_pair(B!20, A!21))) | in(C, set_union2(C!19, unordered_pair(B!20, A!21))))) | (~in(B!20, unordered_pair(B!20, A!21))) | in(B!20, set_union2(C!19, unordered_pair(B!20, A!21)))),
% 18.12/18.33 inference(modus_ponens,[status(thm)],[366, 365])).
% 18.12/18.33 tff(368,plain,
% 18.12/18.33 (in(B!20, set_union2(C!19, unordered_pair(B!20, A!21)))),
% 18.12/18.34 inference(unit_resolution,[status(thm)],[367, 364, 345])).
% 18.12/18.34 tff(369,plain,
% 18.12/18.34 ($false),
% 18.12/18.34 inference(unit_resolution,[status(thm)],[368, 331])).
% 18.12/18.34 % SZS output end Proof
% 18.22/18.39 % E exiting
%------------------------------------------------------------------------------