%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU142+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:27:00 AM UTC 2025
% Result : Theorem 0.48s 0.67s
% Output : Proof 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU142+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:07:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.48/0.67 % SZS status Theorem
% 0.48/0.67 % SZS output start Proof
% 0.48/0.67 tff(tptp_fun_A_12_type, type, (
% 0.48/0.67 tptp_fun_A_12: $i)).
% 0.48/0.67 tff(tptp_fun_D_2_type, type, (
% 0.48/0.67 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.48/0.67 tff(singleton_type, type, (
% 0.48/0.67 singleton: $i > $i)).
% 0.48/0.67 tff(in_type, type, (
% 0.48/0.67 in: ( $i * $i ) > $o)).
% 0.48/0.67 tff(unordered_pair_type, type, (
% 0.48/0.67 unordered_pair: ( $i * $i ) > $i)).
% 0.48/0.67 tff(tptp_fun_C_9_type, type, (
% 0.48/0.67 tptp_fun_C_9: ( $i * $i ) > $i)).
% 0.48/0.67 tff(tptp_fun_A_7_type, type, (
% 0.48/0.67 tptp_fun_A_7: $i)).
% 0.48/0.67 tff(tptp_fun_C_0_type, type, (
% 0.48/0.67 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.48/0.67 tff(1,plain,
% 0.48/0.67 (^[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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))))),
% 0.48/0.67 inference(bind,[status(th)],[])).
% 0.48/0.67 tff(2,plain,
% 0.48/0.67 (![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))),
% 0.48/0.67 inference(quant_intro,[status(thm)],[1])).
% 0.48/0.67 tff(3,plain,
% 0.48/0.67 (![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))),
% 0.48/0.67 inference(pull_quant,[status(thm)],[])).
% 0.48/0.67 tff(4,plain,
% 0.48/0.67 (^[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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))))),
% 0.48/0.67 inference(bind,[status(th)],[])).
% 0.48/0.67 tff(5,plain,
% 0.48/0.67 (![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))),
% 0.48/0.67 inference(quant_intro,[status(thm)],[4])).
% 0.48/0.67 tff(6,plain,
% 0.48/0.67 (![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))),
% 0.48/0.67 inference(transitivity,[status(thm)],[5, 3])).
% 0.48/0.67 tff(7,plain,
% 0.48/0.67 (![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))),
% 0.48/0.67 inference(transitivity,[status(thm)],[6, 2])).
% 0.48/0.67 tff(8,plain,
% 0.48/0.67 (^[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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))))))),
% 0.48/0.67 inference(bind,[status(th)],[])).
% 0.48/0.67 tff(9,plain,
% 0.48/0.67 (![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))),
% 0.48/0.68 inference(quant_intro,[status(thm)],[8])).
% 0.48/0.68 tff(10,plain,
% 0.48/0.68 (![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))),
% 0.48/0.68 inference(transitivity,[status(thm)],[9, 7])).
% 0.48/0.68 tff(11,plain,
% 0.48/0.68 (^[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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))) <=> (~(in(tptp_fun_D_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))))),
% 0.48/0.68 inference(bind,[status(th)],[])).
% 0.48/0.68 tff(12,plain,
% 0.48/0.68 (![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))),
% 0.48/0.68 inference(quant_intro,[status(thm)],[11])).
% 0.48/0.68 tff(13,plain,
% 0.48/0.68 (![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))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(14,plain,
% 0.48/0.68 (^[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)))))),
% 0.48/0.68 inference(bind,[status(th)],[])).
% 0.48/0.68 tff(15,plain,
% 0.48/0.68 (![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))))),
% 0.48/0.68 inference(quant_intro,[status(thm)],[14])).
% 0.48/0.68 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/sandbox2/benchmark/theBenchmark.p','d2_tarski')).
% 0.48/0.68 tff(17,plain,
% 0.48/0.68 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.48/0.68 tff(18,plain,
% 0.48/0.68 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.48/0.68 tff(19,plain,(
% 0.48/0.68 ![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))),
% 0.48/0.68 inference(skolemize,[status(sab)],[18])).
% 0.48/0.68 tff(20,plain,
% 0.48/0.68 (![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.48/0.68 tff(21,plain,
% 0.48/0.68 (![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.48/0.68 tff(22,plain,
% 0.48/0.68 (((~![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))) | (~((~((~(singleton(A!12) = unordered_pair(A!12, A!12))) | (in(tptp_fun_C_9(singleton(A!12), A!7), singleton(A!12)) <=> (tptp_fun_C_9(singleton(A!12), A!7) = A!12)))) | (~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))))))) <=> ((~![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))) | (~((~((~(singleton(A!12) = unordered_pair(A!12, A!12))) | (in(tptp_fun_C_9(singleton(A!12), A!7), singleton(A!12)) <=> (tptp_fun_C_9(singleton(A!12), A!7) = A!12)))) | (~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))))))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(23,plain,
% 0.48/0.68 ((~((~((~(singleton(A!12) = unordered_pair(A!12, A!12))) | (in(tptp_fun_C_9(singleton(A!12), A!7), singleton(A!12)) <=> ((tptp_fun_C_9(singleton(A!12), A!7) = A!12) | (tptp_fun_C_9(singleton(A!12), A!7) = A!12))))) | (~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> ((tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12) | (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))))))) <=> (~((~((~(singleton(A!12) = unordered_pair(A!12, A!12))) | (in(tptp_fun_C_9(singleton(A!12), A!7), singleton(A!12)) <=> (tptp_fun_C_9(singleton(A!12), A!7) = A!12)))) | (~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(24,plain,
% 0.48/0.68 (((~![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))) | (~((~((~(singleton(A!12) = unordered_pair(A!12, A!12))) | (in(tptp_fun_C_9(singleton(A!12), A!7), singleton(A!12)) <=> ((tptp_fun_C_9(singleton(A!12), A!7) = A!12) | (tptp_fun_C_9(singleton(A!12), A!7) = A!12))))) | (~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> ((tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12) | (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))))))))) <=> ((~![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))) | (~((~((~(singleton(A!12) = unordered_pair(A!12, A!12))) | (in(tptp_fun_C_9(singleton(A!12), A!7), singleton(A!12)) <=> (tptp_fun_C_9(singleton(A!12), A!7) = A!12)))) | (~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))))))))),
% 0.48/0.68 inference(monotonicity,[status(thm)],[23])).
% 0.48/0.68 tff(25,plain,
% 0.48/0.68 (((~![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))) | (~((~((~(singleton(A!12) = unordered_pair(A!12, A!12))) | (in(tptp_fun_C_9(singleton(A!12), A!7), singleton(A!12)) <=> ((tptp_fun_C_9(singleton(A!12), A!7) = A!12) | (tptp_fun_C_9(singleton(A!12), A!7) = A!12))))) | (~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> ((tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12) | (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))))))))) <=> ((~![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))) | (~((~((~(singleton(A!12) = unordered_pair(A!12, A!12))) | (in(tptp_fun_C_9(singleton(A!12), A!7), singleton(A!12)) <=> (tptp_fun_C_9(singleton(A!12), A!7) = A!12)))) | (~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))))))))),
% 0.48/0.68 inference(transitivity,[status(thm)],[24, 22])).
% 0.48/0.68 tff(26,plain,
% 0.48/0.68 ((~![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))) | (~((~((~(singleton(A!12) = unordered_pair(A!12, A!12))) | (in(tptp_fun_C_9(singleton(A!12), A!7), singleton(A!12)) <=> ((tptp_fun_C_9(singleton(A!12), A!7) = A!12) | (tptp_fun_C_9(singleton(A!12), A!7) = A!12))))) | (~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> ((tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12) | (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))))))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(27,plain,
% 0.48/0.68 ((~![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_2(C, B, A), C) <=> ((tptp_fun_D_2(C, B, A) = B) | (tptp_fun_D_2(C, B, A) = A))))))))) | (~((~((~(singleton(A!12) = unordered_pair(A!12, A!12))) | (in(tptp_fun_C_9(singleton(A!12), A!7), singleton(A!12)) <=> (tptp_fun_C_9(singleton(A!12), A!7) = A!12)))) | (~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.48/0.68 tff(28,plain,
% 0.48/0.68 (~((~((~(singleton(A!12) = unordered_pair(A!12, A!12))) | (in(tptp_fun_C_9(singleton(A!12), A!7), singleton(A!12)) <=> (tptp_fun_C_9(singleton(A!12), A!7) = A!12)))) | (~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[27, 21])).
% 0.48/0.68 tff(29,plain,
% 0.48/0.68 (((~((~(singleton(A!12) = unordered_pair(A!12, A!12))) | (in(tptp_fun_C_9(singleton(A!12), A!7), singleton(A!12)) <=> (tptp_fun_C_9(singleton(A!12), A!7) = A!12)))) | (~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))))) | ((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))))),
% 0.48/0.68 inference(tautology,[status(thm)],[])).
% 0.48/0.68 tff(30,plain,
% 0.48/0.68 ((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.48/0.68 tff(31,plain,
% 0.48/0.68 ((singleton(A!12) = unordered_pair(A!12, A!12)) <=> (unordered_pair(A!12, A!12) = singleton(A!12))),
% 0.48/0.68 inference(commutativity,[status(thm)],[])).
% 0.48/0.68 tff(32,plain,
% 0.48/0.68 ((unordered_pair(A!12, A!12) = singleton(A!12)) <=> (singleton(A!12) = unordered_pair(A!12, A!12))),
% 0.48/0.68 inference(symmetry,[status(thm)],[31])).
% 0.48/0.68 tff(33,plain,
% 0.48/0.68 ((~(unordered_pair(A!12, A!12) = singleton(A!12))) <=> (~(singleton(A!12) = unordered_pair(A!12, A!12)))),
% 0.48/0.68 inference(monotonicity,[status(thm)],[32])).
% 0.48/0.68 tff(34,plain,
% 0.48/0.68 ((~![A: $i] : (unordered_pair(A, A) = singleton(A))) <=> (~![A: $i] : (unordered_pair(A, A) = singleton(A)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(35,axiom,(~![A: $i] : (unordered_pair(A, A) = singleton(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t69_enumset1')).
% 0.48/0.68 tff(36,plain,
% 0.48/0.68 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.48/0.68 tff(37,plain,
% 0.48/0.68 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[36, 34])).
% 0.48/0.68 tff(38,plain,
% 0.48/0.68 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.48/0.68 tff(39,plain,
% 0.48/0.68 (~![A: $i] : (unordered_pair(A, A) = singleton(A))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.48/0.68 tff(40,plain,(
% 0.48/0.68 ~(unordered_pair(A!12, A!12) = singleton(A!12))),
% 0.48/0.68 inference(skolemize,[status(sab)],[39])).
% 0.48/0.68 tff(41,plain,
% 0.48/0.68 (~(singleton(A!12) = unordered_pair(A!12, A!12))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.48/0.68 tff(42,plain,
% 0.48/0.68 ((~((singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))))) | (singleton(A!12) = unordered_pair(A!12, A!12)) | (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))),
% 0.48/0.68 inference(tautology,[status(thm)],[])).
% 0.48/0.68 tff(43,plain,
% 0.48/0.68 (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[42, 41, 30])).
% 0.48/0.68 tff(44,plain,
% 0.48/0.68 (^[A: $i, B: $i, C: $i] : refl((~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.48/0.68 inference(bind,[status(th)],[])).
% 0.48/0.68 tff(45,plain,
% 0.48/0.68 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.48/0.68 inference(quant_intro,[status(thm)],[44])).
% 0.48/0.68 tff(46,plain,
% 0.48/0.68 (![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.48/0.68 inference(pull_quant,[status(thm)],[])).
% 0.48/0.68 tff(47,plain,
% 0.48/0.68 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> (~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), pull_quant((~![C: $i] : ((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A))))), ((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) <=> ?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> (?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), pull_quant((?[C: $i] : (~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), (((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))) <=> ?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))), pull_quant((~?[C: $i] : ((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.48/0.68 inference(bind,[status(th)],[])).
% 0.48/0.68 tff(48,plain,
% 0.48/0.68 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : ![C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.48/0.68 inference(quant_intro,[status(thm)],[47])).
% 0.48/0.68 tff(49,plain,
% 0.48/0.68 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.48/0.68 inference(transitivity,[status(thm)],[48, 46])).
% 0.48/0.68 tff(50,plain,
% 0.48/0.68 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.48/0.68 inference(transitivity,[status(thm)],[49, 45])).
% 0.48/0.68 tff(51,plain,
% 0.48/0.68 (^[A: $i, B: $i] : rewrite((~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))))),
% 0.48/0.68 inference(bind,[status(th)],[])).
% 0.48/0.68 tff(52,plain,
% 0.48/0.68 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.48/0.68 inference(quant_intro,[status(thm)],[51])).
% 0.48/0.68 tff(53,plain,
% 0.48/0.68 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.48/0.68 inference(transitivity,[status(thm)],[52, 50])).
% 0.48/0.68 tff(54,plain,
% 0.48/0.68 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) <=> ((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))), trans(monotonicity(rewrite((~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))) <=> (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), rewrite(((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))), (((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))) <=> ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))))), rewrite((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))), ((((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))))),
% 0.48/0.68 inference(bind,[status(th)],[])).
% 0.48/0.68 tff(55,plain,
% 0.48/0.68 (![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A))))) <=> ![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.48/0.68 inference(quant_intro,[status(thm)],[54])).
% 0.48/0.68 tff(56,plain,
% 0.48/0.68 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A))) <=> ![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(57,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 0.48/0.68 tff(58,plain,
% 0.48/0.68 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.48/0.68 tff(59,plain,(
% 0.48/0.68 ![A: $i, B: $i] : (((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A))) & ((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))),
% 0.48/0.68 inference(skolemize,[status(sab)],[58])).
% 0.48/0.68 tff(60,plain,
% 0.48/0.68 (![A: $i, B: $i] : (~((~((~(B = singleton(A))) | ![C: $i] : (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.48/0.68 tff(61,plain,
% 0.48/0.68 (![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.48/0.68 tff(62,plain,
% 0.48/0.68 (((~![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_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))) <=> ((~![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_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(63,plain,
% 0.48/0.68 ((~(~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))) <=> (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(64,plain,
% 0.48/0.68 (((~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))) | $false) <=> (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(65,plain,
% 0.48/0.68 ((~$true) <=> $false),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(66,plain,
% 0.48/0.68 (($true | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))) <=> $true),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(67,plain,
% 0.48/0.68 ((~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))) <=> (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(68,plain,
% 0.48/0.68 ((singleton(A!12) = singleton(A!12)) <=> $true),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(69,plain,
% 0.48/0.68 (((singleton(A!12) = singleton(A!12)) | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))) <=> ($true | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))))),
% 0.48/0.68 inference(monotonicity,[status(thm)],[68, 67])).
% 0.48/0.68 tff(70,plain,
% 0.48/0.68 (((singleton(A!12) = singleton(A!12)) | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))) <=> $true),
% 0.48/0.68 inference(transitivity,[status(thm)],[69, 66])).
% 0.48/0.68 tff(71,plain,
% 0.48/0.68 ((~((singleton(A!12) = singleton(A!12)) | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))))) <=> (~$true)),
% 0.53/0.69 inference(monotonicity,[status(thm)],[70])).
% 0.53/0.69 tff(72,plain,
% 0.53/0.69 ((~((singleton(A!12) = singleton(A!12)) | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))))) <=> $false),
% 0.53/0.69 inference(transitivity,[status(thm)],[71, 65])).
% 0.53/0.69 tff(73,plain,
% 0.53/0.69 ((~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))) <=> (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(74,plain,
% 0.53/0.69 (($false | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))) <=> (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(75,plain,
% 0.53/0.69 ((~(singleton(A!12) = singleton(A!12))) <=> (~$true)),
% 0.53/0.69 inference(monotonicity,[status(thm)],[68])).
% 0.53/0.69 tff(76,plain,
% 0.53/0.69 ((~(singleton(A!12) = singleton(A!12))) <=> $false),
% 0.53/0.69 inference(transitivity,[status(thm)],[75, 65])).
% 0.53/0.69 tff(77,plain,
% 0.53/0.69 (((~(singleton(A!12) = singleton(A!12))) | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))) <=> ($false | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))),
% 0.53/0.69 inference(monotonicity,[status(thm)],[76])).
% 0.53/0.69 tff(78,plain,
% 0.53/0.69 (((~(singleton(A!12) = singleton(A!12))) | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))) <=> (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))),
% 0.53/0.69 inference(transitivity,[status(thm)],[77, 74])).
% 0.53/0.69 tff(79,plain,
% 0.53/0.69 ((~((~(singleton(A!12) = singleton(A!12))) | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))) <=> (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))),
% 0.53/0.69 inference(monotonicity,[status(thm)],[78])).
% 0.53/0.69 tff(80,plain,
% 0.53/0.69 ((~((~(singleton(A!12) = singleton(A!12))) | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))) <=> (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))),
% 0.53/0.69 inference(transitivity,[status(thm)],[79, 73])).
% 0.53/0.69 tff(81,plain,
% 0.53/0.69 (((~((~(singleton(A!12) = singleton(A!12))) | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))))) <=> ((~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))) | $false)),
% 0.53/0.69 inference(monotonicity,[status(thm)],[80, 72])).
% 0.53/0.69 tff(82,plain,
% 0.53/0.69 (((~((~(singleton(A!12) = singleton(A!12))) | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))))) <=> (~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))),
% 0.53/0.69 inference(transitivity,[status(thm)],[81, 64])).
% 0.53/0.69 tff(83,plain,
% 0.53/0.69 ((~((~((~(singleton(A!12) = singleton(A!12))) | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))))))) <=> (~(~(in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))))),
% 0.53/0.69 inference(monotonicity,[status(thm)],[82])).
% 0.53/0.69 tff(84,plain,
% 0.53/0.69 ((~((~((~(singleton(A!12) = singleton(A!12))) | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12))))))) <=> (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))),
% 0.53/0.69 inference(transitivity,[status(thm)],[83, 63])).
% 0.53/0.69 tff(85,plain,
% 0.53/0.69 (((~![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!12) = singleton(A!12))) | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))))))) <=> ((~![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_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))),
% 0.53/0.69 inference(monotonicity,[status(thm)],[84])).
% 0.53/0.69 tff(86,plain,
% 0.53/0.69 (((~![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!12) = singleton(A!12))) | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))))))) <=> ((~![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_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))),
% 0.53/0.69 inference(transitivity,[status(thm)],[85, 62])).
% 0.53/0.69 tff(87,plain,
% 0.53/0.69 ((~![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!12) = singleton(A!12))) | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12)))) | (~((singleton(A!12) = singleton(A!12)) | (~(in(tptp_fun_C_0(singleton(A!12), A!12), singleton(A!12)) <=> (tptp_fun_C_0(singleton(A!12), A!12) = A!12)))))))),
% 0.53/0.69 inference(quant_inst,[status(thm)],[])).
% 0.53/0.69 tff(88,plain,
% 0.53/0.69 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (in(tptp_fun_D_2(singleton(A!12), A!12, A!12), singleton(A!12)) <=> (tptp_fun_D_2(singleton(A!12), A!12, A!12) = A!12))),
% 0.53/0.69 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.53/0.69 tff(89,plain,
% 0.53/0.69 ($false),
% 0.53/0.69 inference(unit_resolution,[status(thm)],[88, 61, 43])).
% 0.53/0.69 % SZS output end Proof
% 0.53/0.70 % E exiting
%------------------------------------------------------------------------------