%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU149+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:27:02 AM UTC 2025
% Result : Theorem 30.22s 30.42s
% Output : Proof 30.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU149+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 06:08:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 30.22/30.42 % SZS status Theorem
% 30.22/30.42 % SZS output start Proof
% 30.22/30.42 tff(tptp_fun_A_4_type, type, (
% 30.22/30.42 tptp_fun_A_4: $i)).
% 30.22/30.42 tff(tptp_fun_C_0_type, type, (
% 30.22/30.42 tptp_fun_C_0: ( $i * $i ) > $i)).
% 30.22/30.42 tff(unordered_pair_type, type, (
% 30.22/30.42 unordered_pair: ( $i * $i ) > $i)).
% 30.22/30.42 tff(tptp_fun_C_2_type, type, (
% 30.22/30.42 tptp_fun_C_2: $i)).
% 30.22/30.42 tff(tptp_fun_B_3_type, type, (
% 30.22/30.42 tptp_fun_B_3: $i)).
% 30.22/30.42 tff(in_type, type, (
% 30.22/30.42 in: ( $i * $i ) > $o)).
% 30.22/30.42 tff(singleton_type, type, (
% 30.22/30.42 singleton: $i > $i)).
% 30.22/30.42 tff(tptp_fun_D_1_type, type, (
% 30.22/30.42 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 30.22/30.42 tff(1,assumption,(~in(B!3, unordered_pair(B!3, C!2))), introduced(assumption)).
% 30.22/30.42 tff(2,plain,
% 30.22/30.42 (^[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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 30.22/30.42 inference(bind,[status(th)],[])).
% 30.22/30.42 tff(3,plain,
% 30.22/30.42 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 30.22/30.42 inference(quant_intro,[status(thm)],[2])).
% 30.22/30.42 tff(4,plain,
% 30.22/30.42 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 30.22/30.42 inference(pull_quant,[status(thm)],[])).
% 30.22/30.42 tff(5,plain,
% 30.22/30.42 (^[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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))))),
% 30.22/30.42 inference(bind,[status(th)],[])).
% 30.22/30.42 tff(6,plain,
% 30.22/30.42 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 30.22/30.42 inference(quant_intro,[status(thm)],[5])).
% 30.22/30.42 tff(7,plain,
% 30.22/30.42 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 30.22/30.42 inference(transitivity,[status(thm)],[6, 4])).
% 30.22/30.42 tff(8,plain,
% 30.22/30.42 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 30.22/30.42 inference(transitivity,[status(thm)],[7, 3])).
% 30.22/30.42 tff(9,plain,
% 30.22/30.42 (^[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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))))))),
% 30.22/30.42 inference(bind,[status(th)],[])).
% 30.22/30.42 tff(10,plain,
% 30.22/30.42 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 30.22/30.42 inference(quant_intro,[status(thm)],[9])).
% 30.22/30.42 tff(11,plain,
% 30.22/30.42 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 30.22/30.42 inference(transitivity,[status(thm)],[10, 8])).
% 30.22/30.42 tff(12,plain,
% 30.22/30.42 (^[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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))))),
% 30.22/30.42 inference(bind,[status(th)],[])).
% 30.22/30.42 tff(13,plain,
% 30.22/30.42 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 30.22/30.43 inference(quant_intro,[status(thm)],[12])).
% 30.22/30.43 tff(14,plain,
% 30.22/30.43 (![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))))),
% 30.22/30.43 inference(rewrite,[status(thm)],[])).
% 30.22/30.43 tff(15,plain,
% 30.22/30.43 (^[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)))))),
% 30.22/30.43 inference(bind,[status(th)],[])).
% 30.22/30.43 tff(16,plain,
% 30.22/30.43 (![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))))),
% 30.22/30.43 inference(quant_intro,[status(thm)],[15])).
% 30.22/30.43 tff(17,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')).
% 30.22/30.43 tff(18,plain,
% 30.22/30.43 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 30.22/30.43 inference(modus_ponens,[status(thm)],[17, 16])).
% 30.22/30.43 tff(19,plain,
% 30.22/30.43 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 30.22/30.43 inference(modus_ponens,[status(thm)],[18, 14])).
% 30.22/30.43 tff(20,plain,(
% 30.22/30.43 ![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))),
% 30.22/30.43 inference(skolemize,[status(sab)],[19])).
% 30.22/30.43 tff(21,plain,
% 30.22/30.43 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 30.22/30.43 inference(modus_ponens,[status(thm)],[20, 13])).
% 30.22/30.43 tff(22,plain,
% 30.22/30.43 (![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))),
% 30.22/30.43 inference(modus_ponens,[status(thm)],[21, 11])).
% 30.22/30.43 tff(23,plain,
% 30.22/30.43 (((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(B!3, unordered_pair(B!3, C!2))) <=> ((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(B!3, unordered_pair(B!3, C!2)))),
% 30.22/30.43 inference(rewrite,[status(thm)],[])).
% 30.22/30.43 tff(24,plain,
% 30.22/30.43 ((~(~in(B!3, unordered_pair(B!3, C!2)))) <=> in(B!3, unordered_pair(B!3, C!2))),
% 30.22/30.43 inference(rewrite,[status(thm)],[])).
% 30.22/30.43 tff(25,plain,
% 30.22/30.43 (((~in(B!3, unordered_pair(B!3, C!2))) | $false) <=> (~in(B!3, unordered_pair(B!3, C!2)))),
% 30.22/30.43 inference(rewrite,[status(thm)],[])).
% 30.22/30.43 tff(26,plain,
% 30.22/30.43 ((~$true) <=> $false),
% 30.22/30.43 inference(rewrite,[status(thm)],[])).
% 30.22/30.43 tff(27,plain,
% 30.22/30.43 (($true | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3))))) <=> $true),
% 30.22/30.43 inference(rewrite,[status(thm)],[])).
% 30.22/30.43 tff(28,plain,
% 30.22/30.43 ((~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3)))) <=> (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3))))),
% 30.22/30.43 inference(rewrite,[status(thm)],[])).
% 30.22/30.43 tff(29,plain,
% 30.22/30.43 ((in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3))) <=> (in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3)))),
% 30.22/30.43 inference(rewrite,[status(thm)],[])).
% 30.22/30.43 tff(30,plain,
% 30.22/30.43 ((~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3)))) <=> (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3))))),
% 30.22/30.43 inference(monotonicity,[status(thm)],[29])).
% 30.22/30.43 tff(31,plain,
% 30.22/30.43 ((~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3)))) <=> (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3))))),
% 30.22/30.43 inference(transitivity,[status(thm)],[30, 28])).
% 30.22/30.43 tff(32,plain,
% 30.22/30.43 ((unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2)) <=> $true),
% 30.22/30.43 inference(rewrite,[status(thm)],[])).
% 30.22/30.43 tff(33,plain,
% 30.22/30.43 (((unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2)) | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3))))) <=> ($true | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3)))))),
% 30.22/30.43 inference(monotonicity,[status(thm)],[32, 31])).
% 30.22/30.43 tff(34,plain,
% 30.22/30.43 (((unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2)) | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3))))) <=> $true),
% 30.22/30.43 inference(transitivity,[status(thm)],[33, 27])).
% 30.22/30.43 tff(35,plain,
% 30.22/30.43 ((~((unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2)) | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3)))))) <=> (~$true)),
% 30.22/30.43 inference(monotonicity,[status(thm)],[34])).
% 30.22/30.43 tff(36,plain,
% 30.22/30.43 ((~((unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2)) | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3)))))) <=> $false),
% 30.22/30.43 inference(transitivity,[status(thm)],[35, 26])).
% 30.22/30.43 tff(37,plain,
% 30.22/30.43 ((~((~(unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2))) | (in(B!3, unordered_pair(B!3, C!2)) <=> ((B!3 = C!2) | (B!3 = B!3))))) <=> (~in(B!3, unordered_pair(B!3, C!2)))),
% 30.22/30.43 inference(rewrite,[status(thm)],[])).
% 30.22/30.43 tff(38,plain,
% 30.22/30.43 (((~((~(unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2))) | (in(B!3, unordered_pair(B!3, C!2)) <=> ((B!3 = C!2) | (B!3 = B!3))))) | (~((unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2)) | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3))))))) <=> ((~in(B!3, unordered_pair(B!3, C!2))) | $false)),
% 30.22/30.43 inference(monotonicity,[status(thm)],[37, 36])).
% 30.22/30.43 tff(39,plain,
% 30.22/30.43 (((~((~(unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2))) | (in(B!3, unordered_pair(B!3, C!2)) <=> ((B!3 = C!2) | (B!3 = B!3))))) | (~((unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2)) | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3))))))) <=> (~in(B!3, unordered_pair(B!3, C!2)))),
% 30.22/30.43 inference(transitivity,[status(thm)],[38, 25])).
% 30.22/30.43 tff(40,plain,
% 30.22/30.43 ((~((~((~(unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2))) | (in(B!3, unordered_pair(B!3, C!2)) <=> ((B!3 = C!2) | (B!3 = B!3))))) | (~((unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2)) | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3)))))))) <=> (~(~in(B!3, unordered_pair(B!3, C!2))))),
% 30.22/30.43 inference(monotonicity,[status(thm)],[39])).
% 30.22/30.43 tff(41,plain,
% 30.22/30.43 ((~((~((~(unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2))) | (in(B!3, unordered_pair(B!3, C!2)) <=> ((B!3 = C!2) | (B!3 = B!3))))) | (~((unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2)) | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3)))))))) <=> in(B!3, unordered_pair(B!3, C!2))),
% 30.22/30.43 inference(transitivity,[status(thm)],[40, 24])).
% 30.22/30.43 tff(42,plain,
% 30.22/30.43 (((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2))) | (in(B!3, unordered_pair(B!3, C!2)) <=> ((B!3 = C!2) | (B!3 = B!3))))) | (~((unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2)) | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3))))))))) <=> ((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(B!3, unordered_pair(B!3, C!2)))),
% 30.22/30.43 inference(monotonicity,[status(thm)],[41])).
% 30.22/30.43 tff(43,plain,
% 30.22/30.43 (((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2))) | (in(B!3, unordered_pair(B!3, C!2)) <=> ((B!3 = C!2) | (B!3 = B!3))))) | (~((unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2)) | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3))))))))) <=> ((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(B!3, unordered_pair(B!3, C!2)))),
% 30.22/30.43 inference(transitivity,[status(thm)],[42, 23])).
% 30.22/30.43 tff(44,plain,
% 30.22/30.43 ((~![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_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2))) | (in(B!3, unordered_pair(B!3, C!2)) <=> ((B!3 = C!2) | (B!3 = B!3))))) | (~((unordered_pair(B!3, C!2) = unordered_pair(B!3, C!2)) | (~(in(tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3), unordered_pair(B!3, C!2)) <=> ((tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = C!2) | (tptp_fun_D_1(unordered_pair(B!3, C!2), C!2, B!3) = B!3))))))))),
% 30.22/30.43 inference(quant_inst,[status(thm)],[])).
% 30.22/30.43 tff(45,plain,
% 30.22/30.43 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> ((tptp_fun_D_1(C, B, A) = B) | (tptp_fun_D_1(C, B, A) = A))))))))) | in(B!3, unordered_pair(B!3, C!2))),
% 30.22/30.43 inference(modus_ponens,[status(thm)],[44, 43])).
% 30.22/30.43 tff(46,plain,
% 30.22/30.43 ($false),
% 30.22/30.43 inference(unit_resolution,[status(thm)],[45, 22, 1])).
% 30.22/30.43 tff(47,plain,(in(B!3, unordered_pair(B!3, C!2))), inference(lemma,lemma(discharge,[]))).
% 30.22/30.43 tff(48,plain,
% 30.22/30.43 ((B!3 = A!4) <=> (A!4 = B!3)),
% 30.22/30.43 inference(commutativity,[status(thm)],[])).
% 30.22/30.43 tff(49,plain,
% 30.22/30.43 ((A!4 = B!3) <=> (B!3 = A!4)),
% 30.22/30.43 inference(symmetry,[status(thm)],[48])).
% 30.22/30.43 tff(50,plain,
% 30.22/30.43 ((~(A!4 = B!3)) <=> (~(B!3 = A!4))),
% 30.22/30.43 inference(monotonicity,[status(thm)],[49])).
% 30.22/30.43 tff(51,plain,
% 30.22/30.43 ((~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))) <=> (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 30.22/30.43 inference(rewrite,[status(thm)],[])).
% 30.22/30.43 tff(52,plain,
% 30.22/30.43 ((~![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B))) <=> (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B)))),
% 30.22/30.43 inference(rewrite,[status(thm)],[])).
% 30.22/30.43 tff(53,axiom,(~![A: $i, B: $i, C: $i] : ((singleton(A) = unordered_pair(B, C)) => (A = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_zfmisc_1')).
% 30.22/30.43 tff(54,plain,
% 30.22/30.43 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 30.22/30.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 30.22/30.43 tff(55,plain,
% 30.22/30.43 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 30.22/30.43 inference(modus_ponens,[status(thm)],[54, 51])).
% 30.22/30.43 tff(56,plain,
% 30.22/30.43 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 30.22/30.43 inference(modus_ponens,[status(thm)],[55, 51])).
% 30.22/30.43 tff(57,plain,
% 30.22/30.43 (~![A: $i, B: $i, C: $i] : ((~(singleton(A) = unordered_pair(B, C))) | (A = B))),
% 30.22/30.43 inference(modus_ponens,[status(thm)],[56, 51])).
% 30.22/30.43 tff(58,plain,(
% 30.22/30.43 ~((~(singleton(A!4) = unordered_pair(B!3, C!2))) | (A!4 = B!3))),
% 30.22/30.43 inference(skolemize,[status(sab)],[57])).
% 30.22/30.43 tff(59,plain,
% 30.22/30.43 (~(A!4 = B!3)),
% 30.22/30.43 inference(or_elim,[status(thm)],[58])).
% 30.22/30.43 tff(60,plain,
% 30.22/30.43 (~(B!3 = A!4)),
% 30.22/30.43 inference(modus_ponens,[status(thm)],[59, 50])).
% 30.22/30.43 tff(61,plain,
% 30.22/30.43 ((~(in(B!3, unordered_pair(B!3, C!2)) <=> (B!3 = A!4))) | (~in(B!3, unordered_pair(B!3, C!2))) | (B!3 = A!4)),
% 30.22/30.43 inference(tautology,[status(thm)],[])).
% 30.22/30.43 tff(62,plain,
% 30.22/30.43 (~(in(B!3, unordered_pair(B!3, C!2)) <=> (B!3 = A!4))),
% 30.22/30.43 inference(unit_resolution,[status(thm)],[61, 60, 47])).
% 30.22/30.43 tff(63,plain,
% 30.22/30.43 (singleton(A!4) = unordered_pair(B!3, C!2)),
% 30.22/30.43 inference(or_elim,[status(thm)],[58])).
% 30.22/30.43 tff(64,plain,
% 30.22/30.43 (unordered_pair(B!3, C!2) = singleton(A!4)),
% 30.22/30.43 inference(symmetry,[status(thm)],[63])).
% 30.22/30.43 tff(65,plain,
% 30.22/30.43 ((~((~(unordered_pair(B!3, C!2) = singleton(A!4))) | (in(B!3, unordered_pair(B!3, C!2)) <=> (B!3 = A!4)))) | (~(unordered_pair(B!3, C!2) = singleton(A!4))) | (in(B!3, unordered_pair(B!3, C!2)) <=> (B!3 = A!4))),
% 30.22/30.43 inference(tautology,[status(thm)],[])).
% 30.22/30.43 tff(66,plain,
% 30.22/30.43 (~((~(unordered_pair(B!3, C!2) = singleton(A!4))) | (in(B!3, unordered_pair(B!3, C!2)) <=> (B!3 = A!4)))),
% 30.22/30.43 inference(unit_resolution,[status(thm)],[65, 64, 62])).
% 30.22/30.43 tff(67,plain,
% 30.22/30.43 (((~((~(unordered_pair(B!3, C!2) = singleton(A!4))) | (in(B!3, unordered_pair(B!3, C!2)) <=> (B!3 = A!4)))) | (~((unordered_pair(B!3, C!2) = singleton(A!4)) | (~(in(tptp_fun_C_0(unordered_pair(B!3, C!2), A!4), unordered_pair(B!3, C!2)) <=> (tptp_fun_C_0(unordered_pair(B!3, C!2), A!4) = A!4)))))) | ((~(unordered_pair(B!3, C!2) = singleton(A!4))) | (in(B!3, unordered_pair(B!3, C!2)) <=> (B!3 = A!4)))),
% 30.22/30.43 inference(tautology,[status(thm)],[])).
% 30.22/30.43 tff(68,plain,
% 30.22/30.43 ((~((~(unordered_pair(B!3, C!2) = singleton(A!4))) | (in(B!3, unordered_pair(B!3, C!2)) <=> (B!3 = A!4)))) | (~((unordered_pair(B!3, C!2) = singleton(A!4)) | (~(in(tptp_fun_C_0(unordered_pair(B!3, C!2), A!4), unordered_pair(B!3, C!2)) <=> (tptp_fun_C_0(unordered_pair(B!3, C!2), A!4) = A!4)))))),
% 30.22/30.43 inference(unit_resolution,[status(thm)],[67, 66])).
% 30.22/30.43 tff(69,plain,
% 30.22/30.43 (^[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))))))))),
% 30.22/30.43 inference(bind,[status(th)],[])).
% 30.22/30.43 tff(70,plain,
% 30.22/30.43 (![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)))))))),
% 30.22/30.43 inference(quant_intro,[status(thm)],[69])).
% 30.22/30.43 tff(71,plain,
% 30.22/30.43 (![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)))))))),
% 30.22/30.43 inference(pull_quant,[status(thm)],[])).
% 30.22/30.43 tff(72,plain,
% 30.22/30.43 (^[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)))))))))),
% 30.22/30.43 inference(bind,[status(th)],[])).
% 30.22/30.43 tff(73,plain,
% 30.22/30.43 (![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)))))))),
% 30.22/30.43 inference(quant_intro,[status(thm)],[72])).
% 30.22/30.43 tff(74,plain,
% 30.22/30.43 (![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)))))))),
% 30.22/30.43 inference(transitivity,[status(thm)],[73, 71])).
% 30.22/30.43 tff(75,plain,
% 30.22/30.43 (![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)))))))),
% 30.22/30.43 inference(transitivity,[status(thm)],[74, 70])).
% 30.22/30.43 tff(76,plain,
% 30.22/30.43 (^[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))))))))),
% 30.22/30.43 inference(bind,[status(th)],[])).
% 30.22/30.43 tff(77,plain,
% 30.22/30.43 (![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)))))))),
% 30.22/30.43 inference(quant_intro,[status(thm)],[76])).
% 30.22/30.43 tff(78,plain,
% 30.22/30.43 (![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)))))))),
% 30.22/30.43 inference(transitivity,[status(thm)],[77, 75])).
% 30.22/30.43 tff(79,plain,
% 30.22/30.43 (^[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)))))))))),
% 30.22/30.44 inference(bind,[status(th)],[])).
% 30.22/30.44 tff(80,plain,
% 30.22/30.44 (![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)))))))),
% 30.22/30.44 inference(quant_intro,[status(thm)],[79])).
% 30.22/30.44 tff(81,plain,
% 30.22/30.44 (![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)))),
% 30.22/30.44 inference(rewrite,[status(thm)],[])).
% 30.22/30.44 tff(82,axiom,(![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_tarski')).
% 30.22/30.44 tff(83,plain,
% 30.22/30.44 (![A: $i, B: $i] : ((B = singleton(A)) <=> ![C: $i] : (in(C, B) <=> (C = A)))),
% 30.22/30.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 30.22/30.44 tff(84,plain,(
% 30.22/30.44 ![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)))))),
% 30.22/30.44 inference(skolemize,[status(sab)],[83])).
% 30.22/30.44 tff(85,plain,
% 30.22/30.44 (![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)))))))),
% 30.22/30.44 inference(modus_ponens,[status(thm)],[84, 80])).
% 30.22/30.44 tff(86,plain,
% 30.22/30.44 (![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)))))))),
% 30.22/30.44 inference(modus_ponens,[status(thm)],[85, 78])).
% 30.22/30.44 tff(87,plain,
% 30.22/30.44 ((~![A: $i, B: $i, C: $i] : (~((~((~(B = singleton(A))) | (in(C, B) <=> (C = A)))) | (~((B = singleton(A)) | (~(in(tptp_fun_C_0(B, A), B) <=> (tptp_fun_C_0(B, A) = A)))))))) | (~((~((~(unordered_pair(B!3, C!2) = singleton(A!4))) | (in(B!3, unordered_pair(B!3, C!2)) <=> (B!3 = A!4)))) | (~((unordered_pair(B!3, C!2) = singleton(A!4)) | (~(in(tptp_fun_C_0(unordered_pair(B!3, C!2), A!4), unordered_pair(B!3, C!2)) <=> (tptp_fun_C_0(unordered_pair(B!3, C!2), A!4) = A!4)))))))),
% 30.22/30.44 inference(quant_inst,[status(thm)],[])).
% 30.22/30.44 tff(88,plain,
% 30.22/30.44 ($false),
% 30.22/30.44 inference(unit_resolution,[status(thm)],[87, 86, 68])).
% 30.22/30.44 % SZS output end Proof
% 30.22/30.44 % E exiting
%------------------------------------------------------------------------------