TSTP Solution File: SEU281+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU281+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 : Tue Sep 20 07:28:40 EDT 2022
% Result : Theorem 0.64s 0.64s
% Output : Proof 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU281+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n025.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 : Sat Sep 3 11:38:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.64/0.64 % SZS status Theorem
% 0.64/0.64 % SZS output start Proof
% 0.64/0.64 tff(tptp_fun_D_2_type, type, (
% 0.64/0.64 tptp_fun_D_2: $i > $i)).
% 0.64/0.64 tff(tptp_fun_C_16_type, type, (
% 0.64/0.64 tptp_fun_C_16: ( $i * $i ) > $i)).
% 0.64/0.64 tff(tptp_fun_A_1_type, type, (
% 0.64/0.64 tptp_fun_A_1: $i)).
% 0.64/0.64 tff(tptp_fun_B_0_type, type, (
% 0.64/0.64 tptp_fun_B_0: $i)).
% 0.64/0.64 tff(ordered_pair_type, type, (
% 0.64/0.64 ordered_pair: ( $i * $i ) > $i)).
% 0.64/0.64 tff(singleton_type, type, (
% 0.64/0.64 singleton: $i > $i)).
% 0.64/0.64 tff(tptp_fun_J_19_type, type, (
% 0.64/0.64 tptp_fun_J_19: ( $i * $i ) > $i)).
% 0.64/0.64 tff(tptp_fun_K_18_type, type, (
% 0.64/0.64 tptp_fun_K_18: ( $i * $i ) > $i)).
% 0.64/0.64 tff(in_type, type, (
% 0.64/0.64 in: ( $i * $i ) > $o)).
% 0.64/0.64 tff(cartesian_product2_type, type, (
% 0.64/0.64 cartesian_product2: ( $i * $i ) > $i)).
% 0.64/0.64 tff(tptp_fun_E_17_type, type, (
% 0.64/0.64 tptp_fun_E_17: ( $i * $i * $i ) > $i)).
% 0.64/0.64 tff(tptp_fun_H_15_type, type, (
% 0.64/0.64 tptp_fun_H_15: $i > $i)).
% 0.64/0.64 tff(tptp_fun_I_14_type, type, (
% 0.64/0.64 tptp_fun_I_14: $i > $i)).
% 0.64/0.64 tff(tptp_fun_E_9_type, type, (
% 0.64/0.64 tptp_fun_E_9: $i > $i)).
% 0.64/0.64 tff(tptp_fun_C_11_type, type, (
% 0.64/0.64 tptp_fun_C_11: $i > $i)).
% 0.64/0.64 tff(tptp_fun_F_13_type, type, (
% 0.64/0.64 tptp_fun_F_13: $i > $i)).
% 0.66/0.64 tff(tptp_fun_G_12_type, type, (
% 0.66/0.64 tptp_fun_G_12: $i > $i)).
% 0.66/0.64 tff(tptp_fun_D_10_type, type, (
% 0.66/0.64 tptp_fun_D_10: $i > $i)).
% 0.66/0.64 tff(tptp_fun_E_4_type, type, (
% 0.66/0.64 tptp_fun_E_4: $i > $i)).
% 0.66/0.64 tff(tptp_fun_F_3_type, type, (
% 0.66/0.64 tptp_fun_F_3: $i > $i)).
% 0.66/0.64 tff(1,assumption,(~((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1)))))), introduced(assumption)).
% 0.66/0.64 tff(2,plain,
% 0.66/0.64 (((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1))))) | (tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))),
% 0.66/0.64 inference(tautology,[status(thm)],[])).
% 0.66/0.64 tff(3,plain,
% 0.66/0.64 (tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1)),
% 0.66/0.64 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.66/0.64 tff(4,plain,
% 0.66/0.64 (((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1))))) | (tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))),
% 0.66/0.64 inference(tautology,[status(thm)],[])).
% 0.66/0.64 tff(5,plain,
% 0.66/0.64 (tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1)),
% 0.66/0.64 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.66/0.64 tff(6,plain,
% 0.66/0.64 (tptp_fun_D_10(A!1) = tptp_fun_C_11(A!1)),
% 0.66/0.64 inference(symmetry,[status(thm)],[5])).
% 0.66/0.64 tff(7,plain,
% 0.66/0.64 (tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)),
% 0.66/0.64 inference(transitivity,[status(thm)],[6, 3])).
% 0.66/0.64 tff(8,plain,
% 0.66/0.64 (((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1))))) | (~(tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)))),
% 0.66/0.64 inference(tautology,[status(thm)],[])).
% 0.66/0.64 tff(9,plain,
% 0.66/0.64 (~(tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1))),
% 0.66/0.64 inference(unit_resolution,[status(thm)],[8, 1])).
% 0.66/0.64 tff(10,plain,
% 0.66/0.64 ($false),
% 0.66/0.64 inference(unit_resolution,[status(thm)],[9, 7])).
% 0.66/0.64 tff(11,plain,((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1))))), inference(lemma,lemma(discharge,[]))).
% 0.66/0.64 tff(12,plain,
% 0.66/0.64 (^[A: $i, B: $i] : refl(((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A))))))))) <=> ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A))))))))))),
% 0.66/0.64 inference(bind,[status(th)],[])).
% 0.66/0.64 tff(13,plain,
% 0.66/0.64 (![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A))))))))) <=> ![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))),
% 0.66/0.64 inference(quant_intro,[status(thm)],[12])).
% 0.66/0.64 tff(14,plain,
% 0.66/0.64 (^[A: $i, B: $i] : rewrite(((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A))))))))) <=> ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A))))))))))),
% 0.66/0.64 inference(bind,[status(th)],[])).
% 0.66/0.64 tff(15,plain,
% 0.66/0.64 (![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A))))))))) <=> ![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))),
% 0.66/0.64 inference(quant_intro,[status(thm)],[14])).
% 0.66/0.64 tff(16,plain,
% 0.66/0.64 (![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A))))))))) <=> ![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))),
% 0.66/0.64 inference(transitivity,[status(thm)],[15, 13])).
% 0.66/0.64 tff(17,plain,
% 0.66/0.64 (^[A: $i, B: $i] : rewrite((((tptp_fun_C_11(A) = tptp_fun_D_10(A)) & (ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A)) & in(tptp_fun_F_13(A), A) & (tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A))) & (tptp_fun_C_11(A) = tptp_fun_E_9(A)) & (ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A)) & in(tptp_fun_H_15(A), A) & (tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A))) & (~(tptp_fun_D_10(A) = tptp_fun_E_9(A)))) | ![D: $i] : (((~in(D, tptp_fun_C_16(B, A))) | (in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B)) & (tptp_fun_E_17(D, B, A) = D) & (ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D) & in(tptp_fun_J_19(D, A), A) & (tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A))))) & (in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : (~((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J)))))))) <=> ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A))))))))))),
% 0.66/0.65 inference(bind,[status(th)],[])).
% 0.66/0.65 tff(18,plain,
% 0.66/0.65 (![A: $i, B: $i] : (((tptp_fun_C_11(A) = tptp_fun_D_10(A)) & (ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A)) & in(tptp_fun_F_13(A), A) & (tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A))) & (tptp_fun_C_11(A) = tptp_fun_E_9(A)) & (ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A)) & in(tptp_fun_H_15(A), A) & (tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A))) & (~(tptp_fun_D_10(A) = tptp_fun_E_9(A)))) | ![D: $i] : (((~in(D, tptp_fun_C_16(B, A))) | (in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B)) & (tptp_fun_E_17(D, B, A) = D) & (ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D) & in(tptp_fun_J_19(D, A), A) & (tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A))))) & (in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : (~((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J)))))))) <=> ![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))),
% 0.66/0.65 inference(quant_intro,[status(thm)],[17])).
% 0.66/0.65 tff(19,plain,
% 0.66/0.65 (^[A: $i, B: $i] : rewrite(((((tptp_fun_C_11(A) = tptp_fun_D_10(A)) & ((ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A)) & in(tptp_fun_F_13(A), A) & (tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) & (tptp_fun_C_11(A) = tptp_fun_E_9(A)) & ((ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A)) & in(tptp_fun_H_15(A), A) & (tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A))))) & (~(tptp_fun_D_10(A) = tptp_fun_E_9(A)))) | ![D: $i] : (((~in(D, tptp_fun_C_16(B, A))) | (in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B)) & (tptp_fun_E_17(D, B, A) = D) & ((ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D) & in(tptp_fun_J_19(D, A), A) & (tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))) & (in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : (~((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J)))))))) <=> (((tptp_fun_C_11(A) = tptp_fun_D_10(A)) & (ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A)) & in(tptp_fun_F_13(A), A) & (tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A))) & (tptp_fun_C_11(A) = tptp_fun_E_9(A)) & (ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A)) & in(tptp_fun_H_15(A), A) & (tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A))) & (~(tptp_fun_D_10(A) = tptp_fun_E_9(A)))) | ![D: $i] : (((~in(D, tptp_fun_C_16(B, A))) | (in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B)) & (tptp_fun_E_17(D, B, A) = D) & (ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D) & in(tptp_fun_J_19(D, A), A) & (tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A))))) & (in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : (~((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J)))))))))),
% 0.66/0.65 inference(bind,[status(th)],[])).
% 0.66/0.65 tff(20,plain,
% 0.66/0.65 (![A: $i, B: $i] : ((((tptp_fun_C_11(A) = tptp_fun_D_10(A)) & ((ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A)) & in(tptp_fun_F_13(A), A) & (tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) & (tptp_fun_C_11(A) = tptp_fun_E_9(A)) & ((ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A)) & in(tptp_fun_H_15(A), A) & (tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A))))) & (~(tptp_fun_D_10(A) = tptp_fun_E_9(A)))) | ![D: $i] : (((~in(D, tptp_fun_C_16(B, A))) | (in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B)) & (tptp_fun_E_17(D, B, A) = D) & ((ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D) & in(tptp_fun_J_19(D, A), A) & (tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))) & (in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : (~((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J)))))))) <=> ![A: $i, B: $i] : (((tptp_fun_C_11(A) = tptp_fun_D_10(A)) & (ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A)) & in(tptp_fun_F_13(A), A) & (tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A))) & (tptp_fun_C_11(A) = tptp_fun_E_9(A)) & (ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A)) & in(tptp_fun_H_15(A), A) & (tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A))) & (~(tptp_fun_D_10(A) = tptp_fun_E_9(A)))) | ![D: $i] : (((~in(D, tptp_fun_C_16(B, A))) | (in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B)) & (tptp_fun_E_17(D, B, A) = D) & (ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D) & in(tptp_fun_J_19(D, A), A) & (tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A))))) & (in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : (~((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J))))))))),
% 0.66/0.65 inference(quant_intro,[status(thm)],[19])).
% 0.66/0.65 tff(21,plain,
% 0.66/0.65 (![A: $i, B: $i] : ((~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))) | (D = E))) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, cartesian_product2(A, B)) & (E = D) & ?[J: $i, K: $i] : ((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J)))))) <=> ![A: $i, B: $i] : ((~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))) | (D = E))) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, cartesian_product2(A, B)) & (E = D) & ?[J: $i, K: $i] : ((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J))))))),
% 0.66/0.65 inference(rewrite,[status(thm)],[])).
% 0.66/0.65 tff(22,plain,
% 0.66/0.65 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((C = D) & ?[F: $i, G: $i] : (((ordered_pair(F, G) = D) & in(F, A)) & (G = singleton(F)))) <=> ((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))))), ((((C = D) & ?[F: $i, G: $i] : (((ordered_pair(F, G) = D) & in(F, A)) & (G = singleton(F)))) & (C = E)) <=> (((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F)))) & (C = E)))), rewrite((((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F)))) & (C = E)) <=> ((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E))), ((((C = D) & ?[F: $i, G: $i] : (((ordered_pair(F, G) = D) & in(F, A)) & (G = singleton(F)))) & (C = E)) <=> ((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E)))), quant_intro(proof_bind(^[H: $i, I: $i] : rewrite((((ordered_pair(H, I) = E) & in(H, A)) & (I = singleton(H))) <=> ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))), (?[H: $i, I: $i] : (((ordered_pair(H, I) = E) & in(H, A)) & (I = singleton(H))) <=> ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))), (((((C = D) & ?[F: $i, G: $i] : (((ordered_pair(F, G) = D) & in(F, A)) & (G = singleton(F)))) & (C = E)) & ?[H: $i, I: $i] : (((ordered_pair(H, I) = E) & in(H, A)) & (I = singleton(H)))) <=> (((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E)) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H)))))), rewrite((((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E)) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H)))) <=> ((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))), (((((C = D) & ?[F: $i, G: $i] : (((ordered_pair(F, G) = D) & in(F, A)) & (G = singleton(F)))) & (C = E)) & ?[H: $i, I: $i] : (((ordered_pair(H, I) = E) & in(H, A)) & (I = singleton(H)))) <=> ((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H)))))), ((((((C = D) & ?[F: $i, G: $i] : (((ordered_pair(F, G) = D) & in(F, A)) & (G = singleton(F)))) & (C = E)) & ?[H: $i, I: $i] : (((ordered_pair(H, I) = E) & in(H, A)) & (I = singleton(H)))) => (D = E)) <=> (((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H)))) => (D = E)))), rewrite((((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H)))) => (D = E)) <=> ((~((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))) | (D = E))), ((((((C = D) & ?[F: $i, G: $i] : (((ordered_pair(F, G) = D) & in(F, A)) & (G = singleton(F)))) & (C = E)) & ?[H: $i, I: $i] : (((ordered_pair(H, I) = E) & in(H, A)) & (I = singleton(H)))) => (D = E)) <=> ((~((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))) | (D = E))))), (![C: $i, D: $i, E: $i] : (((((C = D) & ?[F: $i, G: $i] : (((ordered_pair(F, G) = D) & in(F, A)) & (G = singleton(F)))) & (C = E)) & ?[H: $i, I: $i] : (((ordered_pair(H, I) = E) & in(H, A)) & (I = singleton(H)))) => (D = E)) <=> ![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))) | (D = E)))), quant_intro(proof_bind(^[C: $i] : quant_intro(proof_bind(^[D: $i] : rewrite((in(D, C) <=> ?[E: $i] : ((in(E, cartesian_product2(A, B)) & (E = D)) & ?[J: $i, K: $i] : (((ordered_pair(J, K) = D) & in(J, A)) & (K = singleton(J))))) <=> (in(D, C) <=> ?[E: $i] : (in(E, cartesian_product2(A, B)) & (E = D) & ?[J: $i, K: $i] : ((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J))))))), (![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, cartesian_product2(A, B)) & (E = D)) & ?[J: $i, K: $i] : (((ordered_pair(J, K) = D) & in(J, A)) & (K = singleton(J))))) <=> ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, cartesian_product2(A, B)) & (E = D) & ?[J: $i, K: $i] : ((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J)))))))), (?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, cartesian_product2(A, B)) & (E = D)) & ?[J: $i, K: $i] : (((ordered_pair(J, K) = D) & in(J, A)) & (K = singleton(J))))) <=> ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, cartesian_product2(A, B)) & (E = D) & ?[J: $i, K: $i] : ((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J))))))), ((![C: $i, D: $i, E: $i] : (((((C = D) & ?[F: $i, G: $i] : (((ordered_pair(F, G) = D) & in(F, A)) & (G = singleton(F)))) & (C = E)) & ?[H: $i, I: $i] : (((ordered_pair(H, I) = E) & in(H, A)) & (I = singleton(H)))) => (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, cartesian_product2(A, B)) & (E = D)) & ?[J: $i, K: $i] : (((ordered_pair(J, K) = D) & in(J, A)) & (K = singleton(J)))))) <=> (![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))) | (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, cartesian_product2(A, B)) & (E = D) & ?[J: $i, K: $i] : ((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J)))))))), rewrite((![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))) | (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, cartesian_product2(A, B)) & (E = D) & ?[J: $i, K: $i] : ((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J)))))) <=> ((~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))) | (D = E))) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, cartesian_product2(A, B)) & (E = D) & ?[J: $i, K: $i] : ((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J))))))), ((![C: $i, D: $i, E: $i] : (((((C = D) & ?[F: $i, G: $i] : (((ordered_pair(F, G) = D) & in(F, A)) & (G = singleton(F)))) & (C = E)) & ?[H: $i, I: $i] : (((ordered_pair(H, I) = E) & in(H, A)) & (I = singleton(H)))) => (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, cartesian_product2(A, B)) & (E = D)) & ?[J: $i, K: $i] : (((ordered_pair(J, K) = D) & in(J, A)) & (K = singleton(J)))))) <=> ((~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))) | (D = E))) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, cartesian_product2(A, B)) & (E = D) & ?[J: $i, K: $i] : ((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J))))))))),
% 0.66/0.65 inference(bind,[status(th)],[])).
% 0.66/0.65 tff(23,plain,
% 0.66/0.65 (![A: $i, B: $i] : (![C: $i, D: $i, E: $i] : (((((C = D) & ?[F: $i, G: $i] : (((ordered_pair(F, G) = D) & in(F, A)) & (G = singleton(F)))) & (C = E)) & ?[H: $i, I: $i] : (((ordered_pair(H, I) = E) & in(H, A)) & (I = singleton(H)))) => (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, cartesian_product2(A, B)) & (E = D)) & ?[J: $i, K: $i] : (((ordered_pair(J, K) = D) & in(J, A)) & (K = singleton(J)))))) <=> ![A: $i, B: $i] : ((~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))) | (D = E))) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, cartesian_product2(A, B)) & (E = D) & ?[J: $i, K: $i] : ((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J))))))),
% 0.66/0.65 inference(quant_intro,[status(thm)],[22])).
% 0.66/0.65 tff(24,axiom,(![A: $i, B: $i] : (![C: $i, D: $i, E: $i] : (((((C = D) & ?[F: $i, G: $i] : (((ordered_pair(F, G) = D) & in(F, A)) & (G = singleton(F)))) & (C = E)) & ?[H: $i, I: $i] : (((ordered_pair(H, I) = E) & in(H, A)) & (I = singleton(H)))) => (D = E)) => ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : ((in(E, cartesian_product2(A, B)) & (E = D)) & ?[J: $i, K: $i] : (((ordered_pair(J, K) = D) & in(J, A)) & (K = singleton(J))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_tarski__e16_22__wellord2__2')).
% 0.66/0.65 tff(25,plain,
% 0.66/0.65 (![A: $i, B: $i] : ((~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))) | (D = E))) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, cartesian_product2(A, B)) & (E = D) & ?[J: $i, K: $i] : ((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J))))))),
% 0.66/0.65 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.66/0.65 tff(26,plain,
% 0.66/0.65 (![A: $i, B: $i] : ((~![C: $i, D: $i, E: $i] : ((~((C = D) & ?[F: $i, G: $i] : ((ordered_pair(F, G) = D) & in(F, A) & (G = singleton(F))) & (C = E) & ?[H: $i, I: $i] : ((ordered_pair(H, I) = E) & in(H, A) & (I = singleton(H))))) | (D = E))) | ?[C: $i] : ![D: $i] : (in(D, C) <=> ?[E: $i] : (in(E, cartesian_product2(A, B)) & (E = D) & ?[J: $i, K: $i] : ((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J))))))),
% 0.66/0.65 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.66/0.65 tff(27,plain,(
% 0.66/0.65 ![A: $i, B: $i] : ((((tptp_fun_C_11(A) = tptp_fun_D_10(A)) & ((ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A)) & in(tptp_fun_F_13(A), A) & (tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) & (tptp_fun_C_11(A) = tptp_fun_E_9(A)) & ((ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A)) & in(tptp_fun_H_15(A), A) & (tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A))))) & (~(tptp_fun_D_10(A) = tptp_fun_E_9(A)))) | ![D: $i] : (((~in(D, tptp_fun_C_16(B, A))) | (in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B)) & (tptp_fun_E_17(D, B, A) = D) & ((ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D) & in(tptp_fun_J_19(D, A), A) & (tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))) & (in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : (~((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J))))))))),
% 0.66/0.65 inference(skolemize,[status(sab)],[26])).
% 0.66/0.65 tff(28,plain,
% 0.66/0.65 (![A: $i, B: $i] : (((tptp_fun_C_11(A) = tptp_fun_D_10(A)) & (ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A)) & in(tptp_fun_F_13(A), A) & (tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A))) & (tptp_fun_C_11(A) = tptp_fun_E_9(A)) & (ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A)) & in(tptp_fun_H_15(A), A) & (tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A))) & (~(tptp_fun_D_10(A) = tptp_fun_E_9(A)))) | ![D: $i] : (((~in(D, tptp_fun_C_16(B, A))) | (in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B)) & (tptp_fun_E_17(D, B, A) = D) & (ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D) & in(tptp_fun_J_19(D, A), A) & (tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A))))) & (in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : (~((ordered_pair(J, K) = D) & in(J, A) & (K = singleton(J))))))))),
% 0.66/0.65 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.66/0.65 tff(29,plain,
% 0.66/0.65 (![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))),
% 0.66/0.65 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.66/0.65 tff(30,plain,
% 0.66/0.65 (![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))),
% 0.66/0.65 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.66/0.65 tff(31,plain,
% 0.66/0.65 (((~![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))) | ((~((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D)))))))))) <=> ((~![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))) | (~((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D)))))))))),
% 0.66/0.65 inference(rewrite,[status(thm)],[])).
% 0.66/0.65 tff(32,plain,
% 0.66/0.65 (((~((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A!1))))))))) <=> ((~((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D)))))))))),
% 0.66/0.65 inference(rewrite,[status(thm)],[])).
% 0.66/0.65 tff(33,plain,
% 0.66/0.65 (((~![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))) | ((~((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A!1)))))))))) <=> ((~![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))) | ((~((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D))))))))))),
% 0.66/0.66 inference(monotonicity,[status(thm)],[32])).
% 0.66/0.66 tff(34,plain,
% 0.66/0.66 (((~![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))) | ((~((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A!1)))))))))) <=> ((~![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))) | (~((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D)))))))))),
% 0.66/0.66 inference(transitivity,[status(thm)],[33, 31])).
% 0.66/0.66 tff(35,plain,
% 0.66/0.66 ((~![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))) | ((~((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A!1)))))))))),
% 0.66/0.66 inference(quant_inst,[status(thm)],[])).
% 0.66/0.66 tff(36,plain,
% 0.66/0.66 ((~![A: $i, B: $i] : ((~((tptp_fun_D_10(A) = tptp_fun_E_9(A)) | (~(tptp_fun_C_11(A) = tptp_fun_D_10(A))) | (~(ordered_pair(tptp_fun_F_13(A), tptp_fun_G_12(A)) = tptp_fun_D_10(A))) | (~in(tptp_fun_F_13(A), A)) | (~(tptp_fun_G_12(A) = singleton(tptp_fun_F_13(A)))) | (~(tptp_fun_C_11(A) = tptp_fun_E_9(A))) | (~(ordered_pair(tptp_fun_H_15(A), tptp_fun_I_14(A)) = tptp_fun_E_9(A))) | (~in(tptp_fun_H_15(A), A)) | (~(tptp_fun_I_14(A) = singleton(tptp_fun_H_15(A)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B, A))) | (~((~in(tptp_fun_E_17(D, B, A), cartesian_product2(A, B))) | (~(tptp_fun_E_17(D, B, A) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A), tptp_fun_K_18(D, A)) = D)) | (~in(tptp_fun_J_19(D, A), A)) | (~(tptp_fun_K_18(D, A) = singleton(tptp_fun_J_19(D, A)))))))) | (~(in(D, tptp_fun_C_16(B, A)) | ![E: $i] : ((~in(E, cartesian_product2(A, B))) | (~(E = D)) | ![J: $i, K: $i] : ((~(K = singleton(J))) | (~(ordered_pair(J, K) = D)) | (~in(J, A)))))))))) | (~((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D))))))))),
% 0.66/0.66 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.66/0.66 tff(37,plain,
% 0.66/0.66 ((~((tptp_fun_D_10(A!1) = tptp_fun_E_9(A!1)) | (~(tptp_fun_C_11(A!1) = tptp_fun_D_10(A!1))) | (~(ordered_pair(tptp_fun_F_13(A!1), tptp_fun_G_12(A!1)) = tptp_fun_D_10(A!1))) | (~in(tptp_fun_F_13(A!1), A!1)) | (~(tptp_fun_G_12(A!1) = singleton(tptp_fun_F_13(A!1)))) | (~(tptp_fun_C_11(A!1) = tptp_fun_E_9(A!1))) | (~(ordered_pair(tptp_fun_H_15(A!1), tptp_fun_I_14(A!1)) = tptp_fun_E_9(A!1))) | (~in(tptp_fun_H_15(A!1), A!1)) | (~(tptp_fun_I_14(A!1) = singleton(tptp_fun_H_15(A!1)))))) | ![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D))))))))),
% 0.66/0.66 inference(unit_resolution,[status(thm)],[36, 30])).
% 0.66/0.66 tff(38,plain,
% 0.66/0.66 (![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D))))))))),
% 0.66/0.66 inference(unit_resolution,[status(thm)],[37, 11])).
% 0.66/0.66 tff(39,plain,
% 0.66/0.66 (((~![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))))))) <=> ((~![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))))))),
% 0.66/0.66 inference(rewrite,[status(thm)],[])).
% 0.66/0.66 tff(40,plain,
% 0.66/0.66 ((~((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))))) <=> (~((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))))))),
% 0.66/0.66 inference(rewrite,[status(thm)],[])).
% 0.66/0.66 tff(41,plain,
% 0.66/0.66 (((~![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))))))) <=> ((~![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))))))),
% 0.66/0.66 inference(monotonicity,[status(thm)],[40])).
% 0.66/0.66 tff(42,plain,
% 0.66/0.66 (((~![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))))))) <=> ((~![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))))))),
% 0.66/0.67 inference(transitivity,[status(thm)],[41, 39])).
% 0.66/0.67 tff(43,plain,
% 0.66/0.67 ((~![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)) | (~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))))))),
% 0.66/0.67 inference(quant_inst,[status(thm)],[])).
% 0.66/0.67 tff(44,plain,
% 0.66/0.67 ((~![D: $i] : (~((~((~in(D, tptp_fun_C_16(B!0, A!1))) | (~((~in(tptp_fun_E_17(D, B!0, A!1), cartesian_product2(A!1, B!0))) | (~(tptp_fun_E_17(D, B!0, A!1) = D)) | (~(ordered_pair(tptp_fun_J_19(D, A!1), tptp_fun_K_18(D, A!1)) = D)) | (~in(tptp_fun_J_19(D, A!1), A!1)) | (~(tptp_fun_K_18(D, A!1) = singleton(tptp_fun_J_19(D, A!1)))))))) | (~(in(D, tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~(E = D)) | (~in(E, cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = D))))))))) | (~((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))))))),
% 0.66/0.67 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.66/0.67 tff(45,plain,
% 0.66/0.67 (~((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))))),
% 0.66/0.67 inference(unit_resolution,[status(thm)],[44, 38])).
% 0.66/0.67 tff(46,plain,
% 0.66/0.67 (((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))))) | ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))))),
% 0.66/0.67 inference(tautology,[status(thm)],[])).
% 0.66/0.67 tff(47,plain,
% 0.66/0.67 ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1))))),
% 0.66/0.67 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.66/0.67 tff(48,assumption,(~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))), introduced(assumption)).
% 0.66/0.67 tff(49,plain,
% 0.66/0.67 (^[C: $i] : rewrite((~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E)))))))) <=> (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E)))))))))),
% 0.66/0.67 inference(bind,[status(th)],[])).
% 0.66/0.67 tff(50,plain,
% 0.66/0.67 (![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E)))))))) <=> ![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))),
% 0.66/0.67 inference(quant_intro,[status(thm)],[49])).
% 0.66/0.67 tff(51,plain,
% 0.66/0.67 (^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0)) & (ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)) & in(tptp_fun_E_4(C), A!1) & (tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) <=> (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)))))), ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0)) & (ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)) & in(tptp_fun_E_4(C), A!1) & (tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C))))) <=> (in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)))))))), rewrite((in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)))))) <=> (in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))), ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0)) & (ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)) & in(tptp_fun_E_4(C), A!1) & (tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C))))) <=> (in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)))))))), trans(monotonicity(quant_intro(proof_bind(^[E: $i, F: $i] : trans(monotonicity(rewrite(((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E))) <=> (~((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E)))))), ((~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E)))) <=> (~(~((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E)))))))), rewrite((~(~((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E)))))) <=> ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))), ((~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E)))) <=> ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))), (![E: $i, F: $i] : (~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E)))) <=> ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E)))))), (((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : (~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E))))) <=> ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))), rewrite(((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))) <=> ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E)))))), (((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : (~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E))))) <=> ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))), (((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0)) & (ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)) & in(tptp_fun_E_4(C), A!1) & (tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C))))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : (~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E)))))) <=> ((in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)))))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E)))))))), rewrite(((in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)))))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E)))))) <=> (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))), (((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0)) & (ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)) & in(tptp_fun_E_4(C), A!1) & (tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C))))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : (~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E)))))) <=> (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))))),
% 0.66/0.67 inference(bind,[status(th)],[])).
% 0.66/0.67 tff(52,plain,
% 0.66/0.67 (![C: $i] : ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0)) & (ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)) & in(tptp_fun_E_4(C), A!1) & (tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C))))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : (~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E)))))) <=> ![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))),
% 0.66/0.67 inference(quant_intro,[status(thm)],[51])).
% 0.66/0.67 tff(53,plain,
% 0.66/0.67 (^[C: $i] : rewrite(((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0)) & ((ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)) & in(tptp_fun_E_4(C), A!1) & (tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))))) & ((~in(tptp_fun_D_2(C), C)) | ((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : (~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E))))))) <=> ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0)) & (ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)) & in(tptp_fun_E_4(C), A!1) & (tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C))))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : (~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E)))))))),
% 0.66/0.67 inference(bind,[status(th)],[])).
% 0.66/0.67 tff(54,plain,
% 0.66/0.67 (![C: $i] : ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0)) & ((ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)) & in(tptp_fun_E_4(C), A!1) & (tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))))) & ((~in(tptp_fun_D_2(C), C)) | ((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : (~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E))))))) <=> ![C: $i] : ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0)) & (ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)) & in(tptp_fun_E_4(C), A!1) & (tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C))))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : (~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E))))))),
% 0.66/0.67 inference(quant_intro,[status(thm)],[53])).
% 0.66/0.67 tff(55,plain,
% 0.66/0.67 ((~![A: $i, B: $i] : ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A, B)) & ?[E: $i, F: $i] : ((ordered_pair(E, F) = D) & in(E, A) & (F = singleton(E)))))) <=> (~![A: $i, B: $i] : ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A, B)) & ?[E: $i, F: $i] : ((ordered_pair(E, F) = D) & in(E, A) & (F = singleton(E))))))),
% 0.66/0.67 inference(rewrite,[status(thm)],[])).
% 0.66/0.67 tff(56,plain,
% 0.66/0.67 ((~![A: $i, B: $i] : ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A, B)) & ?[E: $i, F: $i] : (((ordered_pair(E, F) = D) & in(E, A)) & (F = singleton(E)))))) <=> (~![A: $i, B: $i] : ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A, B)) & ?[E: $i, F: $i] : ((ordered_pair(E, F) = D) & in(E, A) & (F = singleton(E))))))),
% 0.66/0.67 inference(rewrite,[status(thm)],[])).
% 0.66/0.67 tff(57,axiom,(~![A: $i, B: $i] : ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A, B)) & ?[E: $i, F: $i] : (((ordered_pair(E, F) = D) & in(E, A)) & (F = singleton(E)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_xboole_0__e16_22__wellord2__1')).
% 0.66/0.67 tff(58,plain,
% 0.66/0.67 (~![A: $i, B: $i] : ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A, B)) & ?[E: $i, F: $i] : ((ordered_pair(E, F) = D) & in(E, A) & (F = singleton(E)))))),
% 0.66/0.67 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.66/0.67 tff(59,plain,
% 0.66/0.67 (~![A: $i, B: $i] : ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A, B)) & ?[E: $i, F: $i] : ((ordered_pair(E, F) = D) & in(E, A) & (F = singleton(E)))))),
% 0.66/0.67 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.66/0.67 tff(60,plain,
% 0.66/0.67 (~![A: $i, B: $i] : ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A, B)) & ?[E: $i, F: $i] : ((ordered_pair(E, F) = D) & in(E, A) & (F = singleton(E)))))),
% 0.66/0.67 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.66/0.67 tff(61,plain,
% 0.66/0.67 (~![A: $i, B: $i] : ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A, B)) & ?[E: $i, F: $i] : ((ordered_pair(E, F) = D) & in(E, A) & (F = singleton(E)))))),
% 0.66/0.67 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.66/0.67 tff(62,plain,
% 0.66/0.67 (~![A: $i, B: $i] : ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A, B)) & ?[E: $i, F: $i] : ((ordered_pair(E, F) = D) & in(E, A) & (F = singleton(E)))))),
% 0.66/0.67 inference(modus_ponens,[status(thm)],[61, 55])).
% 0.66/0.67 tff(63,plain,
% 0.66/0.67 (~![A: $i, B: $i] : ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A, B)) & ?[E: $i, F: $i] : ((ordered_pair(E, F) = D) & in(E, A) & (F = singleton(E)))))),
% 0.66/0.67 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.66/0.67 tff(64,plain,
% 0.66/0.67 (~![A: $i, B: $i] : ?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A, B)) & ?[E: $i, F: $i] : ((ordered_pair(E, F) = D) & in(E, A) & (F = singleton(E)))))),
% 0.66/0.67 inference(modus_ponens,[status(thm)],[63, 55])).
% 0.66/0.67 tff(65,plain,(
% 0.66/0.67 $oeq((~?[C: $i] : ![D: $i] : (in(D, C) <=> (in(D, cartesian_product2(A!1, B!0)) & ?[E: $i, F: $i] : ((ordered_pair(E, F) = D) & in(E, A!1) & (F = singleton(E)))))), ![C: $i] : ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0)) & ((ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)) & in(tptp_fun_E_4(C), A!1) & (tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))))) & ((~in(tptp_fun_D_2(C), C)) | ((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : (~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E))))))))),
% 0.66/0.67 inference(transitivity,[status(sab)],[64])).
% 0.66/0.67 tff(66,plain,
% 0.66/0.67 (![C: $i] : ((in(tptp_fun_D_2(C), C) | (in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0)) & (ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C)) & in(tptp_fun_E_4(C), A!1) & (tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C))))) & ((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : (~((ordered_pair(E, F) = tptp_fun_D_2(C)) & in(E, A!1) & (F = singleton(E))))))),
% 0.66/0.67 inference(modus_ponens,[status(thm)],[65, 54])).
% 0.66/0.67 tff(67,plain,
% 0.66/0.67 (![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))),
% 0.66/0.67 inference(modus_ponens,[status(thm)],[66, 52])).
% 0.66/0.67 tff(68,plain,
% 0.66/0.67 (![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))),
% 0.66/0.67 inference(modus_ponens,[status(thm)],[67, 50])).
% 0.66/0.67 tff(69,plain,
% 0.66/0.67 (((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))))) <=> ((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))))))),
% 0.66/0.67 inference(rewrite,[status(thm)],[])).
% 0.66/0.67 tff(70,plain,
% 0.66/0.67 ((~((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(E, A!1)) | (~(F = singleton(E)))))))) <=> (~((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))))),
% 0.66/0.68 inference(rewrite,[status(thm)],[])).
% 0.66/0.68 tff(71,plain,
% 0.66/0.68 (((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(E, A!1)) | (~(F = singleton(E))))))))) <=> ((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))))))),
% 0.66/0.68 inference(monotonicity,[status(thm)],[70])).
% 0.66/0.68 tff(72,plain,
% 0.66/0.68 (((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(E, A!1)) | (~(F = singleton(E))))))))) <=> ((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))))))),
% 0.66/0.68 inference(transitivity,[status(thm)],[71, 69])).
% 0.66/0.68 tff(73,plain,
% 0.66/0.68 ((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(E, A!1)) | (~(F = singleton(E))))))))),
% 0.66/0.68 inference(quant_inst,[status(thm)],[])).
% 0.66/0.68 tff(74,plain,
% 0.66/0.68 ((~![C: $i] : (~((~(in(tptp_fun_D_2(C), C) | (~((~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(C) = singleton(tptp_fun_E_4(C)))) | (~in(tptp_fun_E_4(C), A!1)) | (~(ordered_pair(tptp_fun_E_4(C), tptp_fun_F_3(C)) = tptp_fun_D_2(C))))))) | (~((~in(tptp_fun_D_2(C), C)) | (~in(tptp_fun_D_2(C), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~(ordered_pair(E, F) = tptp_fun_D_2(C))) | (~in(E, A!1)) | (~(F = singleton(E))))))))) | (~((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))))),
% 0.66/0.68 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.66/0.68 tff(75,plain,
% 0.66/0.68 (~((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[74, 68])).
% 0.66/0.68 tff(76,plain,
% 0.66/0.68 (((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))),
% 0.66/0.68 inference(tautology,[status(thm)],[])).
% 0.66/0.68 tff(77,plain,
% 0.66/0.68 (in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.66/0.68 tff(78,plain,
% 0.66/0.68 ((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.68 inference(tautology,[status(thm)],[])).
% 0.66/0.68 tff(79,plain,
% 0.66/0.68 (in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.66/0.68 tff(80,plain,
% 0.66/0.68 (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[79, 48])).
% 0.66/0.68 tff(81,plain,
% 0.66/0.68 (((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))) | (ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))),
% 0.66/0.68 inference(tautology,[status(thm)],[])).
% 0.66/0.68 tff(82,plain,
% 0.66/0.68 (ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.66/0.68 tff(83,plain,
% 0.66/0.68 (((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))) | (tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))),
% 0.66/0.68 inference(tautology,[status(thm)],[])).
% 0.66/0.68 tff(84,plain,
% 0.66/0.68 (tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[83, 80])).
% 0.66/0.68 tff(85,plain,
% 0.66/0.68 (singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))) = tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))),
% 0.66/0.68 inference(symmetry,[status(thm)],[84])).
% 0.66/0.68 tff(86,plain,
% 0.66/0.68 (ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)))),
% 0.66/0.68 inference(monotonicity,[status(thm)],[85])).
% 0.66/0.68 tff(87,plain,
% 0.66/0.68 (ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))),
% 0.66/0.68 inference(transitivity,[status(thm)],[86, 82])).
% 0.66/0.68 tff(88,plain,
% 0.66/0.68 (((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))))) | (~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))))) | (in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))),
% 0.66/0.68 inference(tautology,[status(thm)],[])).
% 0.66/0.68 tff(89,plain,
% 0.66/0.68 (in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[88, 45])).
% 0.66/0.68 tff(90,plain,
% 0.66/0.68 ((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | ![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.68 inference(tautology,[status(thm)],[])).
% 0.66/0.68 tff(91,plain,
% 0.66/0.68 (![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[90, 48, 89])).
% 0.66/0.68 tff(92,assumption,(~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))), introduced(assumption)).
% 0.66/0.68 tff(93,plain,
% 0.66/0.68 (((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))) | in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))),
% 0.66/0.68 inference(tautology,[status(thm)],[])).
% 0.66/0.68 tff(94,plain,
% 0.66/0.68 ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.66/0.68 tff(95,plain,
% 0.66/0.68 (in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))),
% 0.66/0.68 inference(unit_resolution,[status(thm)],[79, 94])).
% 0.66/0.68 tff(96,plain,
% 0.66/0.68 ((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1))))),
% 0.66/0.69 inference(tautology,[status(thm)],[])).
% 0.66/0.69 tff(97,plain,
% 0.66/0.69 (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[96, 95, 47])).
% 0.66/0.69 tff(98,plain,
% 0.66/0.69 (((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1))) | (tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))),
% 0.66/0.69 inference(tautology,[status(thm)],[])).
% 0.66/0.69 tff(99,plain,
% 0.66/0.69 (tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.66/0.69 tff(100,plain,
% 0.66/0.69 (in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0)) <=> in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))),
% 0.66/0.69 inference(monotonicity,[status(thm)],[99])).
% 0.66/0.69 tff(101,plain,
% 0.66/0.69 (in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0)) <=> in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))),
% 0.66/0.69 inference(symmetry,[status(thm)],[100])).
% 0.66/0.69 tff(102,plain,
% 0.66/0.69 ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) <=> (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0)))),
% 0.66/0.69 inference(monotonicity,[status(thm)],[101])).
% 0.66/0.69 tff(103,plain,
% 0.66/0.69 (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[92, 102])).
% 0.66/0.69 tff(104,plain,
% 0.66/0.69 (((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1))) | in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))),
% 0.66/0.69 inference(tautology,[status(thm)],[])).
% 0.66/0.69 tff(105,plain,
% 0.66/0.69 (in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[104, 97])).
% 0.66/0.69 tff(106,plain,
% 0.66/0.69 ($false),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[105, 103])).
% 0.66/0.69 tff(107,plain,(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))), inference(lemma,lemma(discharge,[]))).
% 0.66/0.69 tff(108,plain,
% 0.66/0.69 (((~![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))) | ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))) <=> ((~![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(109,plain,
% 0.66/0.69 (((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | $false | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) <=> ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(110,plain,
% 0.66/0.69 ((~$true) <=> $false),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(111,plain,
% 0.66/0.69 ((tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))) <=> $true),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(112,plain,
% 0.66/0.69 ((~(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) <=> (~$true)),
% 0.66/0.69 inference(monotonicity,[status(thm)],[111])).
% 0.66/0.69 tff(113,plain,
% 0.66/0.69 ((~(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) <=> $false),
% 0.66/0.69 inference(transitivity,[status(thm)],[112, 110])).
% 0.66/0.69 tff(114,plain,
% 0.66/0.69 (((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) <=> ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | $false | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.69 inference(monotonicity,[status(thm)],[113])).
% 0.66/0.69 tff(115,plain,
% 0.66/0.69 (((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) <=> ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.69 inference(transitivity,[status(thm)],[114, 109])).
% 0.66/0.69 tff(116,plain,
% 0.66/0.69 (((~![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))) | ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))) <=> ((~![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))) | ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))),
% 0.66/0.69 inference(monotonicity,[status(thm)],[115])).
% 0.66/0.69 tff(117,plain,
% 0.66/0.69 (((~![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))) | ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))) <=> ((~![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.69 inference(transitivity,[status(thm)],[116, 108])).
% 0.66/0.69 tff(118,plain,
% 0.66/0.69 ((~![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))) | ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.69 inference(quant_inst,[status(thm)],[])).
% 0.66/0.69 tff(119,plain,
% 0.66/0.69 ((~![E: $i] : ((~in(E, cartesian_product2(A!1, B!0))) | (~(E = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.66/0.69 tff(120,plain,
% 0.66/0.69 (![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[119, 107, 91])).
% 0.66/0.69 tff(121,plain,
% 0.66/0.69 (((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))) | in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)),
% 0.66/0.69 inference(tautology,[status(thm)],[])).
% 0.66/0.69 tff(122,plain,
% 0.66/0.69 (in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[121, 80])).
% 0.66/0.69 tff(123,plain,
% 0.66/0.69 (((~![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | ((~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) <=> ((~![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(124,plain,
% 0.66/0.69 (((~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | $false | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))) <=> ((~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(125,plain,
% 0.66/0.69 ((singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) <=> $true),
% 0.66/0.69 inference(rewrite,[status(thm)],[])).
% 0.66/0.69 tff(126,plain,
% 0.66/0.69 ((~(singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) <=> (~$true)),
% 0.66/0.69 inference(monotonicity,[status(thm)],[125])).
% 0.66/0.69 tff(127,plain,
% 0.66/0.69 ((~(singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) <=> $false),
% 0.66/0.69 inference(transitivity,[status(thm)],[126, 110])).
% 0.66/0.69 tff(128,plain,
% 0.66/0.69 (((~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))) <=> ((~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | $false | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.69 inference(monotonicity,[status(thm)],[127])).
% 0.66/0.69 tff(129,plain,
% 0.66/0.69 (((~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))) <=> ((~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.69 inference(transitivity,[status(thm)],[128, 124])).
% 0.66/0.69 tff(130,plain,
% 0.66/0.69 (((~![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | ((~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) <=> ((~![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | ((~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.69 inference(monotonicity,[status(thm)],[129])).
% 0.66/0.69 tff(131,plain,
% 0.66/0.69 (((~![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | ((~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) <=> ((~![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.69 inference(transitivity,[status(thm)],[130, 123])).
% 0.66/0.69 tff(132,plain,
% 0.66/0.69 ((~![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | ((~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.69 inference(quant_inst,[status(thm)],[])).
% 0.66/0.69 tff(133,plain,
% 0.66/0.69 ((~![J: $i, K: $i] : ((~in(J, A!1)) | (~(K = singleton(J))) | (~(ordered_pair(J, K) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))),
% 0.66/0.69 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.66/0.69 tff(134,plain,
% 0.66/0.69 ($false),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[133, 122, 120, 87])).
% 0.66/0.69 tff(135,plain,(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))), inference(lemma,lemma(discharge,[]))).
% 0.66/0.69 tff(136,plain,
% 0.66/0.69 (~((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[96, 135, 47])).
% 0.66/0.69 tff(137,plain,
% 0.66/0.69 (((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1))) | (ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))),
% 0.66/0.69 inference(tautology,[status(thm)],[])).
% 0.66/0.69 tff(138,plain,
% 0.66/0.69 (ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.66/0.69 tff(139,plain,
% 0.66/0.69 (((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1))) | (tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))),
% 0.66/0.69 inference(tautology,[status(thm)],[])).
% 0.66/0.69 tff(140,plain,
% 0.66/0.69 (tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))),
% 0.66/0.69 inference(unit_resolution,[status(thm)],[139, 136])).
% 0.66/0.69 tff(141,plain,
% 0.66/0.69 (singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)),
% 0.66/0.69 inference(symmetry,[status(thm)],[140])).
% 0.66/0.69 tff(142,plain,
% 0.66/0.69 (ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))),
% 0.66/0.69 inference(monotonicity,[status(thm)],[141])).
% 0.66/0.69 tff(143,plain,
% 0.66/0.69 (ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))),
% 0.66/0.69 inference(transitivity,[status(thm)],[142, 138])).
% 0.66/0.69 tff(144,plain,
% 0.66/0.69 (((~(tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_E_17(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), B!0, A!1), cartesian_product2(A!1, B!0))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), tptp_fun_K_18(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1))) | in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)),
% 0.66/0.70 inference(tautology,[status(thm)],[])).
% 0.66/0.70 tff(145,plain,
% 0.66/0.70 (in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[144, 136])).
% 0.66/0.70 tff(146,plain,
% 0.66/0.70 (((~(in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1)) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | (~(tptp_fun_F_3(tptp_fun_C_16(B!0, A!1)) = singleton(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1))))) | (~in(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), A!1)) | (~(ordered_pair(tptp_fun_E_4(tptp_fun_C_16(B!0, A!1)), tptp_fun_F_3(tptp_fun_C_16(B!0, A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | (~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))))) | ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))),
% 0.66/0.70 inference(tautology,[status(thm)],[])).
% 0.66/0.70 tff(147,plain,
% 0.66/0.70 ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[146, 75])).
% 0.66/0.70 tff(148,plain,
% 0.66/0.70 ((~((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.70 inference(tautology,[status(thm)],[])).
% 0.66/0.70 tff(149,plain,
% 0.66/0.70 ((~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), tptp_fun_C_16(B!0, A!1))) | (~in(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), cartesian_product2(A!1, B!0))) | ![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.66/0.70 tff(150,plain,
% 0.66/0.70 (![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[149, 135, 107])).
% 0.66/0.70 tff(151,plain,
% 0.66/0.70 (((~![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | ((~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))) <=> ((~![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(152,plain,
% 0.66/0.70 (((~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)) | $false | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))) <=> ((~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(153,plain,
% 0.66/0.70 ((singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) <=> $true),
% 0.66/0.70 inference(rewrite,[status(thm)],[])).
% 0.66/0.70 tff(154,plain,
% 0.66/0.70 ((~(singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) <=> (~$true)),
% 0.66/0.70 inference(monotonicity,[status(thm)],[153])).
% 0.66/0.70 tff(155,plain,
% 0.66/0.70 ((~(singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) <=> $false),
% 0.66/0.70 inference(transitivity,[status(thm)],[154, 110])).
% 0.66/0.70 tff(156,plain,
% 0.66/0.70 (((~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)) | (~(singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))) <=> ((~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)) | $false | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.70 inference(monotonicity,[status(thm)],[155])).
% 0.66/0.70 tff(157,plain,
% 0.66/0.70 (((~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)) | (~(singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1))))) <=> ((~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))),
% 0.66/0.70 inference(transitivity,[status(thm)],[156, 152])).
% 0.66/0.70 tff(158,plain,
% 0.66/0.70 (((~![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | ((~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)) | (~(singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) <=> ((~![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | ((~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1))))),
% 0.66/0.70 inference(monotonicity,[status(thm)],[157])).
% 0.66/0.70 tff(159,plain,
% 0.66/0.70 (((~![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | ((~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)) | (~(singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) <=> ((~![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)))),
% 0.66/0.70 inference(transitivity,[status(thm)],[158, 151])).
% 0.66/0.70 tff(160,plain,
% 0.66/0.70 ((~![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | ((~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1)) | (~(singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)) = singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1)))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))),
% 0.66/0.70 inference(quant_inst,[status(thm)],[])).
% 0.66/0.70 tff(161,plain,
% 0.66/0.70 ((~![E: $i, F: $i] : ((~in(E, A!1)) | (~(F = singleton(E))) | (~(ordered_pair(E, F) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))))) | (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))) | (~in(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), A!1))),
% 0.66/0.70 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.66/0.70 tff(162,plain,
% 0.66/0.70 (~(ordered_pair(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1), singleton(tptp_fun_J_19(tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)), A!1))) = tptp_fun_D_2(tptp_fun_C_16(B!0, A!1)))),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[161, 150, 145])).
% 0.66/0.70 tff(163,plain,
% 0.66/0.70 ($false),
% 0.66/0.70 inference(unit_resolution,[status(thm)],[162, 143])).
% 0.66/0.70 % SZS output end Proof
%------------------------------------------------------------------------------